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Appuntiweb di Steffo

\n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t\n\t\t);\n\t}\n}\n","import style from './copyright.css';\nimport { Component } from 'preact';\n\nexport default class Copyright extends Component {\n\trender() {\n\t\treturn
© 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente - Supportami
;\n\t}\n}\n","import { h, Component } from 'preact';\n\nexport default function(req) {\n\tfunction Async() {\n\t\tComponent.call(this);\n\n\t\tlet b, old;\n\t\tthis.componentWillMount = () => {\n\t\t\tb = this.base = this.nextBase || this.__b; // short circuits 1st render\n\t\t\treq(m => {\n\t\t\t\tthis.setState({ child: m.default || m });\n\t\t\t});\n\t\t};\n\n\t\tthis.shouldComponentUpdate = (_, nxt) => {\n\t\t\tnxt = nxt.child === void 0;\n\t\t\tif (nxt && old === void 0 && b) {\n\t\t\t\t// Node.TEXT_NODE\n\t\t\t\tif (b.nodeType === 3) {\n\t\t\t\t\told = b.data;\n\t\t\t\t} else {\n\t\t\t\t\told = h(b.nodeName, {\n\t\t\t\t\t\tdangerouslySetInnerHTML: { __html: b.innerHTML },\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\told = ''; // dump it\n\t\t\t}\n\t\t\treturn !nxt;\n\t\t};\n\n\t\tthis.render = (p, s) => (s.child ? h(s.child, p) : old);\n\t}\n\t(Async.prototype = new Component()).constructor = Async;\n\treturn Async;\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./basiDiDati.js\") );\n\t\t\t}, \"route-basiDiDati\");\n\t\t}\n\n\t\texport default Async(load);\n\t","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./home.js\") );\n\t\t\t}, \"route-home\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/**\n * Assign properties from `props` to `obj`\n * @template O, P The obj and props types\n * @param {O} obj The object to copy properties to\n * @param {P} props The object to copy properties from\n * @returns {O & P}\n */\nexport function assign(obj, props) {\n\tfor (let i in props) obj[i] = props[i];\n\treturn /** @type {O & P} */ (obj);\n}\n\n/**\n * Remove a child node from its parent if attached. This is a workaround for\n * IE11 which doesn't support `Element.prototype.remove()`. Using this function\n * is smaller than including a dedicated polyfill.\n * @param {Node} node The node to remove\n */\nexport function removeNode(node) {\n\tlet parentNode = node.parentNode;\n\tif (parentNode) parentNode.removeChild(node);\n}\n","import { cloneElement, createElement, Component, toChildArray } from 'preact';\nimport { exec, prepareVNodeForRanking, assign, pathRankSort } from './util';\n\nlet customHistory = null;\n\nconst ROUTERS = [];\n\nconst subscribers = [];\n\nconst EMPTY = {};\n\nfunction setUrl(url, type='push') {\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tlet url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn `${url.pathname || ''}${url.search || ''}`;\n}\n\n\n\nfunction route(url, replace=false) {\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (let i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) return true;\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL. */\nfunction routeTo(url) {\n\tlet didRoute = false;\n\tfor (let i=0; i {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\n\nclass Router extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tshouldComponentUpdate(props) {\n\t\tif (props.static!==true) return true;\n\t\treturn props.url!==this.props.url || props.onChange!==this.props.onChange;\n\t}\n\n\t/** Check if the given URL can be matched against any children */\n\tcanRoute(url) {\n\t\tconst children = toChildArray(this.props.children);\n\t\treturn this.getMatchingChildren(children, url, false).length > 0;\n\t}\n\n\t/** Re-render children with a new URL to match against. */\n\trouteTo(url) {\n\t\tthis.setState({ url });\n\n\t\tconst didRoute = this.canRoute(url);\n\n\t\t// trigger a manual re-route if we're not in the middle of an update:\n\t\tif (!this.updating) this.forceUpdate();\n\n\t\treturn didRoute;\n\t}\n\n\tcomponentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidMount() {\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen((location) => {\n\t\t\t\tthis.routeTo(`${location.pathname || ''}${location.search || ''}`);\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t}\n\n\tcomponentWillUnmount() {\n\t\tif (typeof this.unlisten==='function') this.unlisten();\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t}\n\n\tcomponentWillUpdate() {\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidUpdate() {\n\t\tthis.updating = false;\n\t}\n\n\tgetMatchingChildren(children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( vnode => {\n\t\t\t\tlet matches = exec(url, vnode.props.path, vnode.props);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tlet newProps = { url, matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t}\n\n\trender({ children, onChange }, { url }) {\n\t\tlet active = this.getMatchingChildren(toChildArray(children), url, true);\n\n\t\tlet current = active[0] || null;\n\n\t\tlet previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl,\n\t\t\t\t\tprevious,\n\t\t\t\t\tactive,\n\t\t\t\t\tcurrent\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t}\n}\n\nconst Link = (props) => (\n\tcreateElement('a', assign({ onClick: handleLinkClick }, props))\n);\n\nconst Route = props => createElement(props.component, props);\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\nRouter.exec = exec;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link, exec };\nexport default Router;\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"copyright\":\"copyright__2FTnU\"};","import options from './options';\n\n/**\n * Create an virtual node (used for JSX)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * constructor for this virtual node\n * @param {object | null | undefined} [props] The properties of the virtual node\n * @param {Array} [children] The children of the virtual node\n * @returns {import('./internal').VNode}\n */\nexport function createElement(type, props, children) {\n\tlet normalizedProps = {},\n\t\ti;\n\tfor (i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\tif (arguments.length > 3) {\n\t\tchildren = [children];\n\t\t// https://github.com/preactjs/preact/issues/1916\n\t\tfor (i = 3; i < arguments.length; i++) {\n\t\t\tchildren.push(arguments[i]);\n\t\t}\n\t}\n\tif (children != null) {\n\t\tnormalizedProps.children = children;\n\t}\n\n\t// If a Component VNode, check for and apply defaultProps\n\t// Note: type may be undefined in development, must never error here.\n\tif (typeof type == 'function' && type.defaultProps != null) {\n\t\tfor (i in type.defaultProps) {\n\t\t\tif (normalizedProps[i] === undefined) {\n\t\t\t\tnormalizedProps[i] = type.defaultProps[i];\n\t\t\t}\n\t\t}\n\t}\n\n\treturn createVNode(\n\t\ttype,\n\t\tnormalizedProps,\n\t\tprops && props.key,\n\t\tprops && props.ref,\n\t\tnull\n\t);\n}\n\n/**\n * Create a VNode (used internally by Preact)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * Constructor for this virtual node\n * @param {object | string | number | null} props The properties of this virtual node.\n * If this virtual node represents a text node, this is the text of the node (string or number).\n * @param {string | number | null} key The key for this virtual node, used when\n * diffing it against its children\n * @param {import('./internal').VNode[\"ref\"]} ref The ref property that will\n * receive a reference to its created child\n * @returns {import('./internal').VNode}\n */\nexport function createVNode(type, props, key, ref, original) {\n\t// V8 seems to be better at detecting type shapes if the object is allocated from the same call site\n\t// Do not inline into createElement and coerceToVNode!\n\tconst vnode = {\n\t\ttype,\n\t\tprops,\n\t\tkey,\n\t\tref,\n\t\t_children: null,\n\t\t_parent: null,\n\t\t_depth: 0,\n\t\t_dom: null,\n\t\t// _nextDom must be initialized to undefined b/c it will eventually\n\t\t// be set to dom.nextSibling which can return `null` and it is important\n\t\t// to be able to distinguish between an uninitialized _nextDom and\n\t\t// a _nextDom that has been set to `null`\n\t\t_nextDom: undefined,\n\t\t_component: null,\n\t\tconstructor: undefined,\n\t\t_original: original\n\t};\n\n\tif (original == null) vnode._original = vnode;\n\tif (options.vnode) options.vnode(vnode);\n\n\treturn vnode;\n}\n\nexport function createRef() {\n\treturn {};\n}\n\nexport function Fragment(props) {\n\treturn props.children;\n}\n\n/**\n * Check if a the argument is a valid Preact VNode.\n * @param {*} vnode\n * @returns {vnode is import('./internal').VNode}\n */\nexport const isValidElement = vnode =>\n\tvnode != null && vnode.constructor === undefined;\n","import { assign } from './util';\nimport { diff, commitRoot } from './diff/index';\nimport options from './options';\nimport { Fragment } from './create-element';\n\n/**\n * Base Component class. Provides `setState()` and `forceUpdate()`, which\n * trigger rendering\n * @param {object} props The initial component props\n * @param {object} context The initial context from parent components'\n * getChildContext\n */\nexport function Component(props, context) {\n\tthis.props = props;\n\tthis.context = context;\n}\n\n/**\n * Update component state and schedule a re-render.\n * @param {object | ((s: object, p: object) => object)} update A hash of state\n * properties to update with new values or a function that given the current\n * state and props returns a new partial state\n * @param {() => void} [callback] A function to be called once component state is\n * updated\n */\nComponent.prototype.setState = function(update, callback) {\n\t// only clone state when copying to nextState the first time.\n\tlet s;\n\tif (this._nextState !== this.state) {\n\t\ts = this._nextState;\n\t} else {\n\t\ts = this._nextState = assign({}, this.state);\n\t}\n\n\tif (typeof update == 'function') {\n\t\tupdate = update(s, this.props);\n\t}\n\n\tif (update) {\n\t\tassign(s, update);\n\t}\n\n\t// Skip update if updater function returned null\n\tif (update == null) return;\n\n\tif (this._vnode) {\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Immediately perform a synchronous re-render of the component\n * @param {() => void} [callback] A function to be called after component is\n * re-rendered\n */\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode) {\n\t\t// Set render mode so that we can differentiate where the render request\n\t\t// is coming from. We need this because forceUpdate should never call\n\t\t// shouldComponentUpdate\n\t\tthis._force = true;\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Accepts `props` and `state`, and returns a new Virtual DOM tree to build.\n * Virtual DOM is generally constructed via [JSX](http://jasonformat.com/wtf-is-jsx).\n * @param {object} props Props (eg: JSX attributes) received from parent\n * element/component\n * @param {object} state The component's current state\n * @param {object} context Context object, as returned by the nearest\n * ancestor's `getChildContext()`\n * @returns {import('./index').ComponentChildren | void}\n */\nComponent.prototype.render = Fragment;\n\n/**\n * @param {import('./internal').VNode} vnode\n * @param {number | null} [childIndex]\n */\nexport function getDomSibling(vnode, childIndex) {\n\tif (childIndex == null) {\n\t\t// Use childIndex==null as a signal to resume the search from the vnode's sibling\n\t\treturn vnode._parent\n\t\t\t? getDomSibling(vnode._parent, vnode._parent._children.indexOf(vnode) + 1)\n\t\t\t: null;\n\t}\n\n\tlet sibling;\n\tfor (; childIndex < vnode._children.length; childIndex++) {\n\t\tsibling = vnode._children[childIndex];\n\n\t\tif (sibling != null && sibling._dom != null) {\n\t\t\t// Since updateParentDomPointers keeps _dom pointer correct,\n\t\t\t// we can rely on _dom to tell us if this subtree contains a\n\t\t\t// rendered DOM node, and what the first rendered DOM node is\n\t\t\treturn sibling._dom;\n\t\t}\n\t}\n\n\t// If we get here, we have not found a DOM node in this vnode's children.\n\t// We must resume from this vnode's sibling (in it's parent _children array)\n\t// Only climb up and search the parent if we aren't searching through a DOM\n\t// VNode (meaning we reached the DOM parent of the original vnode that began\n\t// the search)\n\treturn typeof vnode.type == 'function' ? getDomSibling(vnode) : null;\n}\n\n/**\n * Trigger in-place re-rendering of a component.\n * @param {import('./internal').Component} component The component to rerender\n */\nfunction renderComponent(component) {\n\tlet vnode = component._vnode,\n\t\toldDom = vnode._dom,\n\t\tparentDom = component._parentDom;\n\n\tif (parentDom) {\n\t\tlet commitQueue = [];\n\t\tconst oldVNode = assign({}, vnode);\n\t\toldVNode._original = oldVNode;\n\n\t\tlet newDom = diff(\n\t\t\tparentDom,\n\t\t\tvnode,\n\t\t\toldVNode,\n\t\t\tcomponent._globalContext,\n\t\t\tparentDom.ownerSVGElement !== undefined,\n\t\t\tnull,\n\t\t\tcommitQueue,\n\t\t\toldDom == null ? getDomSibling(vnode) : oldDom\n\t\t);\n\t\tcommitRoot(commitQueue, vnode);\n\n\t\tif (newDom != oldDom) {\n\t\t\tupdateParentDomPointers(vnode);\n\t\t}\n\t}\n}\n\n/**\n * @param {import('./internal').VNode} vnode\n */\nfunction updateParentDomPointers(vnode) {\n\tif ((vnode = vnode._parent) != null && vnode._component != null) {\n\t\tvnode._dom = vnode._component.base = null;\n\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\tlet child = vnode._children[i];\n\t\t\tif (child != null && child._dom != null) {\n\t\t\t\tvnode._dom = vnode._component.base = child._dom;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\treturn updateParentDomPointers(vnode);\n\t}\n}\n\n/**\n * The render queue\n * @type {Array}\n */\nlet rerenderQueue = [];\nlet rerenderCount = 0;\n\n/**\n * Asynchronously schedule a callback\n * @type {(cb: () => void) => void}\n */\n/* istanbul ignore next */\n// Note the following line isn't tree-shaken by rollup cuz of rollup/rollup#2566\nconst defer =\n\ttypeof Promise == 'function'\n\t\t? Promise.prototype.then.bind(Promise.resolve())\n\t\t: setTimeout;\n\n/*\n * The value of `Component.debounce` must asynchronously invoke the passed in callback. It is\n * important that contributors to Preact can consistently reason about what calls to `setState`, etc.\n * do, and when their effects will be applied. See the links below for some further reading on designing\n * asynchronous APIs.\n * * [Designing APIs for Asynchrony](https://blog.izs.me/2013/08/designing-apis-for-asynchrony)\n * * [Callbacks synchronous and asynchronous](https://blog.ometer.com/2011/07/24/callbacks-synchronous-and-asynchronous/)\n */\n\nlet prevDebounce;\n\n/**\n * Enqueue a rerender of a component\n * @param {import('./internal').Component} c The component to rerender\n */\nexport function enqueueRender(c) {\n\tif (\n\t\t(!c._dirty &&\n\t\t\t(c._dirty = true) &&\n\t\t\trerenderQueue.push(c) &&\n\t\t\t!rerenderCount++) ||\n\t\tprevDebounce !== options.debounceRendering\n\t) {\n\t\tprevDebounce = options.debounceRendering;\n\t\t(prevDebounce || defer)(process);\n\t}\n}\n\n/** Flush the render queue by rerendering all queued components */\nfunction process() {\n\tlet queue;\n\twhile ((rerenderCount = rerenderQueue.length)) {\n\t\tqueue = rerenderQueue.sort((a, b) => a._vnode._depth - b._vnode._depth);\n\t\trerenderQueue = [];\n\t\t// Don't update `renderCount` yet. Keep its value non-zero to prevent unnecessary\n\t\t// process() calls from getting scheduled while `queue` is still being consumed.\n\t\tqueue.some(c => {\n\t\t\tif (c._dirty) renderComponent(c);\n\t\t});\n\t}\n}\n","import { diff, unmount, applyRef } from './index';\nimport { createVNode } from '../create-element';\nimport { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { removeNode } from '../util';\nimport { getDomSibling } from '../component';\n\n/**\n * Diff the children of a virtual node\n * @param {import('../internal').PreactElement} parentDom The DOM element whose\n * children are being diffed\n * @param {import('../internal').VNode} newParentVNode The new virtual\n * node whose children should be diff'ed against oldParentVNode\n * @param {import('../internal').VNode} oldParentVNode The old virtual\n * node whose children should be diff'ed against newParentVNode\n * @param {object} globalContext The current context object - modified by getChildContext\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Node | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} isHydrating Whether or not we are in hydration\n */\nexport function diffChildren(\n\tparentDom,\n\tnewParentVNode,\n\toldParentVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet i, j, oldVNode, newDom, sibDom, firstChildDom, refs;\n\n\t// This is a compression of oldParentVNode!=null && oldParentVNode != EMPTY_OBJ && oldParentVNode._children || EMPTY_ARR\n\t// as EMPTY_OBJ._children should be `undefined`.\n\tlet oldChildren = (oldParentVNode && oldParentVNode._children) || EMPTY_ARR;\n\n\tlet oldChildrenLength = oldChildren.length;\n\n\t// Only in very specific places should this logic be invoked (top level `render` and `diffElementNodes`).\n\t// I'm using `EMPTY_OBJ` to signal when `diffChildren` is invoked in these situations. I can't use `null`\n\t// for this purpose, because `null` is a valid value for `oldDom` which can mean to skip to this logic\n\t// (e.g. if mounting a new tree in which the old DOM should be ignored (usually for Fragments).\n\tif (oldDom == EMPTY_OBJ) {\n\t\tif (excessDomChildren != null) {\n\t\t\toldDom = excessDomChildren[0];\n\t\t} else if (oldChildrenLength) {\n\t\t\toldDom = getDomSibling(oldParentVNode, 0);\n\t\t} else {\n\t\t\toldDom = null;\n\t\t}\n\t}\n\n\ti = 0;\n\tnewParentVNode._children = toChildArray(\n\t\tnewParentVNode._children,\n\t\tchildVNode => {\n\t\t\tif (childVNode != null) {\n\t\t\t\tchildVNode._parent = newParentVNode;\n\t\t\t\tchildVNode._depth = newParentVNode._depth + 1;\n\n\t\t\t\t// Check if we find a corresponding element in oldChildren.\n\t\t\t\t// If found, delete the array item by setting to `undefined`.\n\t\t\t\t// We use `undefined`, as `null` is reserved for empty placeholders\n\t\t\t\t// (holes).\n\t\t\t\toldVNode = oldChildren[i];\n\n\t\t\t\tif (\n\t\t\t\t\toldVNode === null ||\n\t\t\t\t\t(oldVNode &&\n\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\tchildVNode.type === oldVNode.type)\n\t\t\t\t) {\n\t\t\t\t\toldChildren[i] = undefined;\n\t\t\t\t} else {\n\t\t\t\t\t// Either oldVNode === undefined or oldChildrenLength > 0,\n\t\t\t\t\t// so after this loop oldVNode == null or oldVNode is a valid value.\n\t\t\t\t\tfor (j = 0; j < oldChildrenLength; j++) {\n\t\t\t\t\t\toldVNode = oldChildren[j];\n\t\t\t\t\t\t// If childVNode is unkeyed, we only match similarly unkeyed nodes, otherwise we match by key.\n\t\t\t\t\t\t// We always match by type (in either case).\n\t\t\t\t\t\tif (\n\t\t\t\t\t\t\toldVNode &&\n\t\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\t\tchildVNode.type === oldVNode.type\n\t\t\t\t\t\t) {\n\t\t\t\t\t\t\toldChildren[j] = undefined;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t\toldVNode = null;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\toldVNode = oldVNode || EMPTY_OBJ;\n\n\t\t\t\t// Morph the old element into the new one, but don't append it to the dom yet\n\t\t\t\tnewDom = diff(\n\t\t\t\t\tparentDom,\n\t\t\t\t\tchildVNode,\n\t\t\t\t\toldVNode,\n\t\t\t\t\tglobalContext,\n\t\t\t\t\tisSvg,\n\t\t\t\t\texcessDomChildren,\n\t\t\t\t\tcommitQueue,\n\t\t\t\t\toldDom,\n\t\t\t\t\tisHydrating\n\t\t\t\t);\n\n\t\t\t\tif ((j = childVNode.ref) && oldVNode.ref != j) {\n\t\t\t\t\tif (!refs) refs = [];\n\t\t\t\t\tif (oldVNode.ref) refs.push(oldVNode.ref, null, childVNode);\n\t\t\t\t\trefs.push(j, childVNode._component || newDom, childVNode);\n\t\t\t\t}\n\n\t\t\t\t// Only proceed if the vnode has not been unmounted by `diff()` above.\n\t\t\t\tif (newDom != null) {\n\t\t\t\t\tif (firstChildDom == null) {\n\t\t\t\t\t\tfirstChildDom = newDom;\n\t\t\t\t\t}\n\n\t\t\t\t\tlet nextDom;\n\t\t\t\t\tif (childVNode._nextDom !== undefined) {\n\t\t\t\t\t\t// Only Fragments or components that return Fragment like VNodes will\n\t\t\t\t\t\t// have a non-undefined _nextDom. Continue the diff from the sibling\n\t\t\t\t\t\t// of last DOM child of this child VNode\n\t\t\t\t\t\tnextDom = childVNode._nextDom;\n\n\t\t\t\t\t\t// Eagerly cleanup _nextDom. We don't need to persist the value because\n\t\t\t\t\t\t// it is only used by `diffChildren` to determine where to resume the diff after\n\t\t\t\t\t\t// diffing Components and Fragments. Once we store it the nextDOM local var, we\n\t\t\t\t\t\t// can clean up the property\n\t\t\t\t\t\tchildVNode._nextDom = undefined;\n\t\t\t\t\t} else if (\n\t\t\t\t\t\texcessDomChildren == oldVNode ||\n\t\t\t\t\t\tnewDom != oldDom ||\n\t\t\t\t\t\tnewDom.parentNode == null\n\t\t\t\t\t) {\n\t\t\t\t\t\t// NOTE: excessDomChildren==oldVNode above:\n\t\t\t\t\t\t// This is a compression of excessDomChildren==null && oldVNode==null!\n\t\t\t\t\t\t// The values only have the same type when `null`.\n\n\t\t\t\t\t\touter: if (oldDom == null || oldDom.parentNode !== parentDom) {\n\t\t\t\t\t\t\tparentDom.appendChild(newDom);\n\t\t\t\t\t\t\tnextDom = null;\n\t\t\t\t\t\t} else {\n\t\t\t\t\t\t\t// `j import('../internal').VNode} [callback]\n * A function to invoke for each child before it is added to the flattened list.\n * @param {Array} [flattened] An flat array of children to modify\n * @returns {import('../internal').VNode[]}\n */\nexport function toChildArray(children, callback, flattened) {\n\tif (flattened == null) flattened = [];\n\n\tif (children == null || typeof children == 'boolean') {\n\t\tif (callback) flattened.push(callback(null));\n\t} else if (Array.isArray(children)) {\n\t\tfor (let i = 0; i < children.length; i++) {\n\t\t\ttoChildArray(children[i], callback, flattened);\n\t\t}\n\t} else if (!callback) {\n\t\tflattened.push(children);\n\t} else if (typeof children == 'string' || typeof children == 'number') {\n\t\tflattened.push(callback(createVNode(null, children, null, null, children)));\n\t} else if (children._dom != null || children._component != null) {\n\t\tflattened.push(\n\t\t\tcallback(\n\t\t\t\tcreateVNode(\n\t\t\t\t\tchildren.type,\n\t\t\t\t\tchildren.props,\n\t\t\t\t\tchildren.key,\n\t\t\t\t\tnull,\n\t\t\t\t\tchildren._original\n\t\t\t\t)\n\t\t\t)\n\t\t);\n\t} else {\n\t\tflattened.push(callback(children));\n\t}\n\n\treturn flattened;\n}\n","import { IS_NON_DIMENSIONAL } from '../constants';\nimport options from '../options';\n\n/**\n * Diff the old and new properties of a VNode and apply changes to the DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to apply\n * changes to\n * @param {object} newProps The new props\n * @param {object} oldProps The old props\n * @param {boolean} isSvg Whether or not this node is an SVG node\n * @param {boolean} hydrate Whether or not we are in hydration mode\n */\nexport function diffProps(dom, newProps, oldProps, isSvg, hydrate) {\n\tlet i;\n\n\tfor (i in oldProps) {\n\t\tif (i !== 'children' && i !== 'key' && !(i in newProps)) {\n\t\t\tsetProperty(dom, i, null, oldProps[i], isSvg);\n\t\t}\n\t}\n\n\tfor (i in newProps) {\n\t\tif (\n\t\t\t(!hydrate || typeof newProps[i] == 'function') &&\n\t\t\ti !== 'children' &&\n\t\t\ti !== 'key' &&\n\t\t\ti !== 'value' &&\n\t\t\ti !== 'checked' &&\n\t\t\toldProps[i] !== newProps[i]\n\t\t) {\n\t\t\tsetProperty(dom, i, newProps[i], oldProps[i], isSvg);\n\t\t}\n\t}\n}\n\nfunction setStyle(style, key, value) {\n\tif (key[0] === '-') {\n\t\tstyle.setProperty(key, value);\n\t} else if (\n\t\ttypeof value == 'number' &&\n\t\tIS_NON_DIMENSIONAL.test(key) === false\n\t) {\n\t\tstyle[key] = value + 'px';\n\t} else if (value == null) {\n\t\tstyle[key] = '';\n\t} else {\n\t\tstyle[key] = value;\n\t}\n}\n\n/**\n * Set a property value on a DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to modify\n * @param {string} name The name of the property to set\n * @param {*} value The value to set the property to\n * @param {*} oldValue The old value the property had\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node or not\n */\nfunction setProperty(dom, name, value, oldValue, isSvg) {\n\tlet s, useCapture, nameLower;\n\n\tif (isSvg) {\n\t\tif (name === 'className') {\n\t\t\tname = 'class';\n\t\t}\n\t} else if (name === 'class') {\n\t\tname = 'className';\n\t}\n\n\tif (name === 'style') {\n\t\ts = dom.style;\n\n\t\tif (typeof value == 'string') {\n\t\t\ts.cssText = value;\n\t\t} else {\n\t\t\tif (typeof oldValue == 'string') {\n\t\t\t\ts.cssText = '';\n\t\t\t\toldValue = null;\n\t\t\t}\n\n\t\t\tif (oldValue) {\n\t\t\t\tfor (let i in oldValue) {\n\t\t\t\t\tif (!(value && i in value)) {\n\t\t\t\t\t\tsetStyle(s, i, '');\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (value) {\n\t\t\t\tfor (let i in value) {\n\t\t\t\t\tif (!oldValue || value[i] !== oldValue[i]) {\n\t\t\t\t\t\tsetStyle(s, i, value[i]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\t// Benchmark for comparison: https://esbench.com/bench/574c954bdb965b9a00965ac6\n\telse if (name[0] === 'o' && name[1] === 'n') {\n\t\tuseCapture = name !== (name = name.replace(/Capture$/, ''));\n\t\tnameLower = name.toLowerCase();\n\t\tname = (nameLower in dom ? nameLower : name).slice(2);\n\n\t\tif (value) {\n\t\t\tif (!oldValue) dom.addEventListener(name, eventProxy, useCapture);\n\t\t\t(dom._listeners || (dom._listeners = {}))[name] = value;\n\t\t} else {\n\t\t\tdom.removeEventListener(name, eventProxy, useCapture);\n\t\t}\n\t} else if (\n\t\tname !== 'list' &&\n\t\tname !== 'tagName' &&\n\t\t// HTMLButtonElement.form and HTMLInputElement.form are read-only but can be set using\n\t\t// setAttribute\n\t\tname !== 'form' &&\n\t\tname !== 'type' &&\n\t\tname !== 'size' &&\n\t\t!isSvg &&\n\t\tname in dom\n\t) {\n\t\tdom[name] = value == null ? '' : value;\n\t} else if (typeof value != 'function' && name !== 'dangerouslySetInnerHTML') {\n\t\tif (name !== (name = name.replace(/^xlink:?/, ''))) {\n\t\t\tif (value == null || value === false) {\n\t\t\t\tdom.removeAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase()\n\t\t\t\t);\n\t\t\t} else {\n\t\t\t\tdom.setAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase(),\n\t\t\t\t\tvalue\n\t\t\t\t);\n\t\t\t}\n\t\t} else if (\n\t\t\tvalue == null ||\n\t\t\t(value === false &&\n\t\t\t\t// ARIA-attributes have a different notion of boolean values.\n\t\t\t\t// The value `false` is different from the attribute not\n\t\t\t\t// existing on the DOM, so we can't remove it. For non-boolean\n\t\t\t\t// ARIA-attributes we could treat false as a removal, but the\n\t\t\t\t// amount of exceptions would cost us too many bytes. On top of\n\t\t\t\t// that other VDOM frameworks also always stringify `false`.\n\t\t\t\t!/^ar/.test(name))\n\t\t) {\n\t\t\tdom.removeAttribute(name);\n\t\t} else {\n\t\t\tdom.setAttribute(name, value);\n\t\t}\n\t}\n}\n\n/**\n * Proxy an event to hooked event handlers\n * @param {Event} e The event object from the browser\n * @private\n */\nfunction eventProxy(e) {\n\tthis._listeners[e.type](options.event ? options.event(e) : e);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { Component } from '../component';\nimport { Fragment } from '../create-element';\nimport { diffChildren } from './children';\nimport { diffProps } from './props';\nimport { assign, removeNode } from '../util';\nimport options from '../options';\n\n/**\n * Diff two virtual nodes and apply proper changes to the DOM\n * @param {import('../internal').PreactElement} parentDom The parent of the DOM element\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object. Modified by getChildContext\n * @param {boolean} isSvg Whether or not this element is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Element | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} [isHydrating] Whether or not we are in hydration\n */\nexport function diff(\n\tparentDom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet tmp,\n\t\tnewType = newVNode.type;\n\n\t// When passing through createElement it assigns the object\n\t// constructor as undefined. This to prevent JSON-injection.\n\tif (newVNode.constructor !== undefined) return null;\n\n\tif ((tmp = options._diff)) tmp(newVNode);\n\n\ttry {\n\t\touter: if (typeof newType == 'function') {\n\t\t\tlet c, isNew, oldProps, oldState, snapshot, clearProcessingException;\n\t\t\tlet newProps = newVNode.props;\n\n\t\t\t// Necessary for createContext api. Setting this property will pass\n\t\t\t// the context value as `this.context` just for this component.\n\t\t\ttmp = newType.contextType;\n\t\t\tlet provider = tmp && globalContext[tmp._id];\n\t\t\tlet componentContext = tmp\n\t\t\t\t? provider\n\t\t\t\t\t? provider.props.value\n\t\t\t\t\t: tmp._defaultValue\n\t\t\t\t: globalContext;\n\n\t\t\t// Get component and set it to `c`\n\t\t\tif (oldVNode._component) {\n\t\t\t\tc = newVNode._component = oldVNode._component;\n\t\t\t\tclearProcessingException = c._processingException = c._pendingError;\n\t\t\t} else {\n\t\t\t\t// Instantiate the new component\n\t\t\t\tif ('prototype' in newType && newType.prototype.render) {\n\t\t\t\t\tnewVNode._component = c = new newType(newProps, componentContext); // eslint-disable-line new-cap\n\t\t\t\t} else {\n\t\t\t\t\tnewVNode._component = c = new Component(newProps, componentContext);\n\t\t\t\t\tc.constructor = newType;\n\t\t\t\t\tc.render = doRender;\n\t\t\t\t}\n\t\t\t\tif (provider) provider.sub(c);\n\n\t\t\t\tc.props = newProps;\n\t\t\t\tif (!c.state) c.state = {};\n\t\t\t\tc.context = componentContext;\n\t\t\t\tc._globalContext = globalContext;\n\t\t\t\tisNew = c._dirty = true;\n\t\t\t\tc._renderCallbacks = [];\n\t\t\t}\n\n\t\t\t// Invoke getDerivedStateFromProps\n\t\t\tif (c._nextState == null) {\n\t\t\t\tc._nextState = c.state;\n\t\t\t}\n\t\t\tif (newType.getDerivedStateFromProps != null) {\n\t\t\t\tif (c._nextState == c.state) {\n\t\t\t\t\tc._nextState = assign({}, c._nextState);\n\t\t\t\t}\n\n\t\t\t\tassign(\n\t\t\t\t\tc._nextState,\n\t\t\t\t\tnewType.getDerivedStateFromProps(newProps, c._nextState)\n\t\t\t\t);\n\t\t\t}\n\n\t\t\toldProps = c.props;\n\t\t\toldState = c.state;\n\n\t\t\t// Invoke pre-render lifecycle methods\n\t\t\tif (isNew) {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tc.componentWillMount != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillMount();\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidMount != null) {\n\t\t\t\t\tc._renderCallbacks.push(c.componentDidMount);\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tnewProps !== oldProps &&\n\t\t\t\t\tc.componentWillReceiveProps != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillReceiveProps(newProps, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (\n\t\t\t\t\t(!c._force &&\n\t\t\t\t\t\tc.shouldComponentUpdate != null &&\n\t\t\t\t\t\tc.shouldComponentUpdate(\n\t\t\t\t\t\t\tnewProps,\n\t\t\t\t\t\t\tc._nextState,\n\t\t\t\t\t\t\tcomponentContext\n\t\t\t\t\t\t) === false) ||\n\t\t\t\t\t(newVNode._original === oldVNode._original && !c._processingException)\n\t\t\t\t) {\n\t\t\t\t\tc.props = newProps;\n\t\t\t\t\tc.state = c._nextState;\n\t\t\t\t\t// More info about this here: https://gist.github.com/JoviDeCroock/bec5f2ce93544d2e6070ef8e0036e4e8\n\t\t\t\t\tif (newVNode._original !== oldVNode._original) c._dirty = false;\n\t\t\t\t\tc._vnode = newVNode;\n\t\t\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t\t\t\tnewVNode._children = oldVNode._children;\n\t\t\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\t\t\tcommitQueue.push(c);\n\t\t\t\t\t}\n\n\t\t\t\t\tfor (tmp = 0; tmp < newVNode._children.length; tmp++) {\n\t\t\t\t\t\tif (newVNode._children[tmp]) {\n\t\t\t\t\t\t\tnewVNode._children[tmp]._parent = newVNode;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t\tbreak outer;\n\t\t\t\t}\n\n\t\t\t\tif (c.componentWillUpdate != null) {\n\t\t\t\t\tc.componentWillUpdate(newProps, c._nextState, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidUpdate != null) {\n\t\t\t\t\tc._renderCallbacks.push(() => {\n\t\t\t\t\t\tc.componentDidUpdate(oldProps, oldState, snapshot);\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tc.context = componentContext;\n\t\t\tc.props = newProps;\n\t\t\tc.state = c._nextState;\n\n\t\t\tif ((tmp = options._render)) tmp(newVNode);\n\n\t\t\tc._dirty = false;\n\t\t\tc._vnode = newVNode;\n\t\t\tc._parentDom = parentDom;\n\n\t\t\ttmp = c.render(c.props, c.state, c.context);\n\t\t\tlet isTopLevelFragment =\n\t\t\t\ttmp != null && tmp.type == Fragment && tmp.key == null;\n\t\t\tnewVNode._children = isTopLevelFragment\n\t\t\t\t? tmp.props.children\n\t\t\t\t: Array.isArray(tmp)\n\t\t\t\t? tmp\n\t\t\t\t: [tmp];\n\n\t\t\tif (c.getChildContext != null) {\n\t\t\t\tglobalContext = assign(assign({}, globalContext), c.getChildContext());\n\t\t\t}\n\n\t\t\tif (!isNew && c.getSnapshotBeforeUpdate != null) {\n\t\t\t\tsnapshot = c.getSnapshotBeforeUpdate(oldProps, oldState);\n\t\t\t}\n\n\t\t\tdiffChildren(\n\t\t\t\tparentDom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\toldDom,\n\t\t\t\tisHydrating\n\t\t\t);\n\n\t\t\tc.base = newVNode._dom;\n\n\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\tcommitQueue.push(c);\n\t\t\t}\n\n\t\t\tif (clearProcessingException) {\n\t\t\t\tc._pendingError = c._processingException = null;\n\t\t\t}\n\n\t\t\tc._force = false;\n\t\t} else if (\n\t\t\texcessDomChildren == null &&\n\t\t\tnewVNode._original === oldVNode._original\n\t\t) {\n\t\t\tnewVNode._children = oldVNode._children;\n\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t} else {\n\t\t\tnewVNode._dom = diffElementNodes(\n\t\t\t\toldVNode._dom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\tif ((tmp = options.diffed)) tmp(newVNode);\n\t} catch (e) {\n\t\tnewVNode._original = null;\n\t\toptions._catchError(e, newVNode, oldVNode);\n\t}\n\n\treturn newVNode._dom;\n}\n\n/**\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {import('../internal').VNode} root\n */\nexport function commitRoot(commitQueue, root) {\n\tif (options._commit) options._commit(root, commitQueue);\n\n\tcommitQueue.some(c => {\n\t\ttry {\n\t\t\tcommitQueue = c._renderCallbacks;\n\t\t\tc._renderCallbacks = [];\n\t\t\tcommitQueue.some(cb => {\n\t\t\t\tcb.call(c);\n\t\t\t});\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t});\n}\n\n/**\n * Diff two virtual nodes representing DOM element\n * @param {import('../internal').PreactElement} dom The DOM element representing\n * the virtual nodes being diffed\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {*} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {boolean} isHydrating Whether or not we are in hydration\n * @returns {import('../internal').PreactElement}\n */\nfunction diffElementNodes(\n\tdom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\tisHydrating\n) {\n\tlet i;\n\tlet oldProps = oldVNode.props;\n\tlet newProps = newVNode.props;\n\n\t// Tracks entering and exiting SVG namespace when descending through the tree.\n\tisSvg = newVNode.type === 'svg' || isSvg;\n\n\tif (excessDomChildren != null) {\n\t\tfor (i = 0; i < excessDomChildren.length; i++) {\n\t\t\tconst child = excessDomChildren[i];\n\n\t\t\t// if newVNode matches an element in excessDomChildren or the `dom`\n\t\t\t// argument matches an element in excessDomChildren, remove it from\n\t\t\t// excessDomChildren so it isn't later removed in diffChildren\n\t\t\tif (\n\t\t\t\tchild != null &&\n\t\t\t\t((newVNode.type === null\n\t\t\t\t\t? child.nodeType === 3\n\t\t\t\t\t: child.localName === newVNode.type) ||\n\t\t\t\t\tdom == child)\n\t\t\t) {\n\t\t\t\tdom = child;\n\t\t\t\texcessDomChildren[i] = null;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\tif (dom == null) {\n\t\tif (newVNode.type === null) {\n\t\t\treturn document.createTextNode(newProps);\n\t\t}\n\n\t\tdom = isSvg\n\t\t\t? document.createElementNS('http://www.w3.org/2000/svg', newVNode.type)\n\t\t\t: document.createElement(\n\t\t\t\t\tnewVNode.type,\n\t\t\t\t\tnewProps.is && { is: newProps.is }\n\t\t\t );\n\t\t// we created a new parent, so none of the previously attached children can be reused:\n\t\texcessDomChildren = null;\n\t\t// we are creating a new node, so we can assume this is a new subtree (in case we are hydrating), this deopts the hydrate\n\t\tisHydrating = false;\n\t}\n\n\tif (newVNode.type === null) {\n\t\tif (oldProps !== newProps && dom.data != newProps) {\n\t\t\tdom.data = newProps;\n\t\t}\n\t} else {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren = EMPTY_ARR.slice.call(dom.childNodes);\n\t\t}\n\n\t\toldProps = oldVNode.props || EMPTY_OBJ;\n\n\t\tlet oldHtml = oldProps.dangerouslySetInnerHTML;\n\t\tlet newHtml = newProps.dangerouslySetInnerHTML;\n\n\t\t// During hydration, props are not diffed at all (including dangerouslySetInnerHTML)\n\t\t// @TODO we should warn in debug mode when props don't match here.\n\t\tif (!isHydrating) {\n\t\t\tif (oldProps === EMPTY_OBJ) {\n\t\t\t\toldProps = {};\n\t\t\t\tfor (let i = 0; i < dom.attributes.length; i++) {\n\t\t\t\t\toldProps[dom.attributes[i].name] = dom.attributes[i].value;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (newHtml || oldHtml) {\n\t\t\t\t// Avoid re-applying the same '__html' if it did not changed between re-render\n\t\t\t\tif (!newHtml || !oldHtml || newHtml.__html != oldHtml.__html) {\n\t\t\t\t\tdom.innerHTML = (newHtml && newHtml.__html) || '';\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tdiffProps(dom, newProps, oldProps, isSvg, isHydrating);\n\n\t\tnewVNode._children = newVNode.props.children;\n\n\t\t// If the new vnode didn't have dangerouslySetInnerHTML, diff its children\n\t\tif (!newHtml) {\n\t\t\tdiffChildren(\n\t\t\t\tdom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tnewVNode.type === 'foreignObject' ? false : isSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tEMPTY_OBJ,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\t// (as above, don't diff props during hydration)\n\t\tif (!isHydrating) {\n\t\t\tif (\n\t\t\t\t'value' in newProps &&\n\t\t\t\tnewProps.value !== undefined &&\n\t\t\t\tnewProps.value !== dom.value\n\t\t\t) {\n\t\t\t\tdom.value = newProps.value == null ? '' : newProps.value;\n\t\t\t}\n\t\t\tif (\n\t\t\t\t'checked' in newProps &&\n\t\t\t\tnewProps.checked !== undefined &&\n\t\t\t\tnewProps.checked !== dom.checked\n\t\t\t) {\n\t\t\t\tdom.checked = newProps.checked;\n\t\t\t}\n\t\t}\n\t}\n\n\treturn dom;\n}\n\n/**\n * Invoke or update a ref, depending on whether it is a function or object ref.\n * @param {object|function} ref\n * @param {any} value\n * @param {import('../internal').VNode} vnode\n */\nexport function applyRef(ref, value, vnode) {\n\ttry {\n\t\tif (typeof ref == 'function') ref(value);\n\t\telse ref.current = value;\n\t} catch (e) {\n\t\toptions._catchError(e, vnode);\n\t}\n}\n\n/**\n * Unmount a virtual node from the tree and apply DOM changes\n * @param {import('../internal').VNode} vnode The virtual node to unmount\n * @param {import('../internal').VNode} parentVNode The parent of the VNode that\n * initiated the unmount\n * @param {boolean} [skipRemove] Flag that indicates that a parent node of the\n * current element is already detached from the DOM.\n */\nexport function unmount(vnode, parentVNode, skipRemove) {\n\tlet r;\n\tif (options.unmount) options.unmount(vnode);\n\n\tif ((r = vnode.ref)) {\n\t\tif (!r.current || r.current === vnode._dom) applyRef(r, null, parentVNode);\n\t}\n\n\tlet dom;\n\tif (!skipRemove && typeof vnode.type != 'function') {\n\t\tskipRemove = (dom = vnode._dom) != null;\n\t}\n\n\t// Must be set to `undefined` to properly clean up `_nextDom`\n\t// for which `null` is a valid value. See comment in `create-element.js`\n\tvnode._dom = vnode._nextDom = undefined;\n\n\tif ((r = vnode._component) != null) {\n\t\tif (r.componentWillUnmount) {\n\t\t\ttry {\n\t\t\t\tr.componentWillUnmount();\n\t\t\t} catch (e) {\n\t\t\t\toptions._catchError(e, parentVNode);\n\t\t\t}\n\t\t}\n\n\t\tr.base = r._parentDom = null;\n\t}\n\n\tif ((r = vnode._children)) {\n\t\tfor (let i = 0; i < r.length; i++) {\n\t\t\tif (r[i]) unmount(r[i], parentVNode, skipRemove);\n\t\t}\n\t}\n\n\tif (dom != null) removeNode(dom);\n}\n\n/** The `.render()` method for a PFC backing instance. */\nfunction doRender(props, state, context) {\n\treturn this.constructor(props, context);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from './constants';\nimport { commitRoot, diff } from './diff/index';\nimport { createElement, Fragment } from './create-element';\nimport options from './options';\n\nconst IS_HYDRATE = EMPTY_OBJ;\n\n/**\n * Render a Preact virtual node into a DOM element\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * render into\n * @param {Element | Text} [replaceNode] Optional: Attempt to re-use an\n * existing DOM tree rooted at `replaceNode`\n */\nexport function render(vnode, parentDom, replaceNode) {\n\tif (options._root) options._root(vnode, parentDom);\n\n\t// We abuse the `replaceNode` parameter in `hydrate()` to signal if we\n\t// are in hydration mode or not by passing `IS_HYDRATE` instead of a\n\t// DOM element.\n\tlet isHydrating = replaceNode === IS_HYDRATE;\n\n\t// To be able to support calling `render()` multiple times on the same\n\t// DOM node, we need to obtain a reference to the previous tree. We do\n\t// this by assigning a new `_children` property to DOM nodes which points\n\t// to the last rendered tree. By default this property is not present, which\n\t// means that we are mounting a new tree for the first time.\n\tlet oldVNode = isHydrating\n\t\t? null\n\t\t: (replaceNode && replaceNode._children) || parentDom._children;\n\tvnode = createElement(Fragment, null, [vnode]);\n\n\t// List of effects that need to be called after diffing.\n\tlet commitQueue = [];\n\tdiff(\n\t\tparentDom,\n\t\t// Determine the new vnode tree and store it on the DOM element on\n\t\t// our custom `_children` property.\n\t\t((isHydrating ? parentDom : replaceNode || parentDom)._children = vnode),\n\t\toldVNode || EMPTY_OBJ,\n\t\tEMPTY_OBJ,\n\t\tparentDom.ownerSVGElement !== undefined,\n\t\treplaceNode && !isHydrating\n\t\t\t? [replaceNode]\n\t\t\t: oldVNode\n\t\t\t? null\n\t\t\t: EMPTY_ARR.slice.call(parentDom.childNodes),\n\t\tcommitQueue,\n\t\treplaceNode || EMPTY_OBJ,\n\t\tisHydrating\n\t);\n\n\t// Flush all queued effects\n\tcommitRoot(commitQueue, vnode);\n}\n\n/**\n * Update an existing DOM element with data from a Preact virtual node\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * update\n */\nexport function hydrate(vnode, parentDom) {\n\trender(vnode, parentDom, IS_HYDRATE);\n}\n","import { assign } from './util';\nimport { EMPTY_ARR } from './constants';\nimport { createVNode } from './create-element';\n\n/**\n * Clones the given VNode, optionally adding attributes/props and replacing its children.\n * @param {import('./internal').VNode} vnode The virtual DOM element to clone\n * @param {object} props Attributes/props to add when cloning\n * @param {Array} rest Any additional arguments will be used as replacement children.\n * @returns {import('./internal').VNode}\n */\nexport function cloneElement(vnode, props) {\n\tprops = assign(assign({}, vnode.props), props);\n\tif (arguments.length > 2) props.children = EMPTY_ARR.slice.call(arguments, 2);\n\treturn createVNode(\n\t\tvnode.type,\n\t\tprops,\n\t\tprops.key || vnode.key,\n\t\tprops.ref || vnode.ref,\n\t\tnull\n\t);\n}\n","import { enqueueRender } from './component';\n\nexport let i = 0;\n\nexport function createContext(defaultValue) {\n\tconst ctx = {};\n\n\tconst context = {\n\t\t_id: '__cC' + i++,\n\t\t_defaultValue: defaultValue,\n\t\tConsumer(props, context) {\n\t\t\treturn props.children(context);\n\t\t},\n\t\tProvider(props) {\n\t\t\tif (!this.getChildContext) {\n\t\t\t\tconst subs = [];\n\t\t\t\tthis.getChildContext = () => {\n\t\t\t\t\tctx[context._id] = this;\n\t\t\t\t\treturn ctx;\n\t\t\t\t};\n\n\t\t\t\tthis.shouldComponentUpdate = _props => {\n\t\t\t\t\tif (this.props.value !== _props.value) {\n\t\t\t\t\t\tsubs.some(c => {\n\t\t\t\t\t\t\tc.context = _props.value;\n\t\t\t\t\t\t\tenqueueRender(c);\n\t\t\t\t\t\t});\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\tthis.sub = c => {\n\t\t\t\t\tsubs.push(c);\n\t\t\t\t\tlet old = c.componentWillUnmount;\n\t\t\t\t\tc.componentWillUnmount = () => {\n\t\t\t\t\t\tsubs.splice(subs.indexOf(c), 1);\n\t\t\t\t\t\told && old.call(c);\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t}\n\n\t\t\treturn props.children;\n\t\t}\n\t};\n\n\tcontext.Consumer.contextType = context;\n\n\treturn context;\n}\n","export const ELEMENT_NODE = 1;\nexport const DOCUMENT_NODE = 9;\nexport const DOCUMENT_FRAGMENT_NODE = 11;\n","import { _catchError } from './diff/catch-error';\n\n/**\n * The `option` object can potentially contain callback functions\n * that are called during various stages of our renderer. This is the\n * foundation on which all our addons like `preact/debug`, `preact/compat`,\n * and `preact/hooks` are based on. See the `Options` type in `internal.d.ts`\n * for a full list of available option hooks (most editors/IDEs allow you to\n * ctrl+click or cmd+click on mac the type definition below).\n * @type {import('./internal').Options}\n */\nconst options = {\n\t_catchError\n};\n\nexport default options;\n","import { enqueueRender } from '../component';\n\n/**\n * Find the closest error boundary to a thrown error and call it\n * @param {object} error The thrown value\n * @param {import('../internal').VNode} vnode The vnode that threw\n * the error that was caught (except for unmounting when this parameter\n * is the highest parent that was being unmounted)\n */\nexport function _catchError(error, vnode) {\n\t/** @type {import('../internal').Component} */\n\tlet component, hasCaught;\n\n\tfor (; (vnode = vnode._parent); ) {\n\t\tif ((component = vnode._component) && !component._processingException) {\n\t\t\ttry {\n\t\t\t\tif (\n\t\t\t\t\tcomponent.constructor &&\n\t\t\t\t\tcomponent.constructor.getDerivedStateFromError != null\n\t\t\t\t) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.setState(\n\t\t\t\t\t\tcomponent.constructor.getDerivedStateFromError(error)\n\t\t\t\t\t);\n\t\t\t\t}\n\n\t\t\t\tif (component.componentDidCatch != null) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.componentDidCatch(error);\n\t\t\t\t}\n\n\t\t\t\tif (hasCaught)\n\t\t\t\t\treturn enqueueRender((component._pendingError = component));\n\t\t\t} catch (e) {\n\t\t\t\terror = e;\n\t\t\t}\n\t\t}\n\t}\n\n\tthrow error;\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./ottimizzazioneLineare.js\") );\n\t\t\t}, \"route-ottimizzazioneLineare\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/* global __webpack_public_path__ */\n\nimport * as Preact from 'preact';\nconst { h, render, hydrate } = Preact;\n\nconst interopDefault = m => (m && m.default ? m.default : m);\n\nconst normalizeURL = url => (url[url.length - 1] === '/' ? url : url + '/');\n\nif (process.env.NODE_ENV === 'development') {\n\t// enable preact devtools\n\trequire('preact/debug');\n\tif (process.env.RHL) {\n\t\t// enable hot loader\n\t\tconst hotLoader = interopDefault(require('react-hot-loader'));\n\t\thotLoader.preact(interopDefault(require('preact')));\n\t}\n\t// only add a debug sw if webpack service worker is not requested.\n\tif (process.env.ADD_SW === undefined && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(__webpack_public_path__ + 'sw-debug.js');\n\t} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(\n\t\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t\t);\n\t}\n} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t// eslint-disable-next-line no-undef\n\tnavigator.serviceWorker.register(\n\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t);\n}\n\nlet app = interopDefault(require('preact-cli-entrypoint'));\n\nif (typeof app === 'function') {\n\tlet root =\n\t\tdocument.getElementById('preact_root') || document.body.firstElementChild;\n\n\tlet init = () => {\n\t\tlet app = interopDefault(require('preact-cli-entrypoint'));\n\t\tlet preRenderData = {};\n\t\tconst inlineDataElement = document.querySelector(\n\t\t\t'[type=\"__PREACT_CLI_DATA__\"]'\n\t\t);\n\t\tif (inlineDataElement) {\n\t\t\tpreRenderData =\n\t\t\t\tJSON.parse(inlineDataElement.innerHTML).preRenderData || preRenderData;\n\t\t}\n\t\t/* An object named CLI_DATA is passed as a prop,\n\t\t * this keeps us future proof if in case we decide,\n\t\t * to send other data like at some point in time.\n\t\t */\n\t\tconst CLI_DATA = { preRenderData };\n\t\tconst currentURL = preRenderData.url ? normalizeURL(preRenderData.url) : '';\n\t\tconst canHydrate =\n\t\t\tprocess.env.PRERENDER &&\n\t\t\tprocess.env.NODE_ENV === 'production' &&\n\t\t\thydrate &&\n\t\t\tcurrentURL === location.pathname;\n\t\tconst doRender = canHydrate ? hydrate : render;\n\t\troot = doRender(h(app, { CLI_DATA }), document.body, root);\n\t};\n\n\tif (module.hot) module.hot.accept('preact-cli-entrypoint', init);\n\n\tinit();\n}\n","export default function _extends() {\n _extends = Object.assign || function (target) {\n for (var i = 1; i < arguments.length; i++) {\n var source = arguments[i];\n\n for (var key in source) {\n if (Object.prototype.hasOwnProperty.call(source, key)) {\n target[key] = source[key];\n }\n }\n }\n\n return target;\n };\n\n return _extends.apply(this, arguments);\n}","function isAbsolute(pathname) {\n return pathname.charAt(0) === '/';\n}\n\n// About 1.5x faster than the two-arg version of Array#splice()\nfunction spliceOne(list, index) {\n for (var i = index, k = i + 1, n = list.length; k < n; i += 1, k += 1) {\n list[i] = list[k];\n }\n\n list.pop();\n}\n\n// This implementation is based heavily on node's url.parse\nfunction resolvePathname(to, from) {\n if (from === undefined) from = '';\n\n var toParts = (to && to.split('/')) || [];\n var fromParts = (from && from.split('/')) || [];\n\n var isToAbs = to && isAbsolute(to);\n var isFromAbs = from && isAbsolute(from);\n var mustEndAbs = isToAbs || isFromAbs;\n\n if (to && isAbsolute(to)) {\n // to is absolute\n fromParts = toParts;\n } else if (toParts.length) {\n // to is relative, drop the filename\n fromParts.pop();\n fromParts = fromParts.concat(toParts);\n }\n\n if (!fromParts.length) return '/';\n\n var hasTrailingSlash;\n if (fromParts.length) {\n var last = fromParts[fromParts.length - 1];\n hasTrailingSlash = last === '.' || last === '..' || last === '';\n } else {\n hasTrailingSlash = false;\n }\n\n var up = 0;\n for (var i = fromParts.length; i >= 0; i--) {\n var part = fromParts[i];\n\n if (part === '.') {\n spliceOne(fromParts, i);\n } else if (part === '..') {\n spliceOne(fromParts, i);\n up++;\n } else if (up) {\n spliceOne(fromParts, i);\n up--;\n }\n }\n\n if (!mustEndAbs) for (; up--; up) fromParts.unshift('..');\n\n if (\n mustEndAbs &&\n fromParts[0] !== '' &&\n (!fromParts[0] || !isAbsolute(fromParts[0]))\n )\n fromParts.unshift('');\n\n var result = fromParts.join('/');\n\n if (hasTrailingSlash && result.substr(-1) !== '/') result += '/';\n\n return result;\n}\n\nexport default resolvePathname;\n","import _extends from '@babel/runtime/helpers/esm/extends';\nimport resolvePathname from 'resolve-pathname';\nimport valueEqual from 'value-equal';\nimport warning from 'tiny-warning';\nimport invariant from 'tiny-invariant';\n\nfunction addLeadingSlash(path) {\n return path.charAt(0) === '/' ? path : '/' + path;\n}\nfunction stripLeadingSlash(path) {\n return path.charAt(0) === '/' ? path.substr(1) : path;\n}\nfunction hasBasename(path, prefix) {\n return path.toLowerCase().indexOf(prefix.toLowerCase()) === 0 && '/?#'.indexOf(path.charAt(prefix.length)) !== -1;\n}\nfunction stripBasename(path, prefix) {\n return hasBasename(path, prefix) ? path.substr(prefix.length) : path;\n}\nfunction stripTrailingSlash(path) {\n return path.charAt(path.length - 1) === '/' ? path.slice(0, -1) : path;\n}\nfunction parsePath(path) {\n var pathname = path || '/';\n var search = '';\n var hash = '';\n var hashIndex = pathname.indexOf('#');\n\n if (hashIndex !== -1) {\n hash = pathname.substr(hashIndex);\n pathname = pathname.substr(0, hashIndex);\n }\n\n var searchIndex = pathname.indexOf('?');\n\n if (searchIndex !== -1) {\n search = pathname.substr(searchIndex);\n pathname = pathname.substr(0, searchIndex);\n }\n\n return {\n pathname: pathname,\n search: search === '?' ? '' : search,\n hash: hash === '#' ? '' : hash\n };\n}\nfunction createPath(location) {\n var pathname = location.pathname,\n search = location.search,\n hash = location.hash;\n var path = pathname || '/';\n if (search && search !== '?') path += search.charAt(0) === '?' ? search : \"?\" + search;\n if (hash && hash !== '#') path += hash.charAt(0) === '#' ? hash : \"#\" + hash;\n return path;\n}\n\nfunction createLocation(path, state, key, currentLocation) {\n var location;\n\n if (typeof path === 'string') {\n // Two-arg form: push(path, state)\n location = parsePath(path);\n location.state = state;\n } else {\n // One-arg form: push(location)\n location = _extends({}, path);\n if (location.pathname === undefined) location.pathname = '';\n\n if (location.search) {\n if (location.search.charAt(0) !== '?') location.search = '?' + location.search;\n } else {\n location.search = '';\n }\n\n if (location.hash) {\n if (location.hash.charAt(0) !== '#') location.hash = '#' + location.hash;\n } else {\n location.hash = '';\n }\n\n if (state !== undefined && location.state === undefined) location.state = state;\n }\n\n try {\n location.pathname = decodeURI(location.pathname);\n } catch (e) {\n if (e instanceof URIError) {\n throw new URIError('Pathname \"' + location.pathname + '\" could not be decoded. ' + 'This is likely caused by an invalid percent-encoding.');\n } else {\n throw e;\n }\n }\n\n if (key) location.key = key;\n\n if (currentLocation) {\n // Resolve incomplete/relative pathname relative to current location.\n if (!location.pathname) {\n location.pathname = currentLocation.pathname;\n } else if (location.pathname.charAt(0) !== '/') {\n location.pathname = resolvePathname(location.pathname, currentLocation.pathname);\n }\n } else {\n // When there is no prior location and pathname is empty, set it to /\n if (!location.pathname) {\n location.pathname = '/';\n }\n }\n\n return location;\n}\nfunction locationsAreEqual(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash && a.key === b.key && valueEqual(a.state, b.state);\n}\n\nfunction createTransitionManager() {\n var prompt = null;\n\n function setPrompt(nextPrompt) {\n process.env.NODE_ENV !== \"production\" ? warning(prompt == null, 'A history supports only one prompt at a time') : void 0;\n prompt = nextPrompt;\n return function () {\n if (prompt === nextPrompt) prompt = null;\n };\n }\n\n function confirmTransitionTo(location, action, getUserConfirmation, callback) {\n // TODO: If another transition starts while we're still confirming\n // the previous one, we may end up in a weird state. Figure out the\n // best way to handle this.\n if (prompt != null) {\n var result = typeof prompt === 'function' ? prompt(location, action) : prompt;\n\n if (typeof result === 'string') {\n if (typeof getUserConfirmation === 'function') {\n getUserConfirmation(result, callback);\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'A history needs a getUserConfirmation function in order to use a prompt message') : void 0;\n callback(true);\n }\n } else {\n // Return false from a transition hook to cancel the transition.\n callback(result !== false);\n }\n } else {\n callback(true);\n }\n }\n\n var listeners = [];\n\n function appendListener(fn) {\n var isActive = true;\n\n function listener() {\n if (isActive) fn.apply(void 0, arguments);\n }\n\n listeners.push(listener);\n return function () {\n isActive = false;\n listeners = listeners.filter(function (item) {\n return item !== listener;\n });\n };\n }\n\n function notifyListeners() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n listeners.forEach(function (listener) {\n return listener.apply(void 0, args);\n });\n }\n\n return {\n setPrompt: setPrompt,\n confirmTransitionTo: confirmTransitionTo,\n appendListener: appendListener,\n notifyListeners: notifyListeners\n };\n}\n\nvar canUseDOM = !!(typeof window !== 'undefined' && window.document && window.document.createElement);\nfunction getConfirmation(message, callback) {\n callback(window.confirm(message)); // eslint-disable-line no-alert\n}\n/**\n * Returns true if the HTML5 history API is supported. Taken from Modernizr.\n *\n * https://github.com/Modernizr/Modernizr/blob/master/LICENSE\n * https://github.com/Modernizr/Modernizr/blob/master/feature-detects/history.js\n * changed to avoid false negatives for Windows Phones: https://github.com/reactjs/react-router/issues/586\n */\n\nfunction supportsHistory() {\n var ua = window.navigator.userAgent;\n if ((ua.indexOf('Android 2.') !== -1 || ua.indexOf('Android 4.0') !== -1) && ua.indexOf('Mobile Safari') !== -1 && ua.indexOf('Chrome') === -1 && ua.indexOf('Windows Phone') === -1) return false;\n return window.history && 'pushState' in window.history;\n}\n/**\n * Returns true if browser fires popstate on hash change.\n * IE10 and IE11 do not.\n */\n\nfunction supportsPopStateOnHashChange() {\n return window.navigator.userAgent.indexOf('Trident') === -1;\n}\n/**\n * Returns false if using go(n) with hash history causes a full page reload.\n */\n\nfunction supportsGoWithoutReloadUsingHash() {\n return window.navigator.userAgent.indexOf('Firefox') === -1;\n}\n/**\n * Returns true if a given popstate event is an extraneous WebKit event.\n * Accounts for the fact that Chrome on iOS fires real popstate events\n * containing undefined state when pressing the back button.\n */\n\nfunction isExtraneousPopstateEvent(event) {\n return event.state === undefined && navigator.userAgent.indexOf('CriOS') === -1;\n}\n\nvar PopStateEvent = 'popstate';\nvar HashChangeEvent = 'hashchange';\n\nfunction getHistoryState() {\n try {\n return window.history.state || {};\n } catch (e) {\n // IE 11 sometimes throws when accessing window.history.state\n // See https://github.com/ReactTraining/history/pull/289\n return {};\n }\n}\n/**\n * Creates a history object that uses the HTML5 history API including\n * pushState, replaceState, and the popstate event.\n */\n\n\nfunction createBrowserHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Browser history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canUseHistory = supportsHistory();\n var needsHashChangeListener = !supportsPopStateOnHashChange();\n var _props = props,\n _props$forceRefresh = _props.forceRefresh,\n forceRefresh = _props$forceRefresh === void 0 ? false : _props$forceRefresh,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n\n function getDOMLocation(historyState) {\n var _ref = historyState || {},\n key = _ref.key,\n state = _ref.state;\n\n var _window$location = window.location,\n pathname = _window$location.pathname,\n search = _window$location.search,\n hash = _window$location.hash;\n var path = pathname + search + hash;\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path, state, key);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function handlePopState(event) {\n // Ignore extraneous popstate events in WebKit.\n if (isExtraneousPopstateEvent(event)) return;\n handlePop(getDOMLocation(event.state));\n }\n\n function handleHashChange() {\n handlePop(getDOMLocation(getHistoryState()));\n }\n\n var forceNextPop = false;\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of keys we've seen in sessionStorage.\n // Instead, we just default to 0 for keys we don't know.\n\n var toIndex = allKeys.indexOf(toLocation.key);\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allKeys.indexOf(fromLocation.key);\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n }\n\n var initialLocation = getDOMLocation(getHistoryState());\n var allKeys = [initialLocation.key]; // Public interface\n\n function createHref(location) {\n return basename + createPath(location);\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.pushState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.href = href;\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n var nextKeys = allKeys.slice(0, prevIndex + 1);\n nextKeys.push(location.key);\n allKeys = nextKeys;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot push state in browsers that do not support HTML5 history') : void 0;\n window.location.href = href;\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.replaceState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.replace(href);\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n if (prevIndex !== -1) allKeys[prevIndex] = location.key;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot replace state in browsers that do not support HTML5 history') : void 0;\n window.location.replace(href);\n }\n });\n }\n\n function go(n) {\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.addEventListener(HashChangeEvent, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.removeEventListener(HashChangeEvent, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nvar HashChangeEvent$1 = 'hashchange';\nvar HashPathCoders = {\n hashbang: {\n encodePath: function encodePath(path) {\n return path.charAt(0) === '!' ? path : '!/' + stripLeadingSlash(path);\n },\n decodePath: function decodePath(path) {\n return path.charAt(0) === '!' ? path.substr(1) : path;\n }\n },\n noslash: {\n encodePath: stripLeadingSlash,\n decodePath: addLeadingSlash\n },\n slash: {\n encodePath: addLeadingSlash,\n decodePath: addLeadingSlash\n }\n};\n\nfunction stripHash(url) {\n var hashIndex = url.indexOf('#');\n return hashIndex === -1 ? url : url.slice(0, hashIndex);\n}\n\nfunction getHashPath() {\n // We can't use window.location.hash here because it's not\n // consistent across browsers - Firefox will pre-decode it!\n var href = window.location.href;\n var hashIndex = href.indexOf('#');\n return hashIndex === -1 ? '' : href.substring(hashIndex + 1);\n}\n\nfunction pushHashPath(path) {\n window.location.hash = path;\n}\n\nfunction replaceHashPath(path) {\n window.location.replace(stripHash(window.location.href) + '#' + path);\n}\n\nfunction createHashHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Hash history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canGoWithoutReload = supportsGoWithoutReloadUsingHash();\n var _props = props,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$hashType = _props.hashType,\n hashType = _props$hashType === void 0 ? 'slash' : _props$hashType;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n var _HashPathCoders$hashT = HashPathCoders[hashType],\n encodePath = _HashPathCoders$hashT.encodePath,\n decodePath = _HashPathCoders$hashT.decodePath;\n\n function getDOMLocation() {\n var path = decodePath(getHashPath());\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n var forceNextPop = false;\n var ignorePath = null;\n\n function locationsAreEqual$$1(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash;\n }\n\n function handleHashChange() {\n var path = getHashPath();\n var encodedPath = encodePath(path);\n\n if (path !== encodedPath) {\n // Ensure we always have a properly-encoded hash.\n replaceHashPath(encodedPath);\n } else {\n var location = getDOMLocation();\n var prevLocation = history.location;\n if (!forceNextPop && locationsAreEqual$$1(prevLocation, location)) return; // A hashchange doesn't always == location change.\n\n if (ignorePath === createPath(location)) return; // Ignore this change; we already setState in push/replace.\n\n ignorePath = null;\n handlePop(location);\n }\n }\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of paths we've seen in sessionStorage.\n // Instead, we just default to 0 for paths we don't know.\n\n var toIndex = allPaths.lastIndexOf(createPath(toLocation));\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allPaths.lastIndexOf(createPath(fromLocation));\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n } // Ensure the hash is encoded properly before doing anything else.\n\n\n var path = getHashPath();\n var encodedPath = encodePath(path);\n if (path !== encodedPath) replaceHashPath(encodedPath);\n var initialLocation = getDOMLocation();\n var allPaths = [createPath(initialLocation)]; // Public interface\n\n function createHref(location) {\n var baseTag = document.querySelector('base');\n var href = '';\n\n if (baseTag && baseTag.getAttribute('href')) {\n href = stripHash(window.location.href);\n }\n\n return href + '#' + encodePath(basename + createPath(location));\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot push state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a PUSH, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n pushHashPath(encodedPath);\n var prevIndex = allPaths.lastIndexOf(createPath(history.location));\n var nextPaths = allPaths.slice(0, prevIndex + 1);\n nextPaths.push(path);\n allPaths = nextPaths;\n setState({\n action: action,\n location: location\n });\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'Hash history cannot PUSH the same path; a new entry will not be added to the history stack') : void 0;\n setState();\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot replace state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a REPLACE, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n replaceHashPath(encodedPath);\n }\n\n var prevIndex = allPaths.indexOf(createPath(history.location));\n if (prevIndex !== -1) allPaths[prevIndex] = path;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n process.env.NODE_ENV !== \"production\" ? warning(canGoWithoutReload, 'Hash history go(n) causes a full page reload in this browser') : void 0;\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(HashChangeEvent$1, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(HashChangeEvent$1, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nfunction clamp(n, lowerBound, upperBound) {\n return Math.min(Math.max(n, lowerBound), upperBound);\n}\n/**\n * Creates a history object that stores locations in memory.\n */\n\n\nfunction createMemoryHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n var _props = props,\n getUserConfirmation = _props.getUserConfirmation,\n _props$initialEntries = _props.initialEntries,\n initialEntries = _props$initialEntries === void 0 ? ['/'] : _props$initialEntries,\n _props$initialIndex = _props.initialIndex,\n initialIndex = _props$initialIndex === void 0 ? 0 : _props$initialIndex,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = history.entries.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var index = clamp(initialIndex, 0, initialEntries.length - 1);\n var entries = initialEntries.map(function (entry) {\n return typeof entry === 'string' ? createLocation(entry, undefined, createKey()) : createLocation(entry, undefined, entry.key || createKey());\n }); // Public interface\n\n var createHref = createPath;\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var prevIndex = history.index;\n var nextIndex = prevIndex + 1;\n var nextEntries = history.entries.slice(0);\n\n if (nextEntries.length > nextIndex) {\n nextEntries.splice(nextIndex, nextEntries.length - nextIndex, location);\n } else {\n nextEntries.push(location);\n }\n\n setState({\n action: action,\n location: location,\n index: nextIndex,\n entries: nextEntries\n });\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n history.entries[history.index] = location;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n var nextIndex = clamp(history.index + n, 0, history.entries.length - 1);\n var action = 'POP';\n var location = history.entries[nextIndex];\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location,\n index: nextIndex\n });\n } else {\n // Mimic the behavior of DOM histories by\n // causing a render after a cancelled POP.\n setState();\n }\n });\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n function canGo(n) {\n var nextIndex = history.index + n;\n return nextIndex >= 0 && nextIndex < history.entries.length;\n }\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n return transitionManager.setPrompt(prompt);\n }\n\n function listen(listener) {\n return transitionManager.appendListener(listener);\n }\n\n var history = {\n length: entries.length,\n action: 'POP',\n location: entries[index],\n index: index,\n entries: entries,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n canGo: canGo,\n block: block,\n listen: listen\n };\n return history;\n}\n\nexport { createBrowserHistory, createHashHistory, createMemoryHistory, createLocation, locationsAreEqual, parsePath, createPath };\n","var isProduction = process.env.NODE_ENV === 'production';\nvar prefix = 'Invariant failed';\nfunction invariant(condition, message) {\n if (condition) {\n return;\n }\n if (isProduction) {\n throw new Error(prefix);\n }\n throw new Error(prefix + \": \" + (message || ''));\n}\n\nexport default invariant;\n","import { options, Fragment } from 'preact';\n\n/**\n * Get human readable name of the component/dom node\n * @param {import('./internal').VNode} vnode\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function getDisplayName(vnode) {\n\tif (vnode.type === Fragment) {\n\t\treturn 'Fragment';\n\t} else if (typeof vnode.type == 'function') {\n\t\treturn vnode.type.displayName || vnode.type.name;\n\t} else if (typeof vnode.type == 'string') {\n\t\treturn vnode.type;\n\t}\n\n\treturn '#text';\n}\n\n/**\n * Used to keep track of the currently rendered `vnode` and print it\n * in debug messages.\n */\nlet renderStack = [];\n\n/**\n * Keep track of the current owners. An owner describes a component\n * which was responsible to render a specific `vnode`. This exclude\n * children that are passed via `props.children`, because they belong\n * to the parent owner.\n *\n * ```jsx\n * const Foo = props =>
{props.children}
// div's owner is Foo\n * const Bar = props => {\n * return (\n * // Foo's owner is Bar, span's owner is Bar\n * )\n * }\n * ```\n *\n * Note: A `vnode` may be hoisted to the root scope due to compiler\n * optimiztions. In these cases the `_owner` will be different.\n */\nlet ownerStack = [];\n\n/**\n * Get the currently rendered `vnode`\n * @returns {import('./internal').VNode | null}\n */\nexport function getCurrentVNode() {\n\treturn renderStack.length > 0 ? renderStack[renderStack.length - 1] : null;\n}\n\n/**\n * If the user doesn't have `@babel/plugin-transform-react-jsx-source`\n * somewhere in his tool chain we can't print the filename and source\n * location of a component. In that case we just omit that, but we'll\n * print a helpful message to the console, notifying the user of it.\n */\nlet hasBabelPlugin = false;\n\n/**\n * Check if a `vnode` is a possible owner.\n * @param {import('./internal').VNode} vnode\n */\nfunction isPossibleOwner(vnode) {\n\treturn typeof vnode.type == 'function' && vnode.type != Fragment;\n}\n\n/**\n * Return the component stack that was captured up to this point.\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function getOwnerStack(vnode) {\n\tconst stack = [vnode];\n\tlet next = vnode;\n\twhile (next._owner != null) {\n\t\tstack.push(next._owner);\n\t\tnext = next._owner;\n\t}\n\n\treturn stack.reduce((acc, owner) => {\n\t\tacc += ` in ${getDisplayName(owner)}`;\n\n\t\tconst source = owner.__source;\n\t\tif (source) {\n\t\t\tacc += ` (at ${source.fileName}:${source.lineNumber})`;\n\t\t} else if (!hasBabelPlugin) {\n\t\t\thasBabelPlugin = true;\n\t\t\tconsole.warn(\n\t\t\t\t'Add @babel/plugin-transform-react-jsx-source to get a more detailed component stack. Note that you should not add it to production builds of your App for bundle size reasons.'\n\t\t\t);\n\t\t}\n\n\t\treturn (acc += '\\n');\n\t}, '');\n}\n\n/**\n * Setup code to capture the component trace while rendering. Note that\n * we cannot simply traverse `vnode._parent` upwards, because we have some\n * debug messages for `this.setState` where the `vnode` is `undefined`.\n */\nexport function setupComponentStack() {\n\tlet oldDiff = options._diff;\n\tlet oldDiffed = options.diffed;\n\tlet oldRoot = options._root;\n\tlet oldVNode = options.vnode;\n\tlet oldRender = options._render;\n\n\toptions.diffed = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\townerStack.pop();\n\t\t}\n\t\trenderStack.pop();\n\t\tif (oldDiffed) oldDiffed(vnode);\n\t};\n\n\toptions._diff = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\trenderStack.push(vnode);\n\t\t}\n\t\tif (oldDiff) oldDiff(vnode);\n\t};\n\n\toptions._root = (vnode, parent) => {\n\t\townerStack = [];\n\t\tif (oldRoot) oldRoot(vnode, parent);\n\t};\n\n\toptions.vnode = vnode => {\n\t\tvnode._owner =\n\t\t\townerStack.length > 0 ? ownerStack[ownerStack.length - 1] : null;\n\t\tif (oldVNode) oldVNode(vnode);\n\t};\n\n\toptions._render = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\townerStack.push(vnode);\n\t\t}\n\n\t\tif (oldRender) oldRender(vnode);\n\t};\n}\n","import { checkPropTypes } from './check-props';\nimport { options, Component } from 'preact';\nimport {\n\tELEMENT_NODE,\n\tDOCUMENT_NODE,\n\tDOCUMENT_FRAGMENT_NODE\n} from './constants';\nimport {\n\tgetOwnerStack,\n\tsetupComponentStack,\n\tgetCurrentVNode,\n\tgetDisplayName\n} from './component-stack';\n\nconst isWeakMapSupported = typeof WeakMap == 'function';\n\nfunction getClosestDomNodeParent(parent) {\n\tif (!parent) return {};\n\tif (typeof parent.type == 'function') {\n\t\treturn getClosestDomNodeParent(parent._parent);\n\t}\n\treturn parent;\n}\n\nexport function initDebug() {\n\tsetupComponentStack();\n\n\t/* eslint-disable no-console */\n\tlet oldBeforeDiff = options._diff;\n\tlet oldDiffed = options.diffed;\n\tlet oldVnode = options.vnode;\n\tlet oldCatchError = options._catchError;\n\tlet oldRoot = options._root;\n\tlet oldHook = options._hook;\n\tconst warnedComponents = !isWeakMapSupported\n\t\t? null\n\t\t: {\n\t\t\t\tuseEffect: new WeakMap(),\n\t\t\t\tuseLayoutEffect: new WeakMap(),\n\t\t\t\tlazyPropTypes: new WeakMap()\n\t\t };\n\n\toptions._catchError = (error, vnode, oldVNode) => {\n\t\tlet component = vnode && vnode._component;\n\t\tif (component && typeof error.then == 'function') {\n\t\t\tconst promise = error;\n\t\t\terror = new Error(\n\t\t\t\t`Missing Suspense. The throwing component was: ${getDisplayName(vnode)}`\n\t\t\t);\n\n\t\t\tlet parent = vnode;\n\t\t\tfor (; parent; parent = parent._parent) {\n\t\t\t\tif (parent._component && parent._component._childDidSuspend) {\n\t\t\t\t\terror = promise;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\t// We haven't recovered and we know at this point that there is no\n\t\t\t// Suspense component higher up in the tree\n\t\t\tif (error instanceof Error) {\n\t\t\t\tthrow error;\n\t\t\t}\n\t\t}\n\n\t\toldCatchError(error, vnode, oldVNode);\n\t};\n\n\toptions._root = (vnode, parentNode) => {\n\t\tif (!parentNode) {\n\t\t\tthrow new Error(\n\t\t\t\t'Undefined parent passed to render(), this is the second argument.\\n' +\n\t\t\t\t\t'Check if the element is available in the DOM/has the correct id.'\n\t\t\t);\n\t\t}\n\t\tlet isValid;\n\t\tswitch (parentNode.nodeType) {\n\t\t\tcase ELEMENT_NODE:\n\t\t\tcase DOCUMENT_FRAGMENT_NODE:\n\t\t\tcase DOCUMENT_NODE:\n\t\t\t\tisValid = true;\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tisValid = false;\n\t\t}\n\n\t\tif (!isValid) {\n\t\t\tlet componentName = getDisplayName(vnode);\n\t\t\tthrow new Error(\n\t\t\t\t`Expected a valid HTML node as a second argument to render.\tReceived ${parentNode} instead: render(<${componentName} />, ${parentNode});`\n\t\t\t);\n\t\t}\n\n\t\tif (oldRoot) oldRoot(vnode, parentNode);\n\t};\n\n\toptions._diff = vnode => {\n\t\tlet { type, _parent: parent } = vnode;\n\t\tlet parentVNode = getClosestDomNodeParent(parent);\n\n\t\tif (type === undefined) {\n\t\t\tthrow new Error(\n\t\t\t\t'Undefined component passed to createElement()\\n\\n' +\n\t\t\t\t\t'You likely forgot to export your component or might have mixed up default and named imports' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type != null && typeof type == 'object') {\n\t\t\tif (type._children !== undefined && type._dom !== undefined) {\n\t\t\t\tthrow new Error(\n\t\t\t\t\t`Invalid type passed to createElement(): ${type}\\n\\n` +\n\t\t\t\t\t\t'Did you accidentally pass a JSX literal as JSX twice?\\n\\n' +\n\t\t\t\t\t\t` let My${getDisplayName(vnode)} = ${serializeVNode(type)};\\n` +\n\t\t\t\t\t\t` let vnode = ;\\n\\n` +\n\t\t\t\t\t\t'This usually happens when you export a JSX literal and not the component.' +\n\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t);\n\t\t\t}\n\n\t\t\tthrow new Error(\n\t\t\t\t'Invalid type passed to createElement(): ' +\n\t\t\t\t\t(Array.isArray(type) ? 'array' : type)\n\t\t\t);\n\t\t}\n\n\t\tif (\n\t\t\t(type === 'thead' || type === 'tfoot' || type === 'tbody') &&\n\t\t\tparentVNode.type !== 'table'\n\t\t) {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your should have a
parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (\n\t\t\ttype === 'tr' &&\n\t\t\tparentVNode.type !== 'thead' &&\n\t\t\tparentVNode.type !== 'tfoot' &&\n\t\t\tparentVNode.type !== 'tbody' &&\n\t\t\tparentVNode.type !== 'table'\n\t\t) {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your should have a parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type === 'td' && parentVNode.type !== 'tr') {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type === 'th' && parentVNode.type !== 'tr') {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your .' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t}\n\n\t\tif (\n\t\t\tvnode.ref !== undefined &&\n\t\t\ttypeof vnode.ref != 'function' &&\n\t\t\ttypeof vnode.ref != 'object' &&\n\t\t\t!('$$typeof' in vnode) // allow string refs when preact-compat is installed\n\t\t) {\n\t\t\tthrow new Error(\n\t\t\t\t`Component's \"ref\" property should be a function, or an object created ` +\n\t\t\t\t\t`by createRef(), but got [${typeof vnode.ref}] instead\\n` +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t}\n\n\t\tif (typeof vnode.type == 'string') {\n\t\t\tfor (const key in vnode.props) {\n\t\t\t\tif (\n\t\t\t\t\tkey[0] === 'o' &&\n\t\t\t\t\tkey[1] === 'n' &&\n\t\t\t\t\ttypeof vnode.props[key] != 'function' &&\n\t\t\t\t\tvnode.props[key] != null\n\t\t\t\t) {\n\t\t\t\t\tthrow new Error(\n\t\t\t\t\t\t`Component's \"${key}\" property should be a function, ` +\n\t\t\t\t\t\t\t`but got [${typeof vnode.props[key]}] instead\\n` +\n\t\t\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\t// Check prop-types if available\n\t\tif (typeof vnode.type == 'function' && vnode.type.propTypes) {\n\t\t\tif (\n\t\t\t\tvnode.type.displayName === 'Lazy' &&\n\t\t\t\twarnedComponents &&\n\t\t\t\t!warnedComponents.lazyPropTypes.has(vnode.type)\n\t\t\t) {\n\t\t\t\tconst m =\n\t\t\t\t\t'PropTypes are not supported on lazy(). 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';\n\t\t\t\ttry {\n\t\t\t\t\tconst lazyVNode = vnode.type();\n\t\t\t\t\twarnedComponents.lazyPropTypes.set(vnode.type, true);\n\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\tm + `Component wrapped in lazy() is ${getDisplayName(lazyVNode)}`\n\t\t\t\t\t);\n\t\t\t\t} catch (promise) {\n\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\tm + \"We will log the wrapped component's name once it is loaded.\"\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t}\n\t\t\tcheckPropTypes(\n\t\t\t\tvnode.type.propTypes,\n\t\t\t\tvnode.props,\n\t\t\t\t'prop',\n\t\t\t\tgetDisplayName(vnode)\n\t\t\t);\n\t\t}\n\n\t\tif (oldBeforeDiff) oldBeforeDiff(vnode);\n\t};\n\n\toptions._hook = comp => {\n\t\tif (!comp) {\n\t\t\tthrow new Error('Hook can only be invoked from render methods.');\n\t\t}\n\n\t\tif (oldHook) oldHook(comp);\n\t};\n\n\tconst warn = (property, err) => ({\n\t\tget() {\n\t\t\tthrow new Error(`getting vnode.${property} is deprecated, ${err}`);\n\t\t},\n\t\tset() {\n\t\t\tthrow new Error(`setting vnode.${property} is not allowed, ${err}`);\n\t\t}\n\t});\n\n\tconst deprecatedAttributes = {\n\t\tnodeName: warn('nodeName', 'use vnode.type'),\n\t\tattributes: warn('attributes', 'use vnode.props'),\n\t\tchildren: warn('children', 'use vnode.props.children')\n\t};\n\n\tconst deprecatedProto = Object.create({}, deprecatedAttributes);\n\n\toptions.vnode = vnode => {\n\t\tconst props = vnode.props;\n\t\tif (\n\t\t\tvnode.type !== null &&\n\t\t\tprops != null &&\n\t\t\t('__source' in props || '__self' in props)\n\t\t) {\n\t\t\tconst newProps = (vnode.props = {});\n\t\t\tfor (let i in props) {\n\t\t\t\tconst v = props[i];\n\t\t\t\tif (i === '__source') vnode.__source = v;\n\t\t\t\telse if (i === '__self') vnode.__self = v;\n\t\t\t\telse newProps[i] = v;\n\t\t\t}\n\t\t}\n\t\tObject.setPrototypeOf(vnode, deprecatedProto);\n\t\tif (oldVnode) oldVnode(vnode);\n\t};\n\n\toptions.diffed = vnode => {\n\t\t// Check if the user passed plain objects as children. Note that we cannot\n\t\t// move this check into `options.vnode` because components can receive\n\t\t// children in any shape they want (e.g.\n\t\t// `{{ foo: 123, bar: \"abc\" }}`).\n\t\t// Putting this check in `options.diffed` ensures that\n\t\t// `vnode._children` is set and that we only validate the children\n\t\t// that were actually rendered.\n\t\tif (vnode._children) {\n\t\t\tvnode._children.forEach(child => {\n\t\t\t\tif (child && child.type === undefined) {\n\t\t\t\t\t// Remove internal vnode keys that will always be patched\n\t\t\t\t\tdelete child._parent;\n\t\t\t\t\tdelete child._depth;\n\t\t\t\t\tconst keys = Object.keys(child).join(',');\n\t\t\t\t\tthrow new Error(\n\t\t\t\t\t\t`Objects are not valid as a child. Encountered an object with the keys {${keys}}.` +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t});\n\t\t}\n\n\t\t/** @type {import('./internal').Component} */\n\t\tconst component = vnode._component;\n\t\tif (component && component.__hooks) {\n\t\t\tlet hooks = component.__hooks;\n\t\t\tif (Array.isArray(hooks._list)) {\n\t\t\t\thooks._list.forEach(hook => {\n\t\t\t\t\tif (hook._factory && (!hook._args || !Array.isArray(hook._args))) {\n\t\t\t\t\t\tlet componentName = getDisplayName(vnode);\n\t\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\t\t`In ${componentName} you are calling useMemo/useCallback without passing arguments.\\n` +\n\t\t\t\t\t\t\t\t`This is a noop since it will not be able to memoize, it will execute it every render.` +\n\t\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t\t);\n\t\t\t\t\t}\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\tif (oldDiffed) oldDiffed(vnode);\n\n\t\tif (vnode._children != null) {\n\t\t\tconst keys = [];\n\t\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\t\tconst child = vnode._children[i];\n\t\t\t\tif (!child || child.key == null) continue;\n\n\t\t\t\tconst key = child.key;\n\t\t\t\tif (keys.indexOf(key) !== -1) {\n\t\t\t\t\tconsole.error(\n\t\t\t\t\t\t'Following component has two or more children with the ' +\n\t\t\t\t\t\t\t`same key attribute: \"${key}\". This may cause glitches and misbehavior ` +\n\t\t\t\t\t\t\t'in rendering process. Component: \\n\\n' +\n\t\t\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\n\t\t\t\t\t// Break early to not spam the console\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\n\t\t\t\tkeys.push(key);\n\t\t\t}\n\t\t}\n\t};\n}\n\nconst setState = Component.prototype.setState;\nComponent.prototype.setState = function(update, callback) {\n\tif (this._vnode == null) {\n\t\t// `this._vnode` will be `null` during componentWillMount. But it\n\t\t// is perfectly valid to call `setState` during cWM. So we\n\t\t// need an additional check to verify that we are dealing with a\n\t\t// call inside constructor.\n\t\tif (this.state == null) {\n\t\t\tconsole.warn(\n\t\t\t\t`Calling \"this.setState\" inside the constructor of a component is a ` +\n\t\t\t\t\t`no-op and might be a bug in your application. Instead, set ` +\n\t\t\t\t\t`\"this.state = {}\" directly.\\n\\n${getOwnerStack(getCurrentVNode())}`\n\t\t\t);\n\t\t}\n\t} else if (this._parentDom == null) {\n\t\tconsole.warn(\n\t\t\t`Can't call \"this.setState\" on an unmounted component. This is a no-op, ` +\n\t\t\t\t`but it indicates a memory leak in your application. To fix, cancel all ` +\n\t\t\t\t`subscriptions and asynchronous tasks in the componentWillUnmount method.` +\n\t\t\t\t`\\n\\n${getOwnerStack(this._vnode)}`\n\t\t);\n\t}\n\n\treturn setState.call(this, update, callback);\n};\n\nconst forceUpdate = Component.prototype.forceUpdate;\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode == null) {\n\t\tconsole.warn(\n\t\t\t`Calling \"this.forceUpdate\" inside the constructor of a component is a ` +\n\t\t\t\t`no-op and might be a bug in your application.\\n\\n${getOwnerStack(\n\t\t\t\t\tgetCurrentVNode()\n\t\t\t\t)}`\n\t\t);\n\t} else if (this._parentDom == null) {\n\t\tconsole.warn(\n\t\t\t`Can't call \"this.forceUpdate\" on an unmounted component. This is a no-op, ` +\n\t\t\t\t`but it indicates a memory leak in your application. To fix, cancel all ` +\n\t\t\t\t`subscriptions and asynchronous tasks in the componentWillUnmount method.` +\n\t\t\t\t`\\n\\n${getOwnerStack(this._vnode)}`\n\t\t);\n\t}\n\treturn forceUpdate.call(this, callback);\n};\n\n/**\n * Serialize a vnode tree to a string\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function serializeVNode(vnode) {\n\tlet { props } = vnode;\n\tlet name = getDisplayName(vnode);\n\n\tlet attrs = '';\n\tfor (let prop in props) {\n\t\tif (props.hasOwnProperty(prop) && prop !== 'children') {\n\t\t\tlet value = props[prop];\n\n\t\t\t// If it is an object but doesn't have toString(), use Object.toString\n\t\t\tif (typeof value == 'function') {\n\t\t\t\tvalue = `function ${value.displayName || value.name}() {}`;\n\t\t\t}\n\n\t\t\tvalue =\n\t\t\t\tObject(value) === value && !value.toString\n\t\t\t\t\t? Object.prototype.toString.call(value)\n\t\t\t\t\t: value + '';\n\n\t\t\tattrs += ` ${prop}=${JSON.stringify(value)}`;\n\t\t}\n\t}\n\n\tlet children = props.children;\n\treturn `<${name}${attrs}${\n\t\tchildren && children.length ? '>..' : ' />'\n\t}`;\n}\n","import { options, Fragment } from 'preact';\n\nexport function initDevTools() {\n\tif (typeof window != 'undefined' && window.__PREACT_DEVTOOLS__) {\n\t\twindow.__PREACT_DEVTOOLS__.attachPreact('10.0.5', options, {\n\t\t\tFragment\n\t\t});\n\t}\n}\n","const ReactPropTypesSecret = 'SECRET_DO_NOT_PASS_THIS_OR_YOU_WILL_BE_FIRED';\n\nlet loggedTypeFailures = {};\n\n/**\n * Reset the history of which prop type warnings have been logged.\n */\nexport function resetPropWarnings() {\n\tloggedTypeFailures = {};\n}\n\n/**\n * Assert that the values match with the type specs.\n * Error messages are memorized and will only be shown once.\n *\n * Adapted from https://github.com/facebook/prop-types/blob/master/checkPropTypes.js\n *\n * @param {object} typeSpecs Map of name to a ReactPropType\n * @param {object} values Runtime values that need to be type-checked\n * @param {string} location e.g. \"prop\", \"context\", \"child context\"\n * @param {string} componentName Name of the component for error messages.\n * @param {?Function} getStack Returns the component stack.\n */\nexport function checkPropTypes(\n\ttypeSpecs,\n\tvalues,\n\tlocation,\n\tcomponentName,\n\tgetStack\n) {\n\tObject.keys(typeSpecs).forEach(typeSpecName => {\n\t\tlet error;\n\t\ttry {\n\t\t\terror = typeSpecs[typeSpecName](\n\t\t\t\tvalues,\n\t\t\t\ttypeSpecName,\n\t\t\t\tcomponentName,\n\t\t\t\tlocation,\n\t\t\t\tnull,\n\t\t\t\tReactPropTypesSecret\n\t\t\t);\n\t\t} catch (e) {\n\t\t\terror = e;\n\t\t}\n\t\tif (error && !(error.message in loggedTypeFailures)) {\n\t\t\tloggedTypeFailures[error.message] = true;\n\t\t\tconsole.error(\n\t\t\t\t`Failed ${location} type: ${error.message}${(getStack && getStack()) ||\n\t\t\t\t\t''}`\n\t\t\t);\n\t\t}\n\t});\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( 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Appuntiweb di Steffo

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This is a workaround for\n * IE11 which doesn't support `Element.prototype.remove()`. Using this function\n * is smaller than including a dedicated polyfill.\n * @param {Node} node The node to remove\n */\nexport function removeNode(node) {\n\tlet parentNode = node.parentNode;\n\tif (parentNode) parentNode.removeChild(node);\n}\n","import { cloneElement, createElement, Component, toChildArray } from 'preact';\nimport { exec, prepareVNodeForRanking, assign, pathRankSort } from './util';\n\nlet customHistory = null;\n\nconst ROUTERS = [];\n\nconst subscribers = [];\n\nconst EMPTY = {};\n\nfunction setUrl(url, type='push') {\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tlet url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn `${url.pathname || ''}${url.search || ''}`;\n}\n\n\n\nfunction route(url, replace=false) {\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (let i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) return true;\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL. */\nfunction routeTo(url) {\n\tlet didRoute = false;\n\tfor (let i=0; i {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\n\nclass Router extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tshouldComponentUpdate(props) {\n\t\tif (props.static!==true) return true;\n\t\treturn props.url!==this.props.url || props.onChange!==this.props.onChange;\n\t}\n\n\t/** Check if the given URL can be matched against any children */\n\tcanRoute(url) {\n\t\tconst children = toChildArray(this.props.children);\n\t\treturn this.getMatchingChildren(children, url, false).length > 0;\n\t}\n\n\t/** Re-render children with a new URL to match against. */\n\trouteTo(url) {\n\t\tthis.setState({ url });\n\n\t\tconst didRoute = this.canRoute(url);\n\n\t\t// trigger a manual re-route if we're not in the middle of an update:\n\t\tif (!this.updating) this.forceUpdate();\n\n\t\treturn didRoute;\n\t}\n\n\tcomponentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidMount() {\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen((location) => {\n\t\t\t\tthis.routeTo(`${location.pathname || ''}${location.search || ''}`);\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t}\n\n\tcomponentWillUnmount() {\n\t\tif (typeof this.unlisten==='function') this.unlisten();\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t}\n\n\tcomponentWillUpdate() {\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidUpdate() {\n\t\tthis.updating = false;\n\t}\n\n\tgetMatchingChildren(children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( vnode => {\n\t\t\t\tlet matches = exec(url, vnode.props.path, vnode.props);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tlet newProps = { url, matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t}\n\n\trender({ children, onChange }, { url }) {\n\t\tlet active = this.getMatchingChildren(toChildArray(children), url, true);\n\n\t\tlet current = active[0] || null;\n\n\t\tlet previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl,\n\t\t\t\t\tprevious,\n\t\t\t\t\tactive,\n\t\t\t\t\tcurrent\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t}\n}\n\nconst Link = (props) => (\n\tcreateElement('a', assign({ onClick: handleLinkClick }, props))\n);\n\nconst Route = props => createElement(props.component, props);\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\nRouter.exec = exec;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link, exec };\nexport default Router;\n","import options from './options';\n\n/**\n * Create an virtual node (used for JSX)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * constructor for this virtual node\n * @param {object | null | undefined} [props] The properties of the virtual node\n * @param {Array} [children] The children of the virtual node\n * @returns {import('./internal').VNode}\n */\nexport function createElement(type, props, children) {\n\tlet normalizedProps = {},\n\t\ti;\n\tfor (i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\tif (arguments.length > 3) {\n\t\tchildren = [children];\n\t\t// https://github.com/preactjs/preact/issues/1916\n\t\tfor (i = 3; i < arguments.length; i++) {\n\t\t\tchildren.push(arguments[i]);\n\t\t}\n\t}\n\tif (children != null) {\n\t\tnormalizedProps.children = children;\n\t}\n\n\t// If a Component VNode, check for and apply defaultProps\n\t// Note: type may be undefined in development, must never error here.\n\tif (typeof type == 'function' && type.defaultProps != null) {\n\t\tfor (i in type.defaultProps) {\n\t\t\tif (normalizedProps[i] === undefined) {\n\t\t\t\tnormalizedProps[i] = type.defaultProps[i];\n\t\t\t}\n\t\t}\n\t}\n\n\treturn createVNode(\n\t\ttype,\n\t\tnormalizedProps,\n\t\tprops && props.key,\n\t\tprops && props.ref,\n\t\tnull\n\t);\n}\n\n/**\n * Create a VNode (used internally by Preact)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * Constructor for this virtual node\n * @param {object | string | number | null} props The properties of this virtual node.\n * If this virtual node represents a text node, this is the text of the node (string or number).\n * @param {string | number | null} key The key for this virtual node, used when\n * diffing it against its children\n * @param {import('./internal').VNode[\"ref\"]} ref The ref property that will\n * receive a reference to its created child\n * @returns {import('./internal').VNode}\n */\nexport function createVNode(type, props, key, ref, original) {\n\t// V8 seems to be better at detecting type shapes if the object is allocated from the same call site\n\t// Do not inline into createElement and coerceToVNode!\n\tconst vnode = {\n\t\ttype,\n\t\tprops,\n\t\tkey,\n\t\tref,\n\t\t_children: null,\n\t\t_parent: null,\n\t\t_depth: 0,\n\t\t_dom: null,\n\t\t// _nextDom must be initialized to undefined b/c it will eventually\n\t\t// be set to dom.nextSibling which can return `null` and it is important\n\t\t// to be able to distinguish between an uninitialized _nextDom and\n\t\t// a _nextDom that has been set to `null`\n\t\t_nextDom: undefined,\n\t\t_component: null,\n\t\tconstructor: undefined,\n\t\t_original: original\n\t};\n\n\tif (original == null) vnode._original = vnode;\n\tif (options.vnode) options.vnode(vnode);\n\n\treturn vnode;\n}\n\nexport function createRef() {\n\treturn {};\n}\n\nexport function Fragment(props) {\n\treturn props.children;\n}\n\n/**\n * Check if a the argument is a valid Preact VNode.\n * @param {*} vnode\n * @returns {vnode is import('./internal').VNode}\n */\nexport const isValidElement = vnode =>\n\tvnode != null && vnode.constructor === undefined;\n","import { assign } from './util';\nimport { diff, commitRoot } from './diff/index';\nimport options from './options';\nimport { Fragment } from './create-element';\n\n/**\n * Base Component class. Provides `setState()` and `forceUpdate()`, which\n * trigger rendering\n * @param {object} props The initial component props\n * @param {object} context The initial context from parent components'\n * getChildContext\n */\nexport function Component(props, context) {\n\tthis.props = props;\n\tthis.context = context;\n}\n\n/**\n * Update component state and schedule a re-render.\n * @param {object | ((s: object, p: object) => object)} update A hash of state\n * properties to update with new values or a function that given the current\n * state and props returns a new partial state\n * @param {() => void} [callback] A function to be called once component state is\n * updated\n */\nComponent.prototype.setState = function(update, callback) {\n\t// only clone state when copying to nextState the first time.\n\tlet s;\n\tif (this._nextState !== this.state) {\n\t\ts = this._nextState;\n\t} else {\n\t\ts = this._nextState = assign({}, this.state);\n\t}\n\n\tif (typeof update == 'function') {\n\t\tupdate = update(s, this.props);\n\t}\n\n\tif (update) {\n\t\tassign(s, update);\n\t}\n\n\t// Skip update if updater function returned null\n\tif (update == null) return;\n\n\tif (this._vnode) {\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Immediately perform a synchronous re-render of the component\n * @param {() => void} [callback] A function to be called after component is\n * re-rendered\n */\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode) {\n\t\t// Set render mode so that we can differentiate where the render request\n\t\t// is coming from. We need this because forceUpdate should never call\n\t\t// shouldComponentUpdate\n\t\tthis._force = true;\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Accepts `props` and `state`, and returns a new Virtual DOM tree to build.\n * Virtual DOM is generally constructed via [JSX](http://jasonformat.com/wtf-is-jsx).\n * @param {object} props Props (eg: JSX attributes) received from parent\n * element/component\n * @param {object} state The component's current state\n * @param {object} context Context object, as returned by the nearest\n * ancestor's `getChildContext()`\n * @returns {import('./index').ComponentChildren | void}\n */\nComponent.prototype.render = Fragment;\n\n/**\n * @param {import('./internal').VNode} vnode\n * @param {number | null} [childIndex]\n */\nexport function getDomSibling(vnode, childIndex) {\n\tif (childIndex == null) {\n\t\t// Use childIndex==null as a signal to resume the search from the vnode's sibling\n\t\treturn vnode._parent\n\t\t\t? getDomSibling(vnode._parent, vnode._parent._children.indexOf(vnode) + 1)\n\t\t\t: null;\n\t}\n\n\tlet sibling;\n\tfor (; childIndex < vnode._children.length; childIndex++) {\n\t\tsibling = vnode._children[childIndex];\n\n\t\tif (sibling != null && sibling._dom != null) {\n\t\t\t// Since updateParentDomPointers keeps _dom pointer correct,\n\t\t\t// we can rely on _dom to tell us if this subtree contains a\n\t\t\t// rendered DOM node, and what the first rendered DOM node is\n\t\t\treturn sibling._dom;\n\t\t}\n\t}\n\n\t// If we get here, we have not found a DOM node in this vnode's children.\n\t// We must resume from this vnode's sibling (in it's parent _children array)\n\t// Only climb up and search the parent if we aren't searching through a DOM\n\t// VNode (meaning we reached the DOM parent of the original vnode that began\n\t// the search)\n\treturn typeof vnode.type == 'function' ? getDomSibling(vnode) : null;\n}\n\n/**\n * Trigger in-place re-rendering of a component.\n * @param {import('./internal').Component} component The component to rerender\n */\nfunction renderComponent(component) {\n\tlet vnode = component._vnode,\n\t\toldDom = vnode._dom,\n\t\tparentDom = component._parentDom;\n\n\tif (parentDom) {\n\t\tlet commitQueue = [];\n\t\tconst oldVNode = assign({}, vnode);\n\t\toldVNode._original = oldVNode;\n\n\t\tlet newDom = diff(\n\t\t\tparentDom,\n\t\t\tvnode,\n\t\t\toldVNode,\n\t\t\tcomponent._globalContext,\n\t\t\tparentDom.ownerSVGElement !== undefined,\n\t\t\tnull,\n\t\t\tcommitQueue,\n\t\t\toldDom == null ? getDomSibling(vnode) : oldDom\n\t\t);\n\t\tcommitRoot(commitQueue, vnode);\n\n\t\tif (newDom != oldDom) {\n\t\t\tupdateParentDomPointers(vnode);\n\t\t}\n\t}\n}\n\n/**\n * @param {import('./internal').VNode} vnode\n */\nfunction updateParentDomPointers(vnode) {\n\tif ((vnode = vnode._parent) != null && vnode._component != null) {\n\t\tvnode._dom = vnode._component.base = null;\n\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\tlet child = vnode._children[i];\n\t\t\tif (child != null && child._dom != null) {\n\t\t\t\tvnode._dom = vnode._component.base = child._dom;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\treturn updateParentDomPointers(vnode);\n\t}\n}\n\n/**\n * The render queue\n * @type {Array}\n */\nlet rerenderQueue = [];\nlet rerenderCount = 0;\n\n/**\n * Asynchronously schedule a callback\n * @type {(cb: () => void) => void}\n */\n/* istanbul ignore next */\n// Note the following line isn't tree-shaken by rollup cuz of rollup/rollup#2566\nconst defer =\n\ttypeof Promise == 'function'\n\t\t? Promise.prototype.then.bind(Promise.resolve())\n\t\t: setTimeout;\n\n/*\n * The value of `Component.debounce` must asynchronously invoke the passed in callback. It is\n * important that contributors to Preact can consistently reason about what calls to `setState`, etc.\n * do, and when their effects will be applied. See the links below for some further reading on designing\n * asynchronous APIs.\n * * [Designing APIs for Asynchrony](https://blog.izs.me/2013/08/designing-apis-for-asynchrony)\n * * [Callbacks synchronous and asynchronous](https://blog.ometer.com/2011/07/24/callbacks-synchronous-and-asynchronous/)\n */\n\nlet prevDebounce;\n\n/**\n * Enqueue a rerender of a component\n * @param {import('./internal').Component} c The component to rerender\n */\nexport function enqueueRender(c) {\n\tif (\n\t\t(!c._dirty &&\n\t\t\t(c._dirty = true) &&\n\t\t\trerenderQueue.push(c) &&\n\t\t\t!rerenderCount++) ||\n\t\tprevDebounce !== options.debounceRendering\n\t) {\n\t\tprevDebounce = options.debounceRendering;\n\t\t(prevDebounce || defer)(process);\n\t}\n}\n\n/** Flush the render queue by rerendering all queued components */\nfunction process() {\n\tlet queue;\n\twhile ((rerenderCount = rerenderQueue.length)) {\n\t\tqueue = rerenderQueue.sort((a, b) => a._vnode._depth - b._vnode._depth);\n\t\trerenderQueue = [];\n\t\t// Don't update `renderCount` yet. Keep its value non-zero to prevent unnecessary\n\t\t// process() calls from getting scheduled while `queue` is still being consumed.\n\t\tqueue.some(c => {\n\t\t\tif (c._dirty) renderComponent(c);\n\t\t});\n\t}\n}\n","import { diff, unmount, applyRef } from './index';\nimport { createVNode } from '../create-element';\nimport { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { removeNode } from '../util';\nimport { getDomSibling } from '../component';\n\n/**\n * Diff the children of a virtual node\n * @param {import('../internal').PreactElement} parentDom The DOM element whose\n * children are being diffed\n * @param {import('../internal').VNode} newParentVNode The new virtual\n * node whose children should be diff'ed against oldParentVNode\n * @param {import('../internal').VNode} oldParentVNode The old virtual\n * node whose children should be diff'ed against newParentVNode\n * @param {object} globalContext The current context object - modified by getChildContext\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Node | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} isHydrating Whether or not we are in hydration\n */\nexport function diffChildren(\n\tparentDom,\n\tnewParentVNode,\n\toldParentVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet i, j, oldVNode, newDom, sibDom, firstChildDom, refs;\n\n\t// This is a compression of oldParentVNode!=null && oldParentVNode != EMPTY_OBJ && oldParentVNode._children || EMPTY_ARR\n\t// as EMPTY_OBJ._children should be `undefined`.\n\tlet oldChildren = (oldParentVNode && oldParentVNode._children) || EMPTY_ARR;\n\n\tlet oldChildrenLength = oldChildren.length;\n\n\t// Only in very specific places should this logic be invoked (top level `render` and `diffElementNodes`).\n\t// I'm using `EMPTY_OBJ` to signal when `diffChildren` is invoked in these situations. I can't use `null`\n\t// for this purpose, because `null` is a valid value for `oldDom` which can mean to skip to this logic\n\t// (e.g. if mounting a new tree in which the old DOM should be ignored (usually for Fragments).\n\tif (oldDom == EMPTY_OBJ) {\n\t\tif (excessDomChildren != null) {\n\t\t\toldDom = excessDomChildren[0];\n\t\t} else if (oldChildrenLength) {\n\t\t\toldDom = getDomSibling(oldParentVNode, 0);\n\t\t} else {\n\t\t\toldDom = null;\n\t\t}\n\t}\n\n\ti = 0;\n\tnewParentVNode._children = toChildArray(\n\t\tnewParentVNode._children,\n\t\tchildVNode => {\n\t\t\tif (childVNode != null) {\n\t\t\t\tchildVNode._parent = newParentVNode;\n\t\t\t\tchildVNode._depth = newParentVNode._depth + 1;\n\n\t\t\t\t// Check if we find a corresponding element in oldChildren.\n\t\t\t\t// If found, delete the array item by setting to `undefined`.\n\t\t\t\t// We use `undefined`, as `null` is reserved for empty placeholders\n\t\t\t\t// (holes).\n\t\t\t\toldVNode = oldChildren[i];\n\n\t\t\t\tif (\n\t\t\t\t\toldVNode === null ||\n\t\t\t\t\t(oldVNode &&\n\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\tchildVNode.type === oldVNode.type)\n\t\t\t\t) {\n\t\t\t\t\toldChildren[i] = undefined;\n\t\t\t\t} else {\n\t\t\t\t\t// Either oldVNode === undefined or oldChildrenLength > 0,\n\t\t\t\t\t// so after this loop oldVNode == null or oldVNode is a valid value.\n\t\t\t\t\tfor (j = 0; j < oldChildrenLength; j++) {\n\t\t\t\t\t\toldVNode = oldChildren[j];\n\t\t\t\t\t\t// If childVNode is unkeyed, we only match similarly unkeyed nodes, otherwise we match by key.\n\t\t\t\t\t\t// We always match by type (in either case).\n\t\t\t\t\t\tif (\n\t\t\t\t\t\t\toldVNode &&\n\t\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\t\tchildVNode.type === oldVNode.type\n\t\t\t\t\t\t) {\n\t\t\t\t\t\t\toldChildren[j] = undefined;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t\toldVNode = null;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\toldVNode = oldVNode || EMPTY_OBJ;\n\n\t\t\t\t// Morph the old element into the new one, but don't append it to the dom yet\n\t\t\t\tnewDom = diff(\n\t\t\t\t\tparentDom,\n\t\t\t\t\tchildVNode,\n\t\t\t\t\toldVNode,\n\t\t\t\t\tglobalContext,\n\t\t\t\t\tisSvg,\n\t\t\t\t\texcessDomChildren,\n\t\t\t\t\tcommitQueue,\n\t\t\t\t\toldDom,\n\t\t\t\t\tisHydrating\n\t\t\t\t);\n\n\t\t\t\tif ((j = childVNode.ref) && oldVNode.ref != j) {\n\t\t\t\t\tif (!refs) refs = [];\n\t\t\t\t\tif (oldVNode.ref) refs.push(oldVNode.ref, null, childVNode);\n\t\t\t\t\trefs.push(j, childVNode._component || newDom, childVNode);\n\t\t\t\t}\n\n\t\t\t\t// Only proceed if the vnode has not been unmounted by `diff()` above.\n\t\t\t\tif (newDom != null) {\n\t\t\t\t\tif (firstChildDom == null) {\n\t\t\t\t\t\tfirstChildDom = newDom;\n\t\t\t\t\t}\n\n\t\t\t\t\tlet nextDom;\n\t\t\t\t\tif (childVNode._nextDom !== undefined) {\n\t\t\t\t\t\t// Only Fragments or components that return Fragment like VNodes will\n\t\t\t\t\t\t// have a non-undefined _nextDom. Continue the diff from the sibling\n\t\t\t\t\t\t// of last DOM child of this child VNode\n\t\t\t\t\t\tnextDom = childVNode._nextDom;\n\n\t\t\t\t\t\t// Eagerly cleanup _nextDom. We don't need to persist the value because\n\t\t\t\t\t\t// it is only used by `diffChildren` to determine where to resume the diff after\n\t\t\t\t\t\t// diffing Components and Fragments. Once we store it the nextDOM local var, we\n\t\t\t\t\t\t// can clean up the property\n\t\t\t\t\t\tchildVNode._nextDom = undefined;\n\t\t\t\t\t} else if (\n\t\t\t\t\t\texcessDomChildren == oldVNode ||\n\t\t\t\t\t\tnewDom != oldDom ||\n\t\t\t\t\t\tnewDom.parentNode == null\n\t\t\t\t\t) {\n\t\t\t\t\t\t// NOTE: excessDomChildren==oldVNode above:\n\t\t\t\t\t\t// This is a compression of excessDomChildren==null && oldVNode==null!\n\t\t\t\t\t\t// The values only have the same type when `null`.\n\n\t\t\t\t\t\touter: if (oldDom == null || oldDom.parentNode !== parentDom) {\n\t\t\t\t\t\t\tparentDom.appendChild(newDom);\n\t\t\t\t\t\t\tnextDom = null;\n\t\t\t\t\t\t} else {\n\t\t\t\t\t\t\t// `j import('../internal').VNode} [callback]\n * A function to invoke for each child before it is added to the flattened list.\n * @param {Array} [flattened] An flat array of children to modify\n * @returns {import('../internal').VNode[]}\n */\nexport function toChildArray(children, callback, flattened) {\n\tif (flattened == null) flattened = [];\n\n\tif (children == null || typeof children == 'boolean') {\n\t\tif (callback) flattened.push(callback(null));\n\t} else if (Array.isArray(children)) {\n\t\tfor (let i = 0; i < children.length; i++) {\n\t\t\ttoChildArray(children[i], callback, flattened);\n\t\t}\n\t} else if (!callback) {\n\t\tflattened.push(children);\n\t} else if (typeof children == 'string' || typeof children == 'number') {\n\t\tflattened.push(callback(createVNode(null, children, null, null, children)));\n\t} else if (children._dom != null || children._component != null) {\n\t\tflattened.push(\n\t\t\tcallback(\n\t\t\t\tcreateVNode(\n\t\t\t\t\tchildren.type,\n\t\t\t\t\tchildren.props,\n\t\t\t\t\tchildren.key,\n\t\t\t\t\tnull,\n\t\t\t\t\tchildren._original\n\t\t\t\t)\n\t\t\t)\n\t\t);\n\t} else {\n\t\tflattened.push(callback(children));\n\t}\n\n\treturn flattened;\n}\n","import { IS_NON_DIMENSIONAL } from '../constants';\nimport options from '../options';\n\n/**\n * Diff the old and new properties of a VNode and apply changes to the DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to apply\n * changes to\n * @param {object} newProps The new props\n * @param {object} oldProps The old props\n * @param {boolean} isSvg Whether or not this node is an SVG node\n * @param {boolean} hydrate Whether or not we are in hydration mode\n */\nexport function diffProps(dom, newProps, oldProps, isSvg, hydrate) {\n\tlet i;\n\n\tfor (i in oldProps) {\n\t\tif (i !== 'children' && i !== 'key' && !(i in newProps)) {\n\t\t\tsetProperty(dom, i, null, oldProps[i], isSvg);\n\t\t}\n\t}\n\n\tfor (i in newProps) {\n\t\tif (\n\t\t\t(!hydrate || typeof newProps[i] == 'function') &&\n\t\t\ti !== 'children' &&\n\t\t\ti !== 'key' &&\n\t\t\ti !== 'value' &&\n\t\t\ti !== 'checked' &&\n\t\t\toldProps[i] !== newProps[i]\n\t\t) {\n\t\t\tsetProperty(dom, i, newProps[i], oldProps[i], isSvg);\n\t\t}\n\t}\n}\n\nfunction setStyle(style, key, value) {\n\tif (key[0] === '-') {\n\t\tstyle.setProperty(key, value);\n\t} else if (\n\t\ttypeof value == 'number' &&\n\t\tIS_NON_DIMENSIONAL.test(key) === false\n\t) {\n\t\tstyle[key] = value + 'px';\n\t} else if (value == null) {\n\t\tstyle[key] = '';\n\t} else {\n\t\tstyle[key] = value;\n\t}\n}\n\n/**\n * Set a property value on a DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to modify\n * @param {string} name The name of the property to set\n * @param {*} value The value to set the property to\n * @param {*} oldValue The old value the property had\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node or not\n */\nfunction setProperty(dom, name, value, oldValue, isSvg) {\n\tlet s, useCapture, nameLower;\n\n\tif (isSvg) {\n\t\tif (name === 'className') {\n\t\t\tname = 'class';\n\t\t}\n\t} else if (name === 'class') {\n\t\tname = 'className';\n\t}\n\n\tif (name === 'style') {\n\t\ts = dom.style;\n\n\t\tif (typeof value == 'string') {\n\t\t\ts.cssText = value;\n\t\t} else {\n\t\t\tif (typeof oldValue == 'string') {\n\t\t\t\ts.cssText = '';\n\t\t\t\toldValue = null;\n\t\t\t}\n\n\t\t\tif (oldValue) {\n\t\t\t\tfor (let i in oldValue) {\n\t\t\t\t\tif (!(value && i in value)) {\n\t\t\t\t\t\tsetStyle(s, i, '');\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (value) {\n\t\t\t\tfor (let i in value) {\n\t\t\t\t\tif (!oldValue || value[i] !== oldValue[i]) {\n\t\t\t\t\t\tsetStyle(s, i, value[i]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\t// Benchmark for comparison: https://esbench.com/bench/574c954bdb965b9a00965ac6\n\telse if (name[0] === 'o' && name[1] === 'n') {\n\t\tuseCapture = name !== (name = name.replace(/Capture$/, ''));\n\t\tnameLower = name.toLowerCase();\n\t\tname = (nameLower in dom ? nameLower : name).slice(2);\n\n\t\tif (value) {\n\t\t\tif (!oldValue) dom.addEventListener(name, eventProxy, useCapture);\n\t\t\t(dom._listeners || (dom._listeners = {}))[name] = value;\n\t\t} else {\n\t\t\tdom.removeEventListener(name, eventProxy, useCapture);\n\t\t}\n\t} else if (\n\t\tname !== 'list' &&\n\t\tname !== 'tagName' &&\n\t\t// HTMLButtonElement.form and HTMLInputElement.form are read-only but can be set using\n\t\t// setAttribute\n\t\tname !== 'form' &&\n\t\tname !== 'type' &&\n\t\tname !== 'size' &&\n\t\t!isSvg &&\n\t\tname in dom\n\t) {\n\t\tdom[name] = value == null ? '' : value;\n\t} else if (typeof value != 'function' && name !== 'dangerouslySetInnerHTML') {\n\t\tif (name !== (name = name.replace(/^xlink:?/, ''))) {\n\t\t\tif (value == null || value === false) {\n\t\t\t\tdom.removeAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase()\n\t\t\t\t);\n\t\t\t} else {\n\t\t\t\tdom.setAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase(),\n\t\t\t\t\tvalue\n\t\t\t\t);\n\t\t\t}\n\t\t} else if (\n\t\t\tvalue == null ||\n\t\t\t(value === false &&\n\t\t\t\t// ARIA-attributes have a different notion of boolean values.\n\t\t\t\t// The value `false` is different from the attribute not\n\t\t\t\t// existing on the DOM, so we can't remove it. For non-boolean\n\t\t\t\t// ARIA-attributes we could treat false as a removal, but the\n\t\t\t\t// amount of exceptions would cost us too many bytes. On top of\n\t\t\t\t// that other VDOM frameworks also always stringify `false`.\n\t\t\t\t!/^ar/.test(name))\n\t\t) {\n\t\t\tdom.removeAttribute(name);\n\t\t} else {\n\t\t\tdom.setAttribute(name, value);\n\t\t}\n\t}\n}\n\n/**\n * Proxy an event to hooked event handlers\n * @param {Event} e The event object from the browser\n * @private\n */\nfunction eventProxy(e) {\n\tthis._listeners[e.type](options.event ? options.event(e) : e);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { Component } from '../component';\nimport { Fragment } from '../create-element';\nimport { diffChildren } from './children';\nimport { diffProps } from './props';\nimport { assign, removeNode } from '../util';\nimport options from '../options';\n\n/**\n * Diff two virtual nodes and apply proper changes to the DOM\n * @param {import('../internal').PreactElement} parentDom The parent of the DOM element\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object. Modified by getChildContext\n * @param {boolean} isSvg Whether or not this element is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Element | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} [isHydrating] Whether or not we are in hydration\n */\nexport function diff(\n\tparentDom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet tmp,\n\t\tnewType = newVNode.type;\n\n\t// When passing through createElement it assigns the object\n\t// constructor as undefined. This to prevent JSON-injection.\n\tif (newVNode.constructor !== undefined) return null;\n\n\tif ((tmp = options._diff)) tmp(newVNode);\n\n\ttry {\n\t\touter: if (typeof newType == 'function') {\n\t\t\tlet c, isNew, oldProps, oldState, snapshot, clearProcessingException;\n\t\t\tlet newProps = newVNode.props;\n\n\t\t\t// Necessary for createContext api. Setting this property will pass\n\t\t\t// the context value as `this.context` just for this component.\n\t\t\ttmp = newType.contextType;\n\t\t\tlet provider = tmp && globalContext[tmp._id];\n\t\t\tlet componentContext = tmp\n\t\t\t\t? provider\n\t\t\t\t\t? provider.props.value\n\t\t\t\t\t: tmp._defaultValue\n\t\t\t\t: globalContext;\n\n\t\t\t// Get component and set it to `c`\n\t\t\tif (oldVNode._component) {\n\t\t\t\tc = newVNode._component = oldVNode._component;\n\t\t\t\tclearProcessingException = c._processingException = c._pendingError;\n\t\t\t} else {\n\t\t\t\t// Instantiate the new component\n\t\t\t\tif ('prototype' in newType && newType.prototype.render) {\n\t\t\t\t\tnewVNode._component = c = new newType(newProps, componentContext); // eslint-disable-line new-cap\n\t\t\t\t} else {\n\t\t\t\t\tnewVNode._component = c = new Component(newProps, componentContext);\n\t\t\t\t\tc.constructor = newType;\n\t\t\t\t\tc.render = doRender;\n\t\t\t\t}\n\t\t\t\tif (provider) provider.sub(c);\n\n\t\t\t\tc.props = newProps;\n\t\t\t\tif (!c.state) c.state = {};\n\t\t\t\tc.context = componentContext;\n\t\t\t\tc._globalContext = globalContext;\n\t\t\t\tisNew = c._dirty = true;\n\t\t\t\tc._renderCallbacks = [];\n\t\t\t}\n\n\t\t\t// Invoke getDerivedStateFromProps\n\t\t\tif (c._nextState == null) {\n\t\t\t\tc._nextState = c.state;\n\t\t\t}\n\t\t\tif (newType.getDerivedStateFromProps != null) {\n\t\t\t\tif (c._nextState == c.state) {\n\t\t\t\t\tc._nextState = assign({}, c._nextState);\n\t\t\t\t}\n\n\t\t\t\tassign(\n\t\t\t\t\tc._nextState,\n\t\t\t\t\tnewType.getDerivedStateFromProps(newProps, c._nextState)\n\t\t\t\t);\n\t\t\t}\n\n\t\t\toldProps = c.props;\n\t\t\toldState = c.state;\n\n\t\t\t// Invoke pre-render lifecycle methods\n\t\t\tif (isNew) {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tc.componentWillMount != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillMount();\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidMount != null) {\n\t\t\t\t\tc._renderCallbacks.push(c.componentDidMount);\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tnewProps !== oldProps &&\n\t\t\t\t\tc.componentWillReceiveProps != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillReceiveProps(newProps, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (\n\t\t\t\t\t(!c._force &&\n\t\t\t\t\t\tc.shouldComponentUpdate != null &&\n\t\t\t\t\t\tc.shouldComponentUpdate(\n\t\t\t\t\t\t\tnewProps,\n\t\t\t\t\t\t\tc._nextState,\n\t\t\t\t\t\t\tcomponentContext\n\t\t\t\t\t\t) === false) ||\n\t\t\t\t\t(newVNode._original === oldVNode._original && !c._processingException)\n\t\t\t\t) {\n\t\t\t\t\tc.props = newProps;\n\t\t\t\t\tc.state = c._nextState;\n\t\t\t\t\t// More info about this here: https://gist.github.com/JoviDeCroock/bec5f2ce93544d2e6070ef8e0036e4e8\n\t\t\t\t\tif (newVNode._original !== oldVNode._original) c._dirty = false;\n\t\t\t\t\tc._vnode = newVNode;\n\t\t\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t\t\t\tnewVNode._children = oldVNode._children;\n\t\t\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\t\t\tcommitQueue.push(c);\n\t\t\t\t\t}\n\n\t\t\t\t\tfor (tmp = 0; tmp < newVNode._children.length; tmp++) {\n\t\t\t\t\t\tif (newVNode._children[tmp]) {\n\t\t\t\t\t\t\tnewVNode._children[tmp]._parent = newVNode;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\n\t\t\t\t\tbreak outer;\n\t\t\t\t}\n\n\t\t\t\tif (c.componentWillUpdate != null) {\n\t\t\t\t\tc.componentWillUpdate(newProps, c._nextState, componentContext);\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidUpdate != null) {\n\t\t\t\t\tc._renderCallbacks.push(() => {\n\t\t\t\t\t\tc.componentDidUpdate(oldProps, oldState, snapshot);\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tc.context = componentContext;\n\t\t\tc.props = newProps;\n\t\t\tc.state = c._nextState;\n\n\t\t\tif ((tmp = options._render)) tmp(newVNode);\n\n\t\t\tc._dirty = false;\n\t\t\tc._vnode = newVNode;\n\t\t\tc._parentDom = parentDom;\n\n\t\t\ttmp = c.render(c.props, c.state, c.context);\n\t\t\tlet isTopLevelFragment =\n\t\t\t\ttmp != null && tmp.type == Fragment && tmp.key == null;\n\t\t\tnewVNode._children = isTopLevelFragment\n\t\t\t\t? tmp.props.children\n\t\t\t\t: Array.isArray(tmp)\n\t\t\t\t? tmp\n\t\t\t\t: [tmp];\n\n\t\t\tif (c.getChildContext != null) {\n\t\t\t\tglobalContext = assign(assign({}, globalContext), c.getChildContext());\n\t\t\t}\n\n\t\t\tif (!isNew && c.getSnapshotBeforeUpdate != null) {\n\t\t\t\tsnapshot = c.getSnapshotBeforeUpdate(oldProps, oldState);\n\t\t\t}\n\n\t\t\tdiffChildren(\n\t\t\t\tparentDom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\toldDom,\n\t\t\t\tisHydrating\n\t\t\t);\n\n\t\t\tc.base = newVNode._dom;\n\n\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\tcommitQueue.push(c);\n\t\t\t}\n\n\t\t\tif (clearProcessingException) {\n\t\t\t\tc._pendingError = c._processingException = null;\n\t\t\t}\n\n\t\t\tc._force = false;\n\t\t} else if (\n\t\t\texcessDomChildren == null &&\n\t\t\tnewVNode._original === oldVNode._original\n\t\t) {\n\t\t\tnewVNode._children = oldVNode._children;\n\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t} else {\n\t\t\tnewVNode._dom = diffElementNodes(\n\t\t\t\toldVNode._dom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\tif ((tmp = options.diffed)) tmp(newVNode);\n\t} catch (e) {\n\t\tnewVNode._original = null;\n\t\toptions._catchError(e, newVNode, oldVNode);\n\t}\n\n\treturn newVNode._dom;\n}\n\n/**\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {import('../internal').VNode} root\n */\nexport function commitRoot(commitQueue, root) {\n\tif (options._commit) options._commit(root, commitQueue);\n\n\tcommitQueue.some(c => {\n\t\ttry {\n\t\t\tcommitQueue = c._renderCallbacks;\n\t\t\tc._renderCallbacks = [];\n\t\t\tcommitQueue.some(cb => {\n\t\t\t\tcb.call(c);\n\t\t\t});\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t});\n}\n\n/**\n * Diff two virtual nodes representing DOM element\n * @param {import('../internal').PreactElement} dom The DOM element representing\n * the virtual nodes being diffed\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} globalContext The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {*} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {boolean} isHydrating Whether or not we are in hydration\n * @returns {import('../internal').PreactElement}\n */\nfunction diffElementNodes(\n\tdom,\n\tnewVNode,\n\toldVNode,\n\tglobalContext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\tisHydrating\n) {\n\tlet i;\n\tlet oldProps = oldVNode.props;\n\tlet newProps = newVNode.props;\n\n\t// Tracks entering and exiting SVG namespace when descending through the tree.\n\tisSvg = newVNode.type === 'svg' || isSvg;\n\n\tif (excessDomChildren != null) {\n\t\tfor (i = 0; i < excessDomChildren.length; i++) {\n\t\t\tconst child = excessDomChildren[i];\n\n\t\t\t// if newVNode matches an element in excessDomChildren or the `dom`\n\t\t\t// argument matches an element in excessDomChildren, remove it from\n\t\t\t// excessDomChildren so it isn't later removed in diffChildren\n\t\t\tif (\n\t\t\t\tchild != null &&\n\t\t\t\t((newVNode.type === null\n\t\t\t\t\t? child.nodeType === 3\n\t\t\t\t\t: child.localName === newVNode.type) ||\n\t\t\t\t\tdom == child)\n\t\t\t) {\n\t\t\t\tdom = child;\n\t\t\t\texcessDomChildren[i] = null;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\tif (dom == null) {\n\t\tif (newVNode.type === null) {\n\t\t\treturn document.createTextNode(newProps);\n\t\t}\n\n\t\tdom = isSvg\n\t\t\t? document.createElementNS('http://www.w3.org/2000/svg', newVNode.type)\n\t\t\t: document.createElement(\n\t\t\t\t\tnewVNode.type,\n\t\t\t\t\tnewProps.is && { is: newProps.is }\n\t\t\t );\n\t\t// we created a new parent, so none of the previously attached children can be reused:\n\t\texcessDomChildren = null;\n\t\t// we are creating a new node, so we can assume this is a new subtree (in case we are hydrating), this deopts the hydrate\n\t\tisHydrating = false;\n\t}\n\n\tif (newVNode.type === null) {\n\t\tif (oldProps !== newProps && dom.data != newProps) {\n\t\t\tdom.data = newProps;\n\t\t}\n\t} else {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren = EMPTY_ARR.slice.call(dom.childNodes);\n\t\t}\n\n\t\toldProps = oldVNode.props || EMPTY_OBJ;\n\n\t\tlet oldHtml = oldProps.dangerouslySetInnerHTML;\n\t\tlet newHtml = newProps.dangerouslySetInnerHTML;\n\n\t\t// During hydration, props are not diffed at all (including dangerouslySetInnerHTML)\n\t\t// @TODO we should warn in debug mode when props don't match here.\n\t\tif (!isHydrating) {\n\t\t\tif (oldProps === EMPTY_OBJ) {\n\t\t\t\toldProps = {};\n\t\t\t\tfor (let i = 0; i < dom.attributes.length; i++) {\n\t\t\t\t\toldProps[dom.attributes[i].name] = dom.attributes[i].value;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (newHtml || oldHtml) {\n\t\t\t\t// Avoid re-applying the same '__html' if it did not changed between re-render\n\t\t\t\tif (!newHtml || !oldHtml || newHtml.__html != oldHtml.__html) {\n\t\t\t\t\tdom.innerHTML = (newHtml && newHtml.__html) || '';\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tdiffProps(dom, newProps, oldProps, isSvg, isHydrating);\n\n\t\tnewVNode._children = newVNode.props.children;\n\n\t\t// If the new vnode didn't have dangerouslySetInnerHTML, diff its children\n\t\tif (!newHtml) {\n\t\t\tdiffChildren(\n\t\t\t\tdom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tglobalContext,\n\t\t\t\tnewVNode.type === 'foreignObject' ? false : isSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tEMPTY_OBJ,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\t// (as above, don't diff props during hydration)\n\t\tif (!isHydrating) {\n\t\t\tif (\n\t\t\t\t'value' in newProps &&\n\t\t\t\tnewProps.value !== undefined &&\n\t\t\t\tnewProps.value !== dom.value\n\t\t\t) {\n\t\t\t\tdom.value = newProps.value == null ? '' : newProps.value;\n\t\t\t}\n\t\t\tif (\n\t\t\t\t'checked' in newProps &&\n\t\t\t\tnewProps.checked !== undefined &&\n\t\t\t\tnewProps.checked !== dom.checked\n\t\t\t) {\n\t\t\t\tdom.checked = newProps.checked;\n\t\t\t}\n\t\t}\n\t}\n\n\treturn dom;\n}\n\n/**\n * Invoke or update a ref, depending on whether it is a function or object ref.\n * @param {object|function} ref\n * @param {any} value\n * @param {import('../internal').VNode} vnode\n */\nexport function applyRef(ref, value, vnode) {\n\ttry {\n\t\tif (typeof ref == 'function') ref(value);\n\t\telse ref.current = value;\n\t} catch (e) {\n\t\toptions._catchError(e, vnode);\n\t}\n}\n\n/**\n * Unmount a virtual node from the tree and apply DOM changes\n * @param {import('../internal').VNode} vnode The virtual node to unmount\n * @param {import('../internal').VNode} parentVNode The parent of the VNode that\n * initiated the unmount\n * @param {boolean} [skipRemove] Flag that indicates that a parent node of the\n * current element is already detached from the DOM.\n */\nexport function unmount(vnode, parentVNode, skipRemove) {\n\tlet r;\n\tif (options.unmount) options.unmount(vnode);\n\n\tif ((r = vnode.ref)) {\n\t\tif (!r.current || r.current === vnode._dom) applyRef(r, null, parentVNode);\n\t}\n\n\tlet dom;\n\tif (!skipRemove && typeof vnode.type != 'function') {\n\t\tskipRemove = (dom = vnode._dom) != null;\n\t}\n\n\t// Must be set to `undefined` to properly clean up `_nextDom`\n\t// for which `null` is a valid value. See comment in `create-element.js`\n\tvnode._dom = vnode._nextDom = undefined;\n\n\tif ((r = vnode._component) != null) {\n\t\tif (r.componentWillUnmount) {\n\t\t\ttry {\n\t\t\t\tr.componentWillUnmount();\n\t\t\t} catch (e) {\n\t\t\t\toptions._catchError(e, parentVNode);\n\t\t\t}\n\t\t}\n\n\t\tr.base = r._parentDom = null;\n\t}\n\n\tif ((r = vnode._children)) {\n\t\tfor (let i = 0; i < r.length; i++) {\n\t\t\tif (r[i]) unmount(r[i], parentVNode, skipRemove);\n\t\t}\n\t}\n\n\tif (dom != null) removeNode(dom);\n}\n\n/** The `.render()` method for a PFC backing instance. */\nfunction doRender(props, state, context) {\n\treturn this.constructor(props, context);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from './constants';\nimport { commitRoot, diff } from './diff/index';\nimport { createElement, Fragment } from './create-element';\nimport options from './options';\n\nconst IS_HYDRATE = EMPTY_OBJ;\n\n/**\n * Render a Preact virtual node into a DOM element\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * render into\n * @param {Element | Text} [replaceNode] Optional: Attempt to re-use an\n * existing DOM tree rooted at `replaceNode`\n */\nexport function render(vnode, parentDom, replaceNode) {\n\tif (options._root) options._root(vnode, parentDom);\n\n\t// We abuse the `replaceNode` parameter in `hydrate()` to signal if we\n\t// are in hydration mode or not by passing `IS_HYDRATE` instead of a\n\t// DOM element.\n\tlet isHydrating = replaceNode === IS_HYDRATE;\n\n\t// To be able to support calling `render()` multiple times on the same\n\t// DOM node, we need to obtain a reference to the previous tree. We do\n\t// this by assigning a new `_children` property to DOM nodes which points\n\t// to the last rendered tree. By default this property is not present, which\n\t// means that we are mounting a new tree for the first time.\n\tlet oldVNode = isHydrating\n\t\t? null\n\t\t: (replaceNode && replaceNode._children) || parentDom._children;\n\tvnode = createElement(Fragment, null, [vnode]);\n\n\t// List of effects that need to be called after diffing.\n\tlet commitQueue = [];\n\tdiff(\n\t\tparentDom,\n\t\t// Determine the new vnode tree and store it on the DOM element on\n\t\t// our custom `_children` property.\n\t\t((isHydrating ? parentDom : replaceNode || parentDom)._children = vnode),\n\t\toldVNode || EMPTY_OBJ,\n\t\tEMPTY_OBJ,\n\t\tparentDom.ownerSVGElement !== undefined,\n\t\treplaceNode && !isHydrating\n\t\t\t? [replaceNode]\n\t\t\t: oldVNode\n\t\t\t? null\n\t\t\t: EMPTY_ARR.slice.call(parentDom.childNodes),\n\t\tcommitQueue,\n\t\treplaceNode || EMPTY_OBJ,\n\t\tisHydrating\n\t);\n\n\t// Flush all queued effects\n\tcommitRoot(commitQueue, vnode);\n}\n\n/**\n * Update an existing DOM element with data from a Preact virtual node\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * update\n */\nexport function hydrate(vnode, parentDom) {\n\trender(vnode, parentDom, IS_HYDRATE);\n}\n","import { assign } from './util';\nimport { EMPTY_ARR } from './constants';\nimport { createVNode } from './create-element';\n\n/**\n * Clones the given VNode, optionally adding attributes/props and replacing its children.\n * @param {import('./internal').VNode} vnode The virtual DOM element to clone\n * @param {object} props Attributes/props to add when cloning\n * @param {Array} rest Any additional arguments will be used as replacement children.\n * @returns {import('./internal').VNode}\n */\nexport function cloneElement(vnode, props) {\n\tprops = assign(assign({}, vnode.props), props);\n\tif (arguments.length > 2) props.children = EMPTY_ARR.slice.call(arguments, 2);\n\treturn createVNode(\n\t\tvnode.type,\n\t\tprops,\n\t\tprops.key || vnode.key,\n\t\tprops.ref || vnode.ref,\n\t\tnull\n\t);\n}\n","import { enqueueRender } from './component';\n\nexport let i = 0;\n\nexport function createContext(defaultValue) {\n\tconst ctx = {};\n\n\tconst context = {\n\t\t_id: '__cC' + i++,\n\t\t_defaultValue: defaultValue,\n\t\tConsumer(props, context) {\n\t\t\treturn props.children(context);\n\t\t},\n\t\tProvider(props) {\n\t\t\tif (!this.getChildContext) {\n\t\t\t\tconst subs = [];\n\t\t\t\tthis.getChildContext = () => {\n\t\t\t\t\tctx[context._id] = this;\n\t\t\t\t\treturn ctx;\n\t\t\t\t};\n\n\t\t\t\tthis.shouldComponentUpdate = _props => {\n\t\t\t\t\tif (this.props.value !== _props.value) {\n\t\t\t\t\t\tsubs.some(c => {\n\t\t\t\t\t\t\tc.context = _props.value;\n\t\t\t\t\t\t\tenqueueRender(c);\n\t\t\t\t\t\t});\n\t\t\t\t\t}\n\t\t\t\t};\n\n\t\t\t\tthis.sub = c => {\n\t\t\t\t\tsubs.push(c);\n\t\t\t\t\tlet old = c.componentWillUnmount;\n\t\t\t\t\tc.componentWillUnmount = () => {\n\t\t\t\t\t\tsubs.splice(subs.indexOf(c), 1);\n\t\t\t\t\t\told && old.call(c);\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t}\n\n\t\t\treturn props.children;\n\t\t}\n\t};\n\n\tcontext.Consumer.contextType = context;\n\n\treturn context;\n}\n","export const ELEMENT_NODE = 1;\nexport const DOCUMENT_NODE = 9;\nexport const DOCUMENT_FRAGMENT_NODE = 11;\n","import { _catchError } from './diff/catch-error';\n\n/**\n * The `option` object can potentially contain callback functions\n * that are called during various stages of our renderer. This is the\n * foundation on which all our addons like `preact/debug`, `preact/compat`,\n * and `preact/hooks` are based on. See the `Options` type in `internal.d.ts`\n * for a full list of available option hooks (most editors/IDEs allow you to\n * ctrl+click or cmd+click on mac the type definition below).\n * @type {import('./internal').Options}\n */\nconst options = {\n\t_catchError\n};\n\nexport default options;\n","import { enqueueRender } from '../component';\n\n/**\n * Find the closest error boundary to a thrown error and call it\n * @param {object} error The thrown value\n * @param {import('../internal').VNode} vnode The vnode that threw\n * the error that was caught (except for unmounting when this parameter\n * is the highest parent that was being unmounted)\n */\nexport function _catchError(error, vnode) {\n\t/** @type {import('../internal').Component} */\n\tlet component, hasCaught;\n\n\tfor (; (vnode = vnode._parent); ) {\n\t\tif ((component = vnode._component) && !component._processingException) {\n\t\t\ttry {\n\t\t\t\tif (\n\t\t\t\t\tcomponent.constructor &&\n\t\t\t\t\tcomponent.constructor.getDerivedStateFromError != null\n\t\t\t\t) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.setState(\n\t\t\t\t\t\tcomponent.constructor.getDerivedStateFromError(error)\n\t\t\t\t\t);\n\t\t\t\t}\n\n\t\t\t\tif (component.componentDidCatch != null) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.componentDidCatch(error);\n\t\t\t\t}\n\n\t\t\t\tif (hasCaught)\n\t\t\t\t\treturn enqueueRender((component._pendingError = component));\n\t\t\t} catch (e) {\n\t\t\t\terror = e;\n\t\t\t}\n\t\t}\n\t}\n\n\tthrow error;\n}\n","import style from './copyright.css';\nimport { Component } from 'preact';\n\nexport default class Copyright extends Component {\n\trender() {\n\t\treturn
© 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente - Supportami
;\n\t}\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./ottimizzazioneLineare.js\") );\n\t\t\t}, \"route-ottimizzazioneLineare\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/* global __webpack_public_path__ */\n\nimport * as Preact from 'preact';\nconst { h, render, hydrate } = Preact;\n\nconst interopDefault = m => (m && m.default ? m.default : m);\n\nconst normalizeURL = url => (url[url.length - 1] === '/' ? url : url + '/');\n\nif (process.env.NODE_ENV === 'development') {\n\t// enable preact devtools\n\trequire('preact/debug');\n\tif (process.env.RHL) {\n\t\t// enable hot loader\n\t\tconst hotLoader = interopDefault(require('react-hot-loader'));\n\t\thotLoader.preact(interopDefault(require('preact')));\n\t}\n\t// only add a debug sw if webpack service worker is not requested.\n\tif (process.env.ADD_SW === undefined && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(__webpack_public_path__ + 'sw-debug.js');\n\t} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(\n\t\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t\t);\n\t}\n} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t// eslint-disable-next-line no-undef\n\tnavigator.serviceWorker.register(\n\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t);\n}\n\nlet app = interopDefault(require('preact-cli-entrypoint'));\n\nif (typeof app === 'function') {\n\tlet root =\n\t\tdocument.getElementById('preact_root') || document.body.firstElementChild;\n\n\tlet init = () => {\n\t\tlet app = interopDefault(require('preact-cli-entrypoint'));\n\t\tlet preRenderData = {};\n\t\tconst inlineDataElement = document.querySelector(\n\t\t\t'[type=\"__PREACT_CLI_DATA__\"]'\n\t\t);\n\t\tif (inlineDataElement) {\n\t\t\tpreRenderData =\n\t\t\t\tJSON.parse(inlineDataElement.innerHTML).preRenderData || preRenderData;\n\t\t}\n\t\t/* An object named CLI_DATA is passed as a prop,\n\t\t * this keeps us future proof if in case we decide,\n\t\t * to send other data like at some point in time.\n\t\t */\n\t\tconst CLI_DATA = { preRenderData };\n\t\tconst currentURL = preRenderData.url ? normalizeURL(preRenderData.url) : '';\n\t\tconst canHydrate =\n\t\t\tprocess.env.PRERENDER &&\n\t\t\tprocess.env.NODE_ENV === 'production' &&\n\t\t\thydrate &&\n\t\t\tcurrentURL === location.pathname;\n\t\tconst doRender = canHydrate ? hydrate : render;\n\t\troot = doRender(h(app, { CLI_DATA }), document.body, root);\n\t};\n\n\tif (module.hot) module.hot.accept('preact-cli-entrypoint', init);\n\n\tinit();\n}\n","export default function _extends() {\n _extends = Object.assign || function (target) {\n for (var i = 1; i < arguments.length; i++) {\n var source = arguments[i];\n\n for (var key in source) {\n if (Object.prototype.hasOwnProperty.call(source, key)) {\n target[key] = source[key];\n }\n }\n }\n\n return target;\n };\n\n return _extends.apply(this, arguments);\n}","function isAbsolute(pathname) {\n return pathname.charAt(0) === '/';\n}\n\n// About 1.5x faster than the two-arg version of Array#splice()\nfunction spliceOne(list, index) {\n for (var i = index, k = i + 1, n = list.length; k < n; i += 1, k += 1) {\n list[i] = list[k];\n }\n\n list.pop();\n}\n\n// This implementation is based heavily on node's url.parse\nfunction resolvePathname(to, from) {\n if (from === undefined) from = '';\n\n var toParts = (to && to.split('/')) || [];\n var fromParts = (from && from.split('/')) || [];\n\n var isToAbs = to && isAbsolute(to);\n var isFromAbs = from && isAbsolute(from);\n var mustEndAbs = isToAbs || isFromAbs;\n\n if (to && isAbsolute(to)) {\n // to is absolute\n fromParts = toParts;\n } else if (toParts.length) {\n // to is relative, drop the filename\n fromParts.pop();\n fromParts = fromParts.concat(toParts);\n }\n\n if (!fromParts.length) return '/';\n\n var hasTrailingSlash;\n if (fromParts.length) {\n var last = fromParts[fromParts.length - 1];\n hasTrailingSlash = last === '.' || last === '..' || last === '';\n } else {\n hasTrailingSlash = false;\n }\n\n var up = 0;\n for (var i = fromParts.length; i >= 0; i--) {\n var part = fromParts[i];\n\n if (part === '.') {\n spliceOne(fromParts, i);\n } else if (part === '..') {\n spliceOne(fromParts, i);\n up++;\n } else if (up) {\n spliceOne(fromParts, i);\n up--;\n }\n }\n\n if (!mustEndAbs) for (; up--; up) fromParts.unshift('..');\n\n if (\n mustEndAbs &&\n fromParts[0] !== '' &&\n (!fromParts[0] || !isAbsolute(fromParts[0]))\n )\n fromParts.unshift('');\n\n var result = fromParts.join('/');\n\n if (hasTrailingSlash && result.substr(-1) !== '/') result += '/';\n\n return result;\n}\n\nexport default resolvePathname;\n","import _extends from '@babel/runtime/helpers/esm/extends';\nimport resolvePathname from 'resolve-pathname';\nimport valueEqual from 'value-equal';\nimport warning from 'tiny-warning';\nimport invariant from 'tiny-invariant';\n\nfunction addLeadingSlash(path) {\n return path.charAt(0) === '/' ? path : '/' + path;\n}\nfunction stripLeadingSlash(path) {\n return path.charAt(0) === '/' ? path.substr(1) : path;\n}\nfunction hasBasename(path, prefix) {\n return path.toLowerCase().indexOf(prefix.toLowerCase()) === 0 && '/?#'.indexOf(path.charAt(prefix.length)) !== -1;\n}\nfunction stripBasename(path, prefix) {\n return hasBasename(path, prefix) ? path.substr(prefix.length) : path;\n}\nfunction stripTrailingSlash(path) {\n return path.charAt(path.length - 1) === '/' ? path.slice(0, -1) : path;\n}\nfunction parsePath(path) {\n var pathname = path || '/';\n var search = '';\n var hash = '';\n var hashIndex = pathname.indexOf('#');\n\n if (hashIndex !== -1) {\n hash = pathname.substr(hashIndex);\n pathname = pathname.substr(0, hashIndex);\n }\n\n var searchIndex = pathname.indexOf('?');\n\n if (searchIndex !== -1) {\n search = pathname.substr(searchIndex);\n pathname = pathname.substr(0, searchIndex);\n }\n\n return {\n pathname: pathname,\n search: search === '?' ? '' : search,\n hash: hash === '#' ? '' : hash\n };\n}\nfunction createPath(location) {\n var pathname = location.pathname,\n search = location.search,\n hash = location.hash;\n var path = pathname || '/';\n if (search && search !== '?') path += search.charAt(0) === '?' ? search : \"?\" + search;\n if (hash && hash !== '#') path += hash.charAt(0) === '#' ? hash : \"#\" + hash;\n return path;\n}\n\nfunction createLocation(path, state, key, currentLocation) {\n var location;\n\n if (typeof path === 'string') {\n // Two-arg form: push(path, state)\n location = parsePath(path);\n location.state = state;\n } else {\n // One-arg form: push(location)\n location = _extends({}, path);\n if (location.pathname === undefined) location.pathname = '';\n\n if (location.search) {\n if (location.search.charAt(0) !== '?') location.search = '?' + location.search;\n } else {\n location.search = '';\n }\n\n if (location.hash) {\n if (location.hash.charAt(0) !== '#') location.hash = '#' + location.hash;\n } else {\n location.hash = '';\n }\n\n if (state !== undefined && location.state === undefined) location.state = state;\n }\n\n try {\n location.pathname = decodeURI(location.pathname);\n } catch (e) {\n if (e instanceof URIError) {\n throw new URIError('Pathname \"' + location.pathname + '\" could not be decoded. ' + 'This is likely caused by an invalid percent-encoding.');\n } else {\n throw e;\n }\n }\n\n if (key) location.key = key;\n\n if (currentLocation) {\n // Resolve incomplete/relative pathname relative to current location.\n if (!location.pathname) {\n location.pathname = currentLocation.pathname;\n } else if (location.pathname.charAt(0) !== '/') {\n location.pathname = resolvePathname(location.pathname, currentLocation.pathname);\n }\n } else {\n // When there is no prior location and pathname is empty, set it to /\n if (!location.pathname) {\n location.pathname = '/';\n }\n }\n\n return location;\n}\nfunction locationsAreEqual(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash && a.key === b.key && valueEqual(a.state, b.state);\n}\n\nfunction createTransitionManager() {\n var prompt = null;\n\n function setPrompt(nextPrompt) {\n process.env.NODE_ENV !== \"production\" ? warning(prompt == null, 'A history supports only one prompt at a time') : void 0;\n prompt = nextPrompt;\n return function () {\n if (prompt === nextPrompt) prompt = null;\n };\n }\n\n function confirmTransitionTo(location, action, getUserConfirmation, callback) {\n // TODO: If another transition starts while we're still confirming\n // the previous one, we may end up in a weird state. Figure out the\n // best way to handle this.\n if (prompt != null) {\n var result = typeof prompt === 'function' ? prompt(location, action) : prompt;\n\n if (typeof result === 'string') {\n if (typeof getUserConfirmation === 'function') {\n getUserConfirmation(result, callback);\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'A history needs a getUserConfirmation function in order to use a prompt message') : void 0;\n callback(true);\n }\n } else {\n // Return false from a transition hook to cancel the transition.\n callback(result !== false);\n }\n } else {\n callback(true);\n }\n }\n\n var listeners = [];\n\n function appendListener(fn) {\n var isActive = true;\n\n function listener() {\n if (isActive) fn.apply(void 0, arguments);\n }\n\n listeners.push(listener);\n return function () {\n isActive = false;\n listeners = listeners.filter(function (item) {\n return item !== listener;\n });\n };\n }\n\n function notifyListeners() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n listeners.forEach(function (listener) {\n return listener.apply(void 0, args);\n });\n }\n\n return {\n setPrompt: setPrompt,\n confirmTransitionTo: confirmTransitionTo,\n appendListener: appendListener,\n notifyListeners: notifyListeners\n };\n}\n\nvar canUseDOM = !!(typeof window !== 'undefined' && window.document && window.document.createElement);\nfunction getConfirmation(message, callback) {\n callback(window.confirm(message)); // eslint-disable-line no-alert\n}\n/**\n * Returns true if the HTML5 history API is supported. Taken from Modernizr.\n *\n * https://github.com/Modernizr/Modernizr/blob/master/LICENSE\n * https://github.com/Modernizr/Modernizr/blob/master/feature-detects/history.js\n * changed to avoid false negatives for Windows Phones: https://github.com/reactjs/react-router/issues/586\n */\n\nfunction supportsHistory() {\n var ua = window.navigator.userAgent;\n if ((ua.indexOf('Android 2.') !== -1 || ua.indexOf('Android 4.0') !== -1) && ua.indexOf('Mobile Safari') !== -1 && ua.indexOf('Chrome') === -1 && ua.indexOf('Windows Phone') === -1) return false;\n return window.history && 'pushState' in window.history;\n}\n/**\n * Returns true if browser fires popstate on hash change.\n * IE10 and IE11 do not.\n */\n\nfunction supportsPopStateOnHashChange() {\n return window.navigator.userAgent.indexOf('Trident') === -1;\n}\n/**\n * Returns false if using go(n) with hash history causes a full page reload.\n */\n\nfunction supportsGoWithoutReloadUsingHash() {\n return window.navigator.userAgent.indexOf('Firefox') === -1;\n}\n/**\n * Returns true if a given popstate event is an extraneous WebKit event.\n * Accounts for the fact that Chrome on iOS fires real popstate events\n * containing undefined state when pressing the back button.\n */\n\nfunction isExtraneousPopstateEvent(event) {\n return event.state === undefined && navigator.userAgent.indexOf('CriOS') === -1;\n}\n\nvar PopStateEvent = 'popstate';\nvar HashChangeEvent = 'hashchange';\n\nfunction getHistoryState() {\n try {\n return window.history.state || {};\n } catch (e) {\n // IE 11 sometimes throws when accessing window.history.state\n // See https://github.com/ReactTraining/history/pull/289\n return {};\n }\n}\n/**\n * Creates a history object that uses the HTML5 history API including\n * pushState, replaceState, and the popstate event.\n */\n\n\nfunction createBrowserHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Browser history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canUseHistory = supportsHistory();\n var needsHashChangeListener = !supportsPopStateOnHashChange();\n var _props = props,\n _props$forceRefresh = _props.forceRefresh,\n forceRefresh = _props$forceRefresh === void 0 ? false : _props$forceRefresh,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n\n function getDOMLocation(historyState) {\n var _ref = historyState || {},\n key = _ref.key,\n state = _ref.state;\n\n var _window$location = window.location,\n pathname = _window$location.pathname,\n search = _window$location.search,\n hash = _window$location.hash;\n var path = pathname + search + hash;\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path, state, key);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function handlePopState(event) {\n // Ignore extraneous popstate events in WebKit.\n if (isExtraneousPopstateEvent(event)) return;\n handlePop(getDOMLocation(event.state));\n }\n\n function handleHashChange() {\n handlePop(getDOMLocation(getHistoryState()));\n }\n\n var forceNextPop = false;\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of keys we've seen in sessionStorage.\n // Instead, we just default to 0 for keys we don't know.\n\n var toIndex = allKeys.indexOf(toLocation.key);\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allKeys.indexOf(fromLocation.key);\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n }\n\n var initialLocation = getDOMLocation(getHistoryState());\n var allKeys = [initialLocation.key]; // Public interface\n\n function createHref(location) {\n return basename + createPath(location);\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.pushState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.href = href;\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n var nextKeys = allKeys.slice(0, prevIndex + 1);\n nextKeys.push(location.key);\n allKeys = nextKeys;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot push state in browsers that do not support HTML5 history') : void 0;\n window.location.href = href;\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var href = createHref(location);\n var key = location.key,\n state = location.state;\n\n if (canUseHistory) {\n globalHistory.replaceState({\n key: key,\n state: state\n }, null, href);\n\n if (forceRefresh) {\n window.location.replace(href);\n } else {\n var prevIndex = allKeys.indexOf(history.location.key);\n if (prevIndex !== -1) allKeys[prevIndex] = location.key;\n setState({\n action: action,\n location: location\n });\n }\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot replace state in browsers that do not support HTML5 history') : void 0;\n window.location.replace(href);\n }\n });\n }\n\n function go(n) {\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.addEventListener(HashChangeEvent, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(PopStateEvent, handlePopState);\n if (needsHashChangeListener) window.removeEventListener(HashChangeEvent, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nvar HashChangeEvent$1 = 'hashchange';\nvar HashPathCoders = {\n hashbang: {\n encodePath: function encodePath(path) {\n return path.charAt(0) === '!' ? path : '!/' + stripLeadingSlash(path);\n },\n decodePath: function decodePath(path) {\n return path.charAt(0) === '!' ? path.substr(1) : path;\n }\n },\n noslash: {\n encodePath: stripLeadingSlash,\n decodePath: addLeadingSlash\n },\n slash: {\n encodePath: addLeadingSlash,\n decodePath: addLeadingSlash\n }\n};\n\nfunction stripHash(url) {\n var hashIndex = url.indexOf('#');\n return hashIndex === -1 ? url : url.slice(0, hashIndex);\n}\n\nfunction getHashPath() {\n // We can't use window.location.hash here because it's not\n // consistent across browsers - Firefox will pre-decode it!\n var href = window.location.href;\n var hashIndex = href.indexOf('#');\n return hashIndex === -1 ? '' : href.substring(hashIndex + 1);\n}\n\nfunction pushHashPath(path) {\n window.location.hash = path;\n}\n\nfunction replaceHashPath(path) {\n window.location.replace(stripHash(window.location.href) + '#' + path);\n}\n\nfunction createHashHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Hash history needs a DOM') : invariant(false) : void 0;\n var globalHistory = window.history;\n var canGoWithoutReload = supportsGoWithoutReloadUsingHash();\n var _props = props,\n _props$getUserConfirm = _props.getUserConfirmation,\n getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n _props$hashType = _props.hashType,\n hashType = _props$hashType === void 0 ? 'slash' : _props$hashType;\n var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n var _HashPathCoders$hashT = HashPathCoders[hashType],\n encodePath = _HashPathCoders$hashT.encodePath,\n decodePath = _HashPathCoders$hashT.decodePath;\n\n function getDOMLocation() {\n var path = decodePath(getHashPath());\n process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n if (basename) path = stripBasename(path, basename);\n return createLocation(path);\n }\n\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = globalHistory.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n var forceNextPop = false;\n var ignorePath = null;\n\n function locationsAreEqual$$1(a, b) {\n return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash;\n }\n\n function handleHashChange() {\n var path = getHashPath();\n var encodedPath = encodePath(path);\n\n if (path !== encodedPath) {\n // Ensure we always have a properly-encoded hash.\n replaceHashPath(encodedPath);\n } else {\n var location = getDOMLocation();\n var prevLocation = history.location;\n if (!forceNextPop && locationsAreEqual$$1(prevLocation, location)) return; // A hashchange doesn't always == location change.\n\n if (ignorePath === createPath(location)) return; // Ignore this change; we already setState in push/replace.\n\n ignorePath = null;\n handlePop(location);\n }\n }\n\n function handlePop(location) {\n if (forceNextPop) {\n forceNextPop = false;\n setState();\n } else {\n var action = 'POP';\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location\n });\n } else {\n revertPop(location);\n }\n });\n }\n }\n\n function revertPop(fromLocation) {\n var toLocation = history.location; // TODO: We could probably make this more reliable by\n // keeping a list of paths we've seen in sessionStorage.\n // Instead, we just default to 0 for paths we don't know.\n\n var toIndex = allPaths.lastIndexOf(createPath(toLocation));\n if (toIndex === -1) toIndex = 0;\n var fromIndex = allPaths.lastIndexOf(createPath(fromLocation));\n if (fromIndex === -1) fromIndex = 0;\n var delta = toIndex - fromIndex;\n\n if (delta) {\n forceNextPop = true;\n go(delta);\n }\n } // Ensure the hash is encoded properly before doing anything else.\n\n\n var path = getHashPath();\n var encodedPath = encodePath(path);\n if (path !== encodedPath) replaceHashPath(encodedPath);\n var initialLocation = getDOMLocation();\n var allPaths = [createPath(initialLocation)]; // Public interface\n\n function createHref(location) {\n var baseTag = document.querySelector('base');\n var href = '';\n\n if (baseTag && baseTag.getAttribute('href')) {\n href = stripHash(window.location.href);\n }\n\n return href + '#' + encodePath(basename + createPath(location));\n }\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot push state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a PUSH, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n pushHashPath(encodedPath);\n var prevIndex = allPaths.lastIndexOf(createPath(history.location));\n var nextPaths = allPaths.slice(0, prevIndex + 1);\n nextPaths.push(path);\n allPaths = nextPaths;\n setState({\n action: action,\n location: location\n });\n } else {\n process.env.NODE_ENV !== \"production\" ? warning(false, 'Hash history cannot PUSH the same path; a new entry will not be added to the history stack') : void 0;\n setState();\n }\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot replace state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, undefined, undefined, history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var path = createPath(location);\n var encodedPath = encodePath(basename + path);\n var hashChanged = getHashPath() !== encodedPath;\n\n if (hashChanged) {\n // We cannot tell if a hashchange was caused by a REPLACE, so we'd\n // rather setState here and ignore the hashchange. The caveat here\n // is that other hash histories in the page will consider it a POP.\n ignorePath = path;\n replaceHashPath(encodedPath);\n }\n\n var prevIndex = allPaths.indexOf(createPath(history.location));\n if (prevIndex !== -1) allPaths[prevIndex] = path;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n process.env.NODE_ENV !== \"production\" ? warning(canGoWithoutReload, 'Hash history go(n) causes a full page reload in this browser') : void 0;\n globalHistory.go(n);\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n var listenerCount = 0;\n\n function checkDOMListeners(delta) {\n listenerCount += delta;\n\n if (listenerCount === 1 && delta === 1) {\n window.addEventListener(HashChangeEvent$1, handleHashChange);\n } else if (listenerCount === 0) {\n window.removeEventListener(HashChangeEvent$1, handleHashChange);\n }\n }\n\n var isBlocked = false;\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n var unblock = transitionManager.setPrompt(prompt);\n\n if (!isBlocked) {\n checkDOMListeners(1);\n isBlocked = true;\n }\n\n return function () {\n if (isBlocked) {\n isBlocked = false;\n checkDOMListeners(-1);\n }\n\n return unblock();\n };\n }\n\n function listen(listener) {\n var unlisten = transitionManager.appendListener(listener);\n checkDOMListeners(1);\n return function () {\n checkDOMListeners(-1);\n unlisten();\n };\n }\n\n var history = {\n length: globalHistory.length,\n action: 'POP',\n location: initialLocation,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n block: block,\n listen: listen\n };\n return history;\n}\n\nfunction clamp(n, lowerBound, upperBound) {\n return Math.min(Math.max(n, lowerBound), upperBound);\n}\n/**\n * Creates a history object that stores locations in memory.\n */\n\n\nfunction createMemoryHistory(props) {\n if (props === void 0) {\n props = {};\n }\n\n var _props = props,\n getUserConfirmation = _props.getUserConfirmation,\n _props$initialEntries = _props.initialEntries,\n initialEntries = _props$initialEntries === void 0 ? ['/'] : _props$initialEntries,\n _props$initialIndex = _props.initialIndex,\n initialIndex = _props$initialIndex === void 0 ? 0 : _props$initialIndex,\n _props$keyLength = _props.keyLength,\n keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n var transitionManager = createTransitionManager();\n\n function setState(nextState) {\n _extends(history, nextState);\n\n history.length = history.entries.length;\n transitionManager.notifyListeners(history.location, history.action);\n }\n\n function createKey() {\n return Math.random().toString(36).substr(2, keyLength);\n }\n\n var index = clamp(initialIndex, 0, initialEntries.length - 1);\n var entries = initialEntries.map(function (entry) {\n return typeof entry === 'string' ? createLocation(entry, undefined, createKey()) : createLocation(entry, undefined, entry.key || createKey());\n }); // Public interface\n\n var createHref = createPath;\n\n function push(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'PUSH';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n var prevIndex = history.index;\n var nextIndex = prevIndex + 1;\n var nextEntries = history.entries.slice(0);\n\n if (nextEntries.length > nextIndex) {\n nextEntries.splice(nextIndex, nextEntries.length - nextIndex, location);\n } else {\n nextEntries.push(location);\n }\n\n setState({\n action: action,\n location: location,\n index: nextIndex,\n entries: nextEntries\n });\n });\n }\n\n function replace(path, state) {\n process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n var action = 'REPLACE';\n var location = createLocation(path, state, createKey(), history.location);\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (!ok) return;\n history.entries[history.index] = location;\n setState({\n action: action,\n location: location\n });\n });\n }\n\n function go(n) {\n var nextIndex = clamp(history.index + n, 0, history.entries.length - 1);\n var action = 'POP';\n var location = history.entries[nextIndex];\n transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n if (ok) {\n setState({\n action: action,\n location: location,\n index: nextIndex\n });\n } else {\n // Mimic the behavior of DOM histories by\n // causing a render after a cancelled POP.\n setState();\n }\n });\n }\n\n function goBack() {\n go(-1);\n }\n\n function goForward() {\n go(1);\n }\n\n function canGo(n) {\n var nextIndex = history.index + n;\n return nextIndex >= 0 && nextIndex < history.entries.length;\n }\n\n function block(prompt) {\n if (prompt === void 0) {\n prompt = false;\n }\n\n return transitionManager.setPrompt(prompt);\n }\n\n function listen(listener) {\n return transitionManager.appendListener(listener);\n }\n\n var history = {\n length: entries.length,\n action: 'POP',\n location: entries[index],\n index: index,\n entries: entries,\n createHref: createHref,\n push: push,\n replace: replace,\n go: go,\n goBack: goBack,\n goForward: goForward,\n canGo: canGo,\n block: block,\n listen: listen\n };\n return history;\n}\n\nexport { createBrowserHistory, createHashHistory, createMemoryHistory, createLocation, locationsAreEqual, parsePath, createPath };\n","var isProduction = process.env.NODE_ENV === 'production';\nvar prefix = 'Invariant failed';\nfunction invariant(condition, message) {\n if (condition) {\n return;\n }\n if (isProduction) {\n throw new Error(prefix);\n }\n throw new Error(prefix + \": \" + (message || ''));\n}\n\nexport default invariant;\n","import { options, Fragment } from 'preact';\n\n/**\n * Get human readable name of the component/dom node\n * @param {import('./internal').VNode} vnode\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function getDisplayName(vnode) {\n\tif (vnode.type === Fragment) {\n\t\treturn 'Fragment';\n\t} else if (typeof vnode.type == 'function') {\n\t\treturn vnode.type.displayName || vnode.type.name;\n\t} else if (typeof vnode.type == 'string') {\n\t\treturn vnode.type;\n\t}\n\n\treturn '#text';\n}\n\n/**\n * Used to keep track of the currently rendered `vnode` and print it\n * in debug messages.\n */\nlet renderStack = [];\n\n/**\n * Keep track of the current owners. An owner describes a component\n * which was responsible to render a specific `vnode`. This exclude\n * children that are passed via `props.children`, because they belong\n * to the parent owner.\n *\n * ```jsx\n * const Foo = props =>
{props.children}
// div's owner is Foo\n * const Bar = props => {\n * return (\n * // Foo's owner is Bar, span's owner is Bar\n * )\n * }\n * ```\n *\n * Note: A `vnode` may be hoisted to the root scope due to compiler\n * optimiztions. In these cases the `_owner` will be different.\n */\nlet ownerStack = [];\n\n/**\n * Get the currently rendered `vnode`\n * @returns {import('./internal').VNode | null}\n */\nexport function getCurrentVNode() {\n\treturn renderStack.length > 0 ? renderStack[renderStack.length - 1] : null;\n}\n\n/**\n * If the user doesn't have `@babel/plugin-transform-react-jsx-source`\n * somewhere in his tool chain we can't print the filename and source\n * location of a component. In that case we just omit that, but we'll\n * print a helpful message to the console, notifying the user of it.\n */\nlet hasBabelPlugin = false;\n\n/**\n * Check if a `vnode` is a possible owner.\n * @param {import('./internal').VNode} vnode\n */\nfunction isPossibleOwner(vnode) {\n\treturn typeof vnode.type == 'function' && vnode.type != Fragment;\n}\n\n/**\n * Return the component stack that was captured up to this point.\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function getOwnerStack(vnode) {\n\tconst stack = [vnode];\n\tlet next = vnode;\n\twhile (next._owner != null) {\n\t\tstack.push(next._owner);\n\t\tnext = next._owner;\n\t}\n\n\treturn stack.reduce((acc, owner) => {\n\t\tacc += ` in ${getDisplayName(owner)}`;\n\n\t\tconst source = owner.__source;\n\t\tif (source) {\n\t\t\tacc += ` (at ${source.fileName}:${source.lineNumber})`;\n\t\t} else if (!hasBabelPlugin) {\n\t\t\thasBabelPlugin = true;\n\t\t\tconsole.warn(\n\t\t\t\t'Add @babel/plugin-transform-react-jsx-source to get a more detailed component stack. Note that you should not add it to production builds of your App for bundle size reasons.'\n\t\t\t);\n\t\t}\n\n\t\treturn (acc += '\\n');\n\t}, '');\n}\n\n/**\n * Setup code to capture the component trace while rendering. Note that\n * we cannot simply traverse `vnode._parent` upwards, because we have some\n * debug messages for `this.setState` where the `vnode` is `undefined`.\n */\nexport function setupComponentStack() {\n\tlet oldDiff = options._diff;\n\tlet oldDiffed = options.diffed;\n\tlet oldRoot = options._root;\n\tlet oldVNode = options.vnode;\n\tlet oldRender = options._render;\n\n\toptions.diffed = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\townerStack.pop();\n\t\t}\n\t\trenderStack.pop();\n\t\tif (oldDiffed) oldDiffed(vnode);\n\t};\n\n\toptions._diff = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\trenderStack.push(vnode);\n\t\t}\n\t\tif (oldDiff) oldDiff(vnode);\n\t};\n\n\toptions._root = (vnode, parent) => {\n\t\townerStack = [];\n\t\tif (oldRoot) oldRoot(vnode, parent);\n\t};\n\n\toptions.vnode = vnode => {\n\t\tvnode._owner =\n\t\t\townerStack.length > 0 ? ownerStack[ownerStack.length - 1] : null;\n\t\tif (oldVNode) oldVNode(vnode);\n\t};\n\n\toptions._render = vnode => {\n\t\tif (isPossibleOwner(vnode)) {\n\t\t\townerStack.push(vnode);\n\t\t}\n\n\t\tif (oldRender) oldRender(vnode);\n\t};\n}\n","import { checkPropTypes } from './check-props';\nimport { options, Component } from 'preact';\nimport {\n\tELEMENT_NODE,\n\tDOCUMENT_NODE,\n\tDOCUMENT_FRAGMENT_NODE\n} from './constants';\nimport {\n\tgetOwnerStack,\n\tsetupComponentStack,\n\tgetCurrentVNode,\n\tgetDisplayName\n} from './component-stack';\n\nconst isWeakMapSupported = typeof WeakMap == 'function';\n\nfunction getClosestDomNodeParent(parent) {\n\tif (!parent) return {};\n\tif (typeof parent.type == 'function') {\n\t\treturn getClosestDomNodeParent(parent._parent);\n\t}\n\treturn parent;\n}\n\nexport function initDebug() {\n\tsetupComponentStack();\n\n\t/* eslint-disable no-console */\n\tlet oldBeforeDiff = options._diff;\n\tlet oldDiffed = options.diffed;\n\tlet oldVnode = options.vnode;\n\tlet oldCatchError = options._catchError;\n\tlet oldRoot = options._root;\n\tlet oldHook = options._hook;\n\tconst warnedComponents = !isWeakMapSupported\n\t\t? null\n\t\t: {\n\t\t\t\tuseEffect: new WeakMap(),\n\t\t\t\tuseLayoutEffect: new WeakMap(),\n\t\t\t\tlazyPropTypes: new WeakMap()\n\t\t };\n\n\toptions._catchError = (error, vnode, oldVNode) => {\n\t\tlet component = vnode && vnode._component;\n\t\tif (component && typeof error.then == 'function') {\n\t\t\tconst promise = error;\n\t\t\terror = new Error(\n\t\t\t\t`Missing Suspense. The throwing component was: ${getDisplayName(vnode)}`\n\t\t\t);\n\n\t\t\tlet parent = vnode;\n\t\t\tfor (; parent; parent = parent._parent) {\n\t\t\t\tif (parent._component && parent._component._childDidSuspend) {\n\t\t\t\t\terror = promise;\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\t// We haven't recovered and we know at this point that there is no\n\t\t\t// Suspense component higher up in the tree\n\t\t\tif (error instanceof Error) {\n\t\t\t\tthrow error;\n\t\t\t}\n\t\t}\n\n\t\toldCatchError(error, vnode, oldVNode);\n\t};\n\n\toptions._root = (vnode, parentNode) => {\n\t\tif (!parentNode) {\n\t\t\tthrow new Error(\n\t\t\t\t'Undefined parent passed to render(), this is the second argument.\\n' +\n\t\t\t\t\t'Check if the element is available in the DOM/has the correct id.'\n\t\t\t);\n\t\t}\n\t\tlet isValid;\n\t\tswitch (parentNode.nodeType) {\n\t\t\tcase ELEMENT_NODE:\n\t\t\tcase DOCUMENT_FRAGMENT_NODE:\n\t\t\tcase DOCUMENT_NODE:\n\t\t\t\tisValid = true;\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\tisValid = false;\n\t\t}\n\n\t\tif (!isValid) {\n\t\t\tlet componentName = getDisplayName(vnode);\n\t\t\tthrow new Error(\n\t\t\t\t`Expected a valid HTML node as a second argument to render.\tReceived ${parentNode} instead: render(<${componentName} />, ${parentNode});`\n\t\t\t);\n\t\t}\n\n\t\tif (oldRoot) oldRoot(vnode, parentNode);\n\t};\n\n\toptions._diff = vnode => {\n\t\tlet { type, _parent: parent } = vnode;\n\t\tlet parentVNode = getClosestDomNodeParent(parent);\n\n\t\tif (type === undefined) {\n\t\t\tthrow new Error(\n\t\t\t\t'Undefined component passed to createElement()\\n\\n' +\n\t\t\t\t\t'You likely forgot to export your component or might have mixed up default and named imports' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type != null && typeof type == 'object') {\n\t\t\tif (type._children !== undefined && type._dom !== undefined) {\n\t\t\t\tthrow new Error(\n\t\t\t\t\t`Invalid type passed to createElement(): ${type}\\n\\n` +\n\t\t\t\t\t\t'Did you accidentally pass a JSX literal as JSX twice?\\n\\n' +\n\t\t\t\t\t\t` let My${getDisplayName(vnode)} = ${serializeVNode(type)};\\n` +\n\t\t\t\t\t\t` let vnode = ;\\n\\n` +\n\t\t\t\t\t\t'This usually happens when you export a JSX literal and not the component.' +\n\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t);\n\t\t\t}\n\n\t\t\tthrow new Error(\n\t\t\t\t'Invalid type passed to createElement(): ' +\n\t\t\t\t\t(Array.isArray(type) ? 'array' : type)\n\t\t\t);\n\t\t}\n\n\t\tif (\n\t\t\t(type === 'thead' || type === 'tfoot' || type === 'tbody') &&\n\t\t\tparentVNode.type !== 'table'\n\t\t) {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your should have a
parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (\n\t\t\ttype === 'tr' &&\n\t\t\tparentVNode.type !== 'thead' &&\n\t\t\tparentVNode.type !== 'tfoot' &&\n\t\t\tparentVNode.type !== 'tbody' &&\n\t\t\tparentVNode.type !== 'table'\n\t\t) {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your should have a parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type === 'td' && parentVNode.type !== 'tr') {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your parent.' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t} else if (type === 'th' && parentVNode.type !== 'tr') {\n\t\t\tconsole.error(\n\t\t\t\t'Improper nesting of table. Your .' +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t}\n\n\t\tif (\n\t\t\tvnode.ref !== undefined &&\n\t\t\ttypeof vnode.ref != 'function' &&\n\t\t\ttypeof vnode.ref != 'object' &&\n\t\t\t!('$$typeof' in vnode) // allow string refs when preact-compat is installed\n\t\t) {\n\t\t\tthrow new Error(\n\t\t\t\t`Component's \"ref\" property should be a function, or an object created ` +\n\t\t\t\t\t`by createRef(), but got [${typeof vnode.ref}] instead\\n` +\n\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t);\n\t\t}\n\n\t\tif (typeof vnode.type == 'string') {\n\t\t\tfor (const key in vnode.props) {\n\t\t\t\tif (\n\t\t\t\t\tkey[0] === 'o' &&\n\t\t\t\t\tkey[1] === 'n' &&\n\t\t\t\t\ttypeof vnode.props[key] != 'function' &&\n\t\t\t\t\tvnode.props[key] != null\n\t\t\t\t) {\n\t\t\t\t\tthrow new Error(\n\t\t\t\t\t\t`Component's \"${key}\" property should be a function, ` +\n\t\t\t\t\t\t\t`but got [${typeof vnode.props[key]}] instead\\n` +\n\t\t\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\t// Check prop-types if available\n\t\tif (typeof vnode.type == 'function' && vnode.type.propTypes) {\n\t\t\tif (\n\t\t\t\tvnode.type.displayName === 'Lazy' &&\n\t\t\t\twarnedComponents &&\n\t\t\t\t!warnedComponents.lazyPropTypes.has(vnode.type)\n\t\t\t) {\n\t\t\t\tconst m =\n\t\t\t\t\t'PropTypes are not supported on lazy(). Use propTypes on the wrapped component itself. ';\n\t\t\t\ttry {\n\t\t\t\t\tconst lazyVNode = vnode.type();\n\t\t\t\t\twarnedComponents.lazyPropTypes.set(vnode.type, true);\n\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\tm + `Component wrapped in lazy() is ${getDisplayName(lazyVNode)}`\n\t\t\t\t\t);\n\t\t\t\t} catch (promise) {\n\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\tm + \"We will log the wrapped component's name once it is loaded.\"\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t}\n\t\t\tcheckPropTypes(\n\t\t\t\tvnode.type.propTypes,\n\t\t\t\tvnode.props,\n\t\t\t\t'prop',\n\t\t\t\tgetDisplayName(vnode)\n\t\t\t);\n\t\t}\n\n\t\tif (oldBeforeDiff) oldBeforeDiff(vnode);\n\t};\n\n\toptions._hook = comp => {\n\t\tif (!comp) {\n\t\t\tthrow new Error('Hook can only be invoked from render methods.');\n\t\t}\n\n\t\tif (oldHook) oldHook(comp);\n\t};\n\n\tconst warn = (property, err) => ({\n\t\tget() {\n\t\t\tthrow new Error(`getting vnode.${property} is deprecated, ${err}`);\n\t\t},\n\t\tset() {\n\t\t\tthrow new Error(`setting vnode.${property} is not allowed, ${err}`);\n\t\t}\n\t});\n\n\tconst deprecatedAttributes = {\n\t\tnodeName: warn('nodeName', 'use vnode.type'),\n\t\tattributes: warn('attributes', 'use vnode.props'),\n\t\tchildren: warn('children', 'use vnode.props.children')\n\t};\n\n\tconst deprecatedProto = Object.create({}, deprecatedAttributes);\n\n\toptions.vnode = vnode => {\n\t\tconst props = vnode.props;\n\t\tif (\n\t\t\tvnode.type !== null &&\n\t\t\tprops != null &&\n\t\t\t('__source' in props || '__self' in props)\n\t\t) {\n\t\t\tconst newProps = (vnode.props = {});\n\t\t\tfor (let i in props) {\n\t\t\t\tconst v = props[i];\n\t\t\t\tif (i === '__source') vnode.__source = v;\n\t\t\t\telse if (i === '__self') vnode.__self = v;\n\t\t\t\telse newProps[i] = v;\n\t\t\t}\n\t\t}\n\t\tObject.setPrototypeOf(vnode, deprecatedProto);\n\t\tif (oldVnode) oldVnode(vnode);\n\t};\n\n\toptions.diffed = vnode => {\n\t\t// Check if the user passed plain objects as children. Note that we cannot\n\t\t// move this check into `options.vnode` because components can receive\n\t\t// children in any shape they want (e.g.\n\t\t// `{{ foo: 123, bar: \"abc\" }}`).\n\t\t// Putting this check in `options.diffed` ensures that\n\t\t// `vnode._children` is set and that we only validate the children\n\t\t// that were actually rendered.\n\t\tif (vnode._children) {\n\t\t\tvnode._children.forEach(child => {\n\t\t\t\tif (child && child.type === undefined) {\n\t\t\t\t\t// Remove internal vnode keys that will always be patched\n\t\t\t\t\tdelete child._parent;\n\t\t\t\t\tdelete child._depth;\n\t\t\t\t\tconst keys = Object.keys(child).join(',');\n\t\t\t\t\tthrow new Error(\n\t\t\t\t\t\t`Objects are not valid as a child. Encountered an object with the keys {${keys}}.` +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\t\t\t\t}\n\t\t\t});\n\t\t}\n\n\t\t/** @type {import('./internal').Component} */\n\t\tconst component = vnode._component;\n\t\tif (component && component.__hooks) {\n\t\t\tlet hooks = component.__hooks;\n\t\t\tif (Array.isArray(hooks._list)) {\n\t\t\t\thooks._list.forEach(hook => {\n\t\t\t\t\tif (hook._factory && (!hook._args || !Array.isArray(hook._args))) {\n\t\t\t\t\t\tlet componentName = getDisplayName(vnode);\n\t\t\t\t\t\tconsole.warn(\n\t\t\t\t\t\t\t`In ${componentName} you are calling useMemo/useCallback without passing arguments.\\n` +\n\t\t\t\t\t\t\t\t`This is a noop since it will not be able to memoize, it will execute it every render.` +\n\t\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t\t);\n\t\t\t\t\t}\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\tif (oldDiffed) oldDiffed(vnode);\n\n\t\tif (vnode._children != null) {\n\t\t\tconst keys = [];\n\t\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\t\tconst child = vnode._children[i];\n\t\t\t\tif (!child || child.key == null) continue;\n\n\t\t\t\tconst key = child.key;\n\t\t\t\tif (keys.indexOf(key) !== -1) {\n\t\t\t\t\tconsole.error(\n\t\t\t\t\t\t'Following component has two or more children with the ' +\n\t\t\t\t\t\t\t`same key attribute: \"${key}\". This may cause glitches and misbehavior ` +\n\t\t\t\t\t\t\t'in rendering process. Component: \\n\\n' +\n\t\t\t\t\t\t\tserializeVNode(vnode) +\n\t\t\t\t\t\t\t`\\n\\n${getOwnerStack(vnode)}`\n\t\t\t\t\t);\n\n\t\t\t\t\t// Break early to not spam the console\n\t\t\t\t\tbreak;\n\t\t\t\t}\n\n\t\t\t\tkeys.push(key);\n\t\t\t}\n\t\t}\n\t};\n}\n\nconst setState = Component.prototype.setState;\nComponent.prototype.setState = function(update, callback) {\n\tif (this._vnode == null) {\n\t\t// `this._vnode` will be `null` during componentWillMount. But it\n\t\t// is perfectly valid to call `setState` during cWM. So we\n\t\t// need an additional check to verify that we are dealing with a\n\t\t// call inside constructor.\n\t\tif (this.state == null) {\n\t\t\tconsole.warn(\n\t\t\t\t`Calling \"this.setState\" inside the constructor of a component is a ` +\n\t\t\t\t\t`no-op and might be a bug in your application. Instead, set ` +\n\t\t\t\t\t`\"this.state = {}\" directly.\\n\\n${getOwnerStack(getCurrentVNode())}`\n\t\t\t);\n\t\t}\n\t} else if (this._parentDom == null) {\n\t\tconsole.warn(\n\t\t\t`Can't call \"this.setState\" on an unmounted component. This is a no-op, ` +\n\t\t\t\t`but it indicates a memory leak in your application. To fix, cancel all ` +\n\t\t\t\t`subscriptions and asynchronous tasks in the componentWillUnmount method.` +\n\t\t\t\t`\\n\\n${getOwnerStack(this._vnode)}`\n\t\t);\n\t}\n\n\treturn setState.call(this, update, callback);\n};\n\nconst forceUpdate = Component.prototype.forceUpdate;\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode == null) {\n\t\tconsole.warn(\n\t\t\t`Calling \"this.forceUpdate\" inside the constructor of a component is a ` +\n\t\t\t\t`no-op and might be a bug in your application.\\n\\n${getOwnerStack(\n\t\t\t\t\tgetCurrentVNode()\n\t\t\t\t)}`\n\t\t);\n\t} else if (this._parentDom == null) {\n\t\tconsole.warn(\n\t\t\t`Can't call \"this.forceUpdate\" on an unmounted component. This is a no-op, ` +\n\t\t\t\t`but it indicates a memory leak in your application. To fix, cancel all ` +\n\t\t\t\t`subscriptions and asynchronous tasks in the componentWillUnmount method.` +\n\t\t\t\t`\\n\\n${getOwnerStack(this._vnode)}`\n\t\t);\n\t}\n\treturn forceUpdate.call(this, callback);\n};\n\n/**\n * Serialize a vnode tree to a string\n * @param {import('./internal').VNode} vnode\n * @returns {string}\n */\nexport function serializeVNode(vnode) {\n\tlet { props } = vnode;\n\tlet name = getDisplayName(vnode);\n\n\tlet attrs = '';\n\tfor (let prop in props) {\n\t\tif (props.hasOwnProperty(prop) && prop !== 'children') {\n\t\t\tlet value = props[prop];\n\n\t\t\t// If it is an object but doesn't have toString(), use Object.toString\n\t\t\tif (typeof value == 'function') {\n\t\t\t\tvalue = `function ${value.displayName || value.name}() {}`;\n\t\t\t}\n\n\t\t\tvalue =\n\t\t\t\tObject(value) === value && !value.toString\n\t\t\t\t\t? Object.prototype.toString.call(value)\n\t\t\t\t\t: value + '';\n\n\t\t\tattrs += ` ${prop}=${JSON.stringify(value)}`;\n\t\t}\n\t}\n\n\tlet children = props.children;\n\treturn `<${name}${attrs}${\n\t\tchildren && children.length ? '>..' : ' />'\n\t}`;\n}\n","import { options, Fragment } from 'preact';\n\nexport function initDevTools() {\n\tif (typeof window != 'undefined' && window.__PREACT_DEVTOOLS__) {\n\t\twindow.__PREACT_DEVTOOLS__.attachPreact('10.0.5', options, {\n\t\t\tFragment\n\t\t});\n\t}\n}\n","const ReactPropTypesSecret = 'SECRET_DO_NOT_PASS_THIS_OR_YOU_WILL_BE_FIRED';\n\nlet loggedTypeFailures = {};\n\n/**\n * Reset the history of which prop type warnings have been logged.\n */\nexport function resetPropWarnings() {\n\tloggedTypeFailures = {};\n}\n\n/**\n * Assert that the values match with the type specs.\n * Error messages are memorized and will only be shown once.\n *\n * Adapted from https://github.com/facebook/prop-types/blob/master/checkPropTypes.js\n *\n * @param {object} typeSpecs Map of name to a ReactPropType\n * @param {object} values Runtime values that need to be type-checked\n * @param {string} location e.g. \"prop\", \"context\", \"child context\"\n * @param {string} componentName Name of the component for error messages.\n * @param {?Function} getStack Returns the component stack.\n */\nexport function checkPropTypes(\n\ttypeSpecs,\n\tvalues,\n\tlocation,\n\tcomponentName,\n\tgetStack\n) {\n\tObject.keys(typeSpecs).forEach(typeSpecName => {\n\t\tlet error;\n\t\ttry {\n\t\t\terror = typeSpecs[typeSpecName](\n\t\t\t\tvalues,\n\t\t\t\ttypeSpecName,\n\t\t\t\tcomponentName,\n\t\t\t\tlocation,\n\t\t\t\tnull,\n\t\t\t\tReactPropTypesSecret\n\t\t\t);\n\t\t} catch (e) {\n\t\t\terror = e;\n\t\t}\n\t\tif (error && !(error.message in loggedTypeFailures)) {\n\t\t\tloggedTypeFailures[error.message] = true;\n\t\t\tconsole.error(\n\t\t\t\t`Failed ${location} type: ${error.message}${(getStack && getStack()) ||\n\t\t\t\t\t''}`\n\t\t\t);\n\t\t}\n\t});\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./fisica.js\") );\n\t\t\t}, \"route-fisica\");\n\t\t}\n\n\t\texport default Async(load);\n\t"],"sourceRoot":""} \ No newline at end of file diff --git a/docs/index.html b/docs/index.html index cb34897..73e100d 100644 --- a/docs/index.html +++ b/docs/index.html @@ -1 +1 @@ -Appunti Web \ No newline at end of file +Appunti Web \ No newline at end of file diff --git a/docs/precache-manifest.01e323f5778dc7abb82cf3d35c59f3c3.esm.js b/docs/precache-manifest.01e323f5778dc7abb82cf3d35c59f3c3.esm.js deleted file mode 100644 index a1d09d2..0000000 --- a/docs/precache-manifest.01e323f5778dc7abb82cf3d35c59f3c3.esm.js +++ /dev/null @@ -1,98 +0,0 @@ -self.__precacheManifest = (self.__precacheManifest || []).concat([ - { - "revision": "2b714cf154cd80b3949545dfe0c5939a", - "url": "/assets/icon.png" - }, - { - "revision": "978dc38d859103722100", - "url": "/bundle.0096a.css" - }, - { - "revision": "978dc38d859103722100", - "url": 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\n

Apprendimento ed evoluzione in sistemi artificiali

\n \n \n

\n NetLogo è un software di modellazione sistemi multiagente.\n

\n

\n Si può scaricare o usare da browser.\n

\n

\n Il suo codice sorgente è disponibile su GitHub, e ha una pagina di documentazione.\n

\n \n \n \n \n

\n L'utente di NetLogo, che vive nel contesto globale e dà ordini agli altri agenti.\n

\n \n \n

\n Entità che possono muoversi per il mondo.\n

\n \n Sono più o meno come le Turtle di Computercraft!\n \n

\n Possono essere di una breed (razza) specifica, definite con:\n

\n {r`breed [ ]`}\n \n Le breed sono praticamente sottoclassi di turtle.\n \n \n \n

\n I quadratini del mondo. Possono essere di vari colori e avere varie proprietà.\n

\n \n ...possiamo dire che questi siano i blocchi di Minecraft?\n \n \n \n

\n Collegamenti tra due turtle.\n

\n \n \n \n \n

\n L'observer viene creato automaticamente all'apertura della simulazione.\n

\n \n \n

\n Nuove turtle possono essere create con il comando:\n

\n {r`- `}\n

\n Dove prefisso varia in base al contesto attuale:\n

\n
should have a
should have a
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
ContestoPrefisso
Observer{r`create`}
Turtle{r`hatch`}
Patch{r`sprout`}
\n \n \n \n \n

\n All'inizio del codice:\n

\n {`globals [var1 var2 var3]`}\n \n Sono a tutti gli effetti variabili globali.\n \n \n \n

\n Aggiungi proprietà a tutte le turtle:\n

\n {`turtles-own [var1 var2 var3]`}\n

\n Aggiungi proprietà alle turtle di un breed:\n

\n {`-own [var1 var2 var3]`}\n \n \n

\n Aggiungi proprietà alle patch:\n

\n {r`patches-own [var1 var2 var3]`}\n \n \n

\n Aggiungi proprietà ai link:\n

\n {r`links-own [var1 var2 var3]`}\n \n \n \n \n

\n Si possono creare con:\n

\n {r`let `}\n \n \n

\n Si può impostare il valore di una variabile con:\n

\n {r`set `}\n \n \n \n \n

\n Per cambiare contesto:\n

\n {r`\n ask [\n \n ]\n `}\n

\n Nel caso ci siano più bersagli, verranno eseguiti uno\n

\n \n \n

\n Funzioni che non restituiscono nulla:\n

\n {r`\n to \n \n end\n `}\n

\n Con argomenti:\n

\n {r`\n to [var1 var2 var3]\n \n end\n `}\n \n \n

\n Funzioni che restituiscono un valore:\n

\n {r`\n to-report [var1 var2 var3]\n \n report \n end\n `}\n \n \n \n \n

\n Muoviti di 10 unità:\n

\n {r`\n forward 10\n back 10\n `}\n

\n Nota che la velocità massima delle tartarughe è di 1 unità/tick, quindi muoversi di 10 unità richiederà 10 tick.\n

\n \n \n

\n Ruota di 10 gradi:\n

\n {r`\n left 10\n right 10\n `}\n \n \n\n \n )\n }\n}\n"],"sourceRoot":""} \ No newline at end of file diff --git a/docs/route-apprendimentoSistemiArtificiali.chunk.d0fa4.js b/docs/route-apprendimentoSistemiArtificiali.chunk.d0fa4.js new file mode 100644 index 0000000..5d6b9e7 --- /dev/null +++ b/docs/route-apprendimentoSistemiArtificiali.chunk.d0fa4.js @@ -0,0 +1,2 @@ +(window.webpackJsonp=window.webpackJsonp||[]).push([[3],{UlOE:function(n,t,e){"use strict";e.r(t),function(n){function l(){var n=m(["\n left 10\n right 10\n "]);return l=function(){return n},n}function r(){var n=m(["\n forward 10\n back 10\n "]);return r=function(){return n},n}function i(){var n=m(["\n to-report [var1 var2 var3]\n \n report \n end\n "]);return i=function(){return n},n}function o(){var n=m(["\n to [var1 var2 var3]\n \n end\n "]);return o=function(){return n},n}function u(){var n=m(["\n to \n \n end\n "]);return u=function(){return n},n}function a(){var n=m(["\n ask [\n \n ]\n "]);return a=function(){return n},n}function c(){var n=m(["set "]);return c=function(){return n},n}function s(){var n=m(["let "]);return s=function(){return n},n}function p(){var n=m(["links-own [var1 var2 var3]"]);return p=function(){return n},n}function d(){var n=m(["patches-own [var1 var2 var3]"]);return d=function(){return n},n}function v(){var n=m(["sprout"]);return v=function(){return n},n}function f(){var n=m(["hatch"]);return f=function(){return n},n}function h(){var n=m(["create"]);return h=function(){return n},n}function g(){var n=m(["- "]);return g=function(){return n},n}function b(){var n=m(["breed [ ]"]);return b=function(){return n},n}function m(n,t){return t||(t=n.slice(0)),n.raw=t,n}e.d(t,"default",(function(){return A}));var w=e("hosL"),L=e("lL4N"),k=e("HKwK"),z=e("PEwj"),C=e("3Gjt"),N=String.raw,A=function(t){function e(){return t.apply(this,arguments)||this}var m,w;return w=t,(m=e).prototype=Object.create(w.prototype),m.prototype.constructor=m,m.__proto__=w,e.prototype.render=function(){return n("div",null,n("h1",null,"Apprendimento ed evoluzione in sistemi artificiali"),n(L.a,{title:"NetLogo"},n(k.a,{title:"Cos'è?"},n("p",null,"NetLogo è un software di modellazione sistemi multiagente."),n("p",null,"Si può ",n("a",{href:"https://ccl.northwestern.edu/netlogo/download.shtml"},"scaricare")," o ",n("a",{href:"https://www.netlogoweb.org/launch"},"usare da browser"),"."),n("p",null,"Il suo codice sorgente è disponibile su ",n("a",{href:"https://github.com/NetLogo/NetLogo"},"GitHub"),", e ha una pagina di ",n("a",{href:"https://ccl.northwestern.edu/netlogo/docs/dictionary.html"},"documentazione"),"."))),n(L.a,{title:"Agenti di NetLogo"},n(k.a,{title:"Observer"},n("p",null,"L'",n("b",null,"utente")," di NetLogo, che vive nel contesto globale e dà ordini agli altri agenti.")),n(k.a,{title:"Turtle"},n("p",null,"Entità che possono ",n("b",null,"muoversi")," per il mondo."),n(z.a,null,"Sono più o meno come le ",n("a",{href:"https://www.computercraft.info/wiki/Turtle"},"Turtle di Computercraft"),"!"),n("p",null,"Possono essere di una ",n("i",null,"breed")," (razza) specifica, definite con:"),n(C.a,null,N(b())),n(z.a,null,"Le breed sono praticamente sottoclassi di turtle.")),n(k.a,{title:"Patch"},n("p",null,"I ",n("b",null,"quadratini")," del mondo. Possono essere di vari colori e avere varie proprietà."),n(z.a,null,"...possiamo dire che questi siano i blocchi di Minecraft?")),n(k.a,{title:"Link"},n("p",null,n("b",null,"Collegamenti")," tra due turtle."))),n(L.a,{title:"Creazione di agenti"},n(k.a,{title:"Observer"},n("p",null,"L'observer viene creato automaticamente all'apertura della simulazione.")),n(k.a,{title:"Turtle"},n("p",null,"Nuove turtle possono essere create con il comando:"),n(C.a,null,N(g())),n("p",null,"Dove prefisso varia in base al contesto attuale:"),n("table",null,n("thead",null,n("tr",null,n("th",null,"Contesto"),n("th",null,"Prefisso"))),n("tbody",null,n("tr",null,n("td",null,"Observer"),n("td",null,n("code",null,N(h())))),n("tr",null,n("td",null,"Turtle"),n("td",null,n("code",null,N(f())))),n("tr",null,n("td",null,"Patch"),n("td",null,n("code",null,N(v())))))))),n(L.a,{title:"Variabili"},n(k.a,{title:"Observer"},n("p",null,"All'inizio del codice:"),n(C.a,null,"globals [var1 var2 var3]"),n(z.a,null,"Sono a tutti gli effetti variabili globali.")),n(k.a,{title:"Turtle"},n("p",null,"Aggiungi proprietà a tutte le turtle:"),n(C.a,null,"turtles-own [var1 var2 var3]"),n("p",null,"Aggiungi proprietà alle turtle di un breed:"),n(C.a,null,"-own [var1 var2 var3]")),n(k.a,{title:"Patch"},n("p",null,"Aggiungi proprietà alle patch:"),n(C.a,null,N(d()))),n(k.a,{title:"Link"},n("p",null,"Aggiungi proprietà ai link:"),n(C.a,null,N(p())))),n(L.a,null,n(k.a,{title:"Locali"},n("p",null,"Si possono creare con:"),n(C.a,null,N(s()))),n(k.a,{title:"Set"},n("p",null,"Si può impostare il valore di una variabile con:"),n(C.a,null,N(c())))),n(L.a,{title:"Blocchi di codice"},n(k.a,{title:"Cambi di contesto"},n("p",null,"Per cambiare contesto:"),n(C.a,null,N(a())),n("p",null,"Nel caso ci siano più bersagli, verranno eseguiti uno")),n(k.a,{title:"Commands"},n("p",null,"Funzioni che non restituiscono nulla:"),n(C.a,null,N(u())),n("p",null,"Con argomenti:"),n(C.a,null,N(o()))),n(k.a,{title:"Reporter"},n("p",null,"Funzioni che restituiscono un valore:"),n(C.a,null,N(i())))),n(L.a,{title:"Comandi per turtle"},n(k.a,{title:"Avanti"},n("p",null,"Muoviti di 10 unità:"),n(C.a,null,N(r())),n("p",null,"Nota che la velocità massima delle tartarughe è di 1 unità/tick, quindi muoversi di 10 unità richiederà 10 tick.")),n(k.a,{title:"Ruota"},n("p",null,"Ruota di 10 gradi:"),n(C.a,null,N(l())))))},e}(w.Component)}.call(this,e("hosL").h)}}]); 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\n

Apprendimento ed evoluzione in sistemi artificiali

\n \n \n

\n NetLogo è un software di modellazione sistemi multiagente.\n

\n

\n Si può scaricare o usare da browser.\n

\n

\n Il suo codice sorgente è disponibile su GitHub, e ha una pagina di documentazione.\n

\n \n \n \n \n

\n L'utente di NetLogo, che vive nel contesto globale e dà ordini agli altri agenti.\n

\n \n \n

\n Entità che possono muoversi per il mondo.\n

\n \n Sono più o meno come le Turtle di Computercraft!\n \n

\n Possono essere di una breed (razza) specifica, definite con:\n

\n {r`breed [ ]`}\n \n Le breed sono praticamente sottoclassi di turtle.\n \n \n \n

\n I quadratini del mondo. Possono essere di vari colori e avere varie proprietà.\n

\n \n ...possiamo dire che questi siano i blocchi di Minecraft?\n \n \n \n

\n Collegamenti tra due turtle.\n

\n \n \n \n \n

\n L'observer viene creato automaticamente all'apertura della simulazione.\n

\n \n \n

\n Nuove turtle possono essere create con il comando:\n

\n {r`- `}\n

\n Dove prefisso varia in base al contesto attuale:\n

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
ContestoPrefisso
Observer{r`create`}
Turtle{r`hatch`}
Patch{r`sprout`}
\n \n \n \n \n

\n All'inizio del codice:\n

\n {`globals [var1 var2 var3]`}\n \n Sono a tutti gli effetti variabili globali.\n \n \n \n

\n Aggiungi proprietà a tutte le turtle:\n

\n {`turtles-own [var1 var2 var3]`}\n

\n Aggiungi proprietà alle turtle di un breed:\n

\n {`-own [var1 var2 var3]`}\n \n \n

\n Aggiungi proprietà alle patch:\n

\n {r`patches-own [var1 var2 var3]`}\n \n \n

\n Aggiungi proprietà ai link:\n

\n {r`links-own [var1 var2 var3]`}\n \n \n \n \n

\n Si possono creare con:\n

\n {r`let `}\n \n \n

\n Si può impostare il valore di una variabile con:\n

\n {r`set `}\n \n \n \n \n

\n Per cambiare contesto:\n

\n {r`\n ask [\n \n ]\n `}\n

\n Nel caso ci siano più bersagli, verranno eseguiti uno\n

\n \n \n

\n Funzioni che non restituiscono nulla:\n

\n {r`\n to \n \n end\n `}\n

\n Con argomenti:\n

\n {r`\n to [var1 var2 var3]\n \n end\n `}\n \n \n

\n Funzioni che restituiscono un valore:\n

\n {r`\n to-report [var1 var2 var3]\n \n report \n end\n `}\n \n \n \n \n

\n Muoviti di 10 unità:\n

\n {r`\n forward 10\n back 10\n `}\n

\n Nota che la velocità massima delle tartarughe è di 1 unità/tick, quindi muoversi di 10 unità richiederà 10 tick.\n

\n \n \n

\n Ruota di 10 gradi:\n

\n {r`\n left 10\n right 10\n `}\n \n \n\n
\n )\n }\n}\n"],"sourceRoot":""} \ No newline at end of file diff --git a/docs/route-apprendimentoSistemiArtificiali~route-ottimizzazioneLineare.chunk.0ad22.js b/docs/route-apprendimentoSistemiArtificiali~route-ottimizzazioneLineare.chunk.0ad22.js new file mode 100644 index 0000000..d1e3506 --- /dev/null +++ b/docs/route-apprendimentoSistemiArtificiali~route-ottimizzazioneLineare.chunk.0ad22.js @@ -0,0 +1,2 @@ +(window.webpackJsonp=window.webpackJsonp||[]).push([[0],{"+0sr":function(e){e.exports=function(e){return{case_insensitive:!0,keywords:{literal:".False. .True.",keyword:"kind do while private call intrinsic where elsewhere type endtype endmodule endselect endinterface end enddo endif if forall endforall only contains default return stop then public subroutine|10 function program .and. .or. .not. .le. .eq. .ge. .gt. .lt. goto save else use module select case access blank direct exist file fmt form formatted iostat name named nextrec number opened rec recl sequential status 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Get-CINetworkAdapter Get-CIRole Get-CIUser Get-CIVApp Get-CIVAppNetwork Get-CIVAppStartRule Get-CIVAppTemplate Get-CIVM Get-CIVMTemplate Get-CIView Get-Catalog Get-CisCommand Get-CisService Get-CloudCommand Get-Cluster Get-CompatibleVersionAddtionaPropertiesStr Get-ComplexResourceQualifier Get-ConfigurationErrorCount Get-ContentLibraryItem Get-CustomAttribute Get-DSCResourceModules Get-Datacenter Get-Datastore Get-DatastoreCluster Get-DrsClusterGroup Get-DrsRecommendation Get-DrsRule Get-DrsVMHostRule Get-DscResource Get-EdgeGateway Get-EncryptedPassword Get-ErrorReport Get-EsxCli Get-EsxTop Get-ExternalNetwork Get-FileHash Get-FloppyDrive Get-Folder Get-HAPrimaryVMHost Get-HCXAppliance Get-HCXApplianceCompute Get-HCXApplianceDVS Get-HCXApplianceDatastore Get-HCXApplianceNetwork Get-HCXContainer Get-HCXDatastore Get-HCXGateway Get-HCXInterconnectStatus Get-HCXJob Get-HCXMigration Get-HCXNetwork Get-HCXNetworkExtension Get-HCXReplication Get-HCXReplicationSnapshot Get-HCXService Get-HCXSite Get-HCXSitePairing Get-HCXVM Get-HardDisk Get-IScsiHbaTarget Get-InnerMostErrorRecord Get-InstallPath Get-InstalledModule Get-InstalledScript Get-Inventory Get-ItemPropertyValue Get-KeyManagementServer Get-KmipClientCertificate Get-KmsCluster Get-Log Get-LogType Get-MarkdownOption Get-Media Get-MofInstanceName Get-MofInstanceText Get-NetworkAdapter Get-NetworkPool Get-NfsUser Get-NicTeamingPolicy Get-NsxApplicableMember Get-NsxApplicableSecurityAction Get-NsxBackingDVSwitch Get-NsxBackingPortGroup Get-NsxCliDfwAddrSet Get-NsxCliDfwFilter Get-NsxCliDfwRule Get-NsxClusterStatus Get-NsxController Get-NsxDynamicCriteria Get-NsxDynamicMemberSet Get-NsxEdge Get-NsxEdgeBgp Get-NsxEdgeBgpNeighbour Get-NsxEdgeCertificate Get-NsxEdgeCsr Get-NsxEdgeFirewall Get-NsxEdgeFirewallRule Get-NsxEdgeInterface Get-NsxEdgeInterfaceAddress Get-NsxEdgeNat Get-NsxEdgeNatRule Get-NsxEdgeOspf Get-NsxEdgeOspfArea Get-NsxEdgeOspfInterface Get-NsxEdgePrefix Get-NsxEdgeRedistributionRule Get-NsxEdgeRouting Get-NsxEdgeStaticRoute Get-NsxEdgeSubInterface Get-NsxFirewallExclusionListMember Get-NsxFirewallGlobalConfiguration Get-NsxFirewallPublishStatus Get-NsxFirewallRule Get-NsxFirewallRuleMember Get-NsxFirewallSavedConfiguration Get-NsxFirewallSection Get-NsxFirewallThreshold Get-NsxIpPool Get-NsxIpSet Get-NsxLicense Get-NsxLoadBalancer Get-NsxLoadBalancerApplicationProfile Get-NsxLoadBalancerApplicationRule Get-NsxLoadBalancerMonitor Get-NsxLoadBalancerPool Get-NsxLoadBalancerPoolMember Get-NsxLoadBalancerStats Get-NsxLoadBalancerVip Get-NsxLogicalRouter Get-NsxLogicalRouterBgp Get-NsxLogicalRouterBgpNeighbour Get-NsxLogicalRouterBridge Get-NsxLogicalRouterBridging Get-NsxLogicalRouterInterface Get-NsxLogicalRouterOspf Get-NsxLogicalRouterOspfArea Get-NsxLogicalRouterOspfInterface Get-NsxLogicalRouterPrefix Get-NsxLogicalRouterRedistributionRule Get-NsxLogicalRouterRouting Get-NsxLogicalRouterStaticRoute Get-NsxLogicalSwitch Get-NsxMacSet Get-NsxManagerBackup Get-NsxManagerCertificate Get-NsxManagerComponentSummary Get-NsxManagerNetwork Get-NsxManagerRole Get-NsxManagerSsoConfig Get-NsxManagerSyncStatus Get-NsxManagerSyslogServer Get-NsxManagerSystemSummary Get-NsxManagerTimeSettings Get-NsxManagerVcenterConfig Get-NsxSecondaryManager Get-NsxSecurityGroup Get-NsxSecurityGroupEffectiveIpAddress Get-NsxSecurityGroupEffectiveMacAddress Get-NsxSecurityGroupEffectiveMember Get-NsxSecurityGroupEffectiveVirtualMachine Get-NsxSecurityGroupEffectiveVnic Get-NsxSecurityGroupMemberTypes Get-NsxSecurityPolicy Get-NsxSecurityPolicyHighestUsedPrecedence Get-NsxSecurityPolicyRule Get-NsxSecurityTag Get-NsxSecurityTagAssignment Get-NsxSegmentIdRange Get-NsxService Get-NsxServiceDefinition Get-NsxServiceGroup Get-NsxServiceGroupMember Get-NsxServiceProfile Get-NsxSpoofguardNic Get-NsxSpoofguardPolicy Get-NsxSslVpn Get-NsxSslVpnAuthServer Get-NsxSslVpnClientInstallationPackage Get-NsxSslVpnIpPool Get-NsxSslVpnPrivateNetwork Get-NsxSslVpnUser Get-NsxTransportZone Get-NsxUserRole Get-NsxVdsContext Get-NsxtPolicyService Get-NsxtService Get-OSCustomizationNicMapping Get-OSCustomizationSpec Get-Org Get-OrgNetwork Get-OrgVdc Get-OrgVdcNetwork Get-OvfConfiguration Get-PSCurrentConfigurationNode Get-PSDefaultConfigurationDocument Get-PSMetaConfigDocumentInstVersionInfo Get-PSMetaConfigurationProcessed Get-PSReadLineKeyHandler Get-PSReadLineOption Get-PSRepository Get-PSTopConfigurationName Get-PSVersion Get-Package Get-PackageProvider Get-PackageSource Get-PassthroughDevice Get-PositionInfo Get-PowerCLICommunity Get-PowerCLIConfiguration Get-PowerCLIHelp Get-PowerCLIVersion Get-PowerNsxVersion Get-ProviderVdc Get-PublicKeyFromFile Get-PublicKeyFromStore Get-ResourcePool Get-Runspace Get-RunspaceDebug Get-ScsiController Get-ScsiLun Get-ScsiLunPath Get-SecurityInfo Get-SecurityPolicy Get-Snapshot Get-SpbmCapability Get-SpbmCompatibleStorage Get-SpbmEntityConfiguration Get-SpbmFaultDomain Get-SpbmPointInTimeReplica Get-SpbmReplicationGroup Get-SpbmReplicationPair Get-SpbmStoragePolicy Get-Stat Get-StatInterval Get-StatType Get-Tag Get-TagAssignment Get-TagCategory Get-Task Get-Template Get-TimeZone Get-Uptime Get-UsbDevice Get-VAIOFilter Get-VApp Get-VDBlockedPolicy Get-VDPort Get-VDPortgroup Get-VDPortgroupOverridePolicy Get-VDSecurityPolicy Get-VDSwitch Get-VDSwitchPrivateVlan Get-VDTrafficShapingPolicy Get-VDUplinkLacpPolicy Get-VDUplinkTeamingPolicy Get-VDisk Get-VIAccount Get-VICommand Get-VICredentialStoreItem Get-VIEvent Get-VIObjectByVIView Get-VIPermission Get-VIPrivilege Get-VIProperty Get-VIRole Get-VM Get-VMGuest Get-VMHost Get-VMHostAccount Get-VMHostAdvancedConfiguration Get-VMHostAuthentication Get-VMHostAvailableTimeZone Get-VMHostDiagnosticPartition Get-VMHostDisk Get-VMHostDiskPartition Get-VMHostFirewallDefaultPolicy Get-VMHostFirewallException Get-VMHostFirmware Get-VMHostHardware Get-VMHostHba Get-VMHostModule Get-VMHostNetwork Get-VMHostNetworkAdapter Get-VMHostNtpServer Get-VMHostPatch Get-VMHostPciDevice Get-VMHostProfile Get-VMHostProfileImageCacheConfiguration Get-VMHostProfileRequiredInput Get-VMHostProfileStorageDeviceConfiguration Get-VMHostProfileUserConfiguration Get-VMHostProfileVmPortGroupConfiguration Get-VMHostRoute Get-VMHostService Get-VMHostSnmp Get-VMHostStartPolicy Get-VMHostStorage Get-VMHostSysLogServer Get-VMQuestion Get-VMResourceConfiguration Get-VMStartPolicy Get-VTpm Get-VTpmCSR Get-VTpmCertificate Get-VasaProvider Get-VasaStorageArray Get-View Get-VirtualPortGroup Get-VirtualSwitch Get-VmcSddcNetworkService Get-VmcService Get-VsanClusterConfiguration Get-VsanComponent Get-VsanDisk Get-VsanDiskGroup Get-VsanEvacuationPlan Get-VsanFaultDomain Get-VsanIscsiInitiatorGroup Get-VsanIscsiInitiatorGroupTargetAssociation Get-VsanIscsiLun Get-VsanIscsiTarget Get-VsanObject Get-VsanResyncingComponent Get-VsanRuntimeInfo Get-VsanSpaceUsage Get-VsanStat Get-VsanView Get-vRAApplianceServiceStatus Get-vRAAuthorizationRole Get-vRABlueprint Get-vRABusinessGroup Get-vRACatalogItem Get-vRACatalogItemRequestTemplate Get-vRACatalogPrincipal Get-vRAComponentRegistryService Get-vRAComponentRegistryServiceEndpoint Get-vRAComponentRegistryServiceStatus Get-vRAContent Get-vRAContentData Get-vRAContentType Get-vRACustomForm Get-vRAEntitledCatalogItem Get-vRAEntitledService Get-vRAEntitlement Get-vRAExternalNetworkProfile Get-vRAGroupPrincipal Get-vRAIcon Get-vRANATNetworkProfile Get-vRANetworkProfileIPAddressList Get-vRANetworkProfileIPRangeSummary Get-vRAPackage Get-vRAPackageContent Get-vRAPropertyDefinition Get-vRAPropertyGroup Get-vRARequest Get-vRARequestDetail Get-vRAReservation Get-vRAReservationComputeResource Get-vRAReservationComputeResourceMemory Get-vRAReservationComputeResourceNetwork Get-vRAReservationComputeResourceResourcePool Get-vRAReservationComputeResourceStorage Get-vRAReservationPolicy Get-vRAReservationTemplate Get-vRAReservationType Get-vRAResource Get-vRAResourceAction Get-vRAResourceActionRequestTemplate Get-vRAResourceMetric Get-vRAResourceOperation Get-vRAResourceType Get-vRARoutedNetworkProfile Get-vRAService Get-vRAServiceBlueprint Get-vRASourceMachine Get-vRAStorageReservationPolicy Get-vRATenant Get-vRATenantDirectory Get-vRATenantDirectoryStatus Get-vRATenantRole Get-vRAUserPrincipal Get-vRAUserPrincipalGroupMembership Get-vRAVersion Get-vRNIAPIVersion Get-vRNIApplication Get-vRNIApplicationTier Get-vRNIDataSource Get-vRNIDataSourceSNMPConfig Get-vRNIDatastore Get-vRNIDistributedSwitch Get-vRNIDistributedSwitchPortGroup Get-vRNIEntity Get-vRNIEntityName Get-vRNIFirewallRule Get-vRNIFlow Get-vRNIHost Get-vRNIHostVMKNic Get-vRNIIPSet Get-vRNIL2Network Get-vRNINSXManager Get-vRNINodes Get-vRNIProblem Get-vRNIRecommendedRules Get-vRNIRecommendedRulesNsxBundle Get-vRNISecurityGroup Get-vRNISecurityTag Get-vRNIService Get-vRNIServiceGroup Get-vRNIVM Get-vRNIVMvNIC Get-vRNIvCenter Get-vRNIvCenterCluster Get-vRNIvCenterDatacenter Get-vRNIvCenterFolder Grant-NsxSpoofguardNicApproval Import-CIVApp Import-CIVAppTemplate Import-NsxObject Import-PackageProvider Import-PowerShellDataFile Import-SpbmStoragePolicy Import-VApp Import-VMHostProfile Import-vRAContentData Import-vRAIcon Import-vRAPackage Initialize-ConfigurationRuntimeState Install-Module Install-NsxCluster Install-Package Install-PackageProvider Install-Script Install-VMHostPatch Invoke-DrsRecommendation Invoke-NsxCli Invoke-NsxClusterResolveAll Invoke-NsxManagerSync Invoke-NsxRestMethod Invoke-NsxWebRequest Invoke-VMHostProfile Invoke-VMScript Invoke-XpathQuery Invoke-vRADataCollection Invoke-vRARestMethod Invoke-vRATenantDirectorySync Invoke-vRNIRestMethod Join-String Mount-Tools Move-Cluster Move-Datacenter Move-Datastore Move-Folder Move-HardDisk Move-Inventory Move-NsxSecurityPolicyRule Move-ResourcePool Move-Template Move-VApp Move-VDisk Move-VM Move-VMHost New-AdvancedSetting New-AlarmAction New-AlarmActionTrigger New-CDDrive New-CIAccessControlRule New-CIVApp New-CIVAppNetwork New-CIVAppTemplate New-CIVM New-Cluster New-CustomAttribute New-Datacenter New-Datastore New-DatastoreCluster New-DatastoreDrive New-DrsClusterGroup New-DrsRule New-DrsVMHostRule New-DscChecksum New-FloppyDrive New-Folder New-Guid New-HCXAppliance New-HCXMigration New-HCXNetworkExtension New-HCXNetworkMapping New-HCXReplication New-HCXSitePairing New-HCXStaticRoute New-HardDisk New-IScsiHbaTarget New-KmipClientCertificate New-NetworkAdapter New-NfsUser New-NsxAddressSpec New-NsxClusterVxlanConfig New-NsxController New-NsxDynamicCriteriaSpec New-NsxEdge New-NsxEdgeBgpNeighbour New-NsxEdgeCsr New-NsxEdgeFirewallRule New-NsxEdgeInterfaceSpec New-NsxEdgeNatRule New-NsxEdgeOspfArea New-NsxEdgeOspfInterface New-NsxEdgePrefix New-NsxEdgeRedistributionRule New-NsxEdgeSelfSignedCertificate New-NsxEdgeStaticRoute New-NsxEdgeSubInterface New-NsxEdgeSubInterfaceSpec New-NsxFirewallRule New-NsxFirewallSavedConfiguration New-NsxFirewallSection New-NsxIpPool New-NsxIpSet New-NsxLoadBalancerApplicationProfile New-NsxLoadBalancerApplicationRule New-NsxLoadBalancerMemberSpec New-NsxLoadBalancerMonitor New-NsxLoadBalancerPool New-NsxLogicalRouter New-NsxLogicalRouterBgpNeighbour New-NsxLogicalRouterBridge New-NsxLogicalRouterInterface New-NsxLogicalRouterInterfaceSpec New-NsxLogicalRouterOspfArea New-NsxLogicalRouterOspfInterface New-NsxLogicalRouterPrefix New-NsxLogicalRouterRedistributionRule New-NsxLogicalRouterStaticRoute New-NsxLogicalSwitch New-NsxMacSet New-NsxManager New-NsxSecurityGroup New-NsxSecurityPolicy New-NsxSecurityPolicyAssignment New-NsxSecurityPolicyFirewallRuleSpec New-NsxSecurityPolicyGuestIntrospectionSpec New-NsxSecurityPolicyNetworkIntrospectionSpec New-NsxSecurityTag New-NsxSecurityTagAssignment New-NsxSegmentIdRange New-NsxService New-NsxServiceGroup New-NsxSpoofguardPolicy New-NsxSslVpnAuthServer New-NsxSslVpnClientInstallationPackage New-NsxSslVpnIpPool New-NsxSslVpnPrivateNetwork New-NsxSslVpnUser New-NsxTransportZone New-NsxVdsContext New-OSCustomizationNicMapping New-OSCustomizationSpec New-Org New-OrgNetwork New-OrgVdc New-OrgVdcNetwork New-ResourcePool New-ScriptFileInfo New-ScsiController New-Snapshot New-SpbmRule New-SpbmRuleSet New-SpbmStoragePolicy New-StatInterval New-Tag New-TagAssignment New-TagCategory New-Template New-TemporaryFile New-VAIOFilter New-VApp New-VDPortgroup New-VDSwitch New-VDSwitchPrivateVlan New-VDisk New-VICredentialStoreItem New-VIInventoryDrive New-VIPermission New-VIProperty New-VIRole New-VISamlSecurityContext New-VM New-VMHostAccount New-VMHostNetworkAdapter New-VMHostProfile New-VMHostProfileVmPortGroupConfiguration New-VMHostRoute New-VTpm New-VasaProvider New-VcsOAuthSecurityContext New-VirtualPortGroup New-VirtualSwitch New-VsanDisk New-VsanDiskGroup New-VsanFaultDomain New-VsanIscsiInitiatorGroup New-VsanIscsiInitiatorGroupTargetAssociation New-VsanIscsiLun New-VsanIscsiTarget New-vRABusinessGroup New-vRAEntitlement New-vRAExternalNetworkProfile New-vRAGroupPrincipal New-vRANATNetworkProfile New-vRANetworkProfileIPRangeDefinition New-vRAPackage New-vRAPropertyDefinition New-vRAPropertyGroup New-vRAReservation New-vRAReservationNetworkDefinition New-vRAReservationPolicy New-vRAReservationStorageDefinition New-vRARoutedNetworkProfile New-vRAService New-vRAStorageReservationPolicy New-vRATenant New-vRATenantDirectory New-vRAUserPrincipal New-vRNIApplication New-vRNIApplicationTier New-vRNIDataSource Open-VMConsoleWindow Publish-Module Publish-NsxSpoofguardPolicy Publish-Script Register-PSRepository Register-PackageSource Remove-AdvancedSetting Remove-AlarmAction Remove-AlarmActionTrigger Remove-Alias Remove-CDDrive Remove-CIAccessControlRule Remove-CIVApp Remove-CIVAppNetwork Remove-CIVAppTemplate Remove-Cluster Remove-CustomAttribute Remove-Datacenter Remove-Datastore Remove-DatastoreCluster Remove-DrsClusterGroup Remove-DrsRule Remove-DrsVMHostRule Remove-FloppyDrive Remove-Folder Remove-HCXAppliance Remove-HCXNetworkExtension Remove-HCXReplication Remove-HCXSitePairing Remove-HardDisk Remove-IScsiHbaTarget Remove-Inventory Remove-KeyManagementServer Remove-NetworkAdapter Remove-NfsUser Remove-NsxCluster Remove-NsxClusterVxlanConfig Remove-NsxController Remove-NsxDynamicCriteria Remove-NsxDynamicMemberSet Remove-NsxEdge Remove-NsxEdgeBgpNeighbour Remove-NsxEdgeCertificate Remove-NsxEdgeCsr Remove-NsxEdgeFirewallRule Remove-NsxEdgeInterfaceAddress Remove-NsxEdgeNatRule Remove-NsxEdgeOspfArea Remove-NsxEdgeOspfInterface Remove-NsxEdgePrefix Remove-NsxEdgeRedistributionRule Remove-NsxEdgeStaticRoute Remove-NsxEdgeSubInterface Remove-NsxFirewallExclusionListMember Remove-NsxFirewallRule Remove-NsxFirewallRuleMember Remove-NsxFirewallSavedConfiguration Remove-NsxFirewallSection Remove-NsxIpPool Remove-NsxIpSet Remove-NsxIpSetMember Remove-NsxLoadBalancerApplicationProfile Remove-NsxLoadBalancerMonitor Remove-NsxLoadBalancerPool Remove-NsxLoadBalancerPoolMember Remove-NsxLoadBalancerVip Remove-NsxLogicalRouter Remove-NsxLogicalRouterBgpNeighbour Remove-NsxLogicalRouterBridge Remove-NsxLogicalRouterInterface Remove-NsxLogicalRouterOspfArea Remove-NsxLogicalRouterOspfInterface Remove-NsxLogicalRouterPrefix Remove-NsxLogicalRouterRedistributionRule Remove-NsxLogicalRouterStaticRoute Remove-NsxLogicalSwitch Remove-NsxMacSet Remove-NsxSecondaryManager Remove-NsxSecurityGroup Remove-NsxSecurityGroupMember Remove-NsxSecurityPolicy Remove-NsxSecurityPolicyAssignment Remove-NsxSecurityPolicyRule Remove-NsxSecurityPolicyRuleGroup Remove-NsxSecurityPolicyRuleService Remove-NsxSecurityTag Remove-NsxSecurityTagAssignment Remove-NsxSegmentIdRange Remove-NsxService Remove-NsxServiceGroup Remove-NsxSpoofguardPolicy Remove-NsxSslVpnClientInstallationPackage Remove-NsxSslVpnIpPool Remove-NsxSslVpnPrivateNetwork Remove-NsxSslVpnUser Remove-NsxTransportZone Remove-NsxTransportZoneMember Remove-NsxVdsContext Remove-OSCustomizationNicMapping Remove-OSCustomizationSpec Remove-Org Remove-OrgNetwork Remove-OrgVdc Remove-OrgVdcNetwork Remove-PSReadLineKeyHandler Remove-PassthroughDevice Remove-ResourcePool Remove-Snapshot Remove-SpbmStoragePolicy Remove-StatInterval Remove-Tag Remove-TagAssignment Remove-TagCategory Remove-Template Remove-UsbDevice Remove-VAIOFilter Remove-VApp Remove-VDPortGroup Remove-VDSwitch Remove-VDSwitchPhysicalNetworkAdapter Remove-VDSwitchPrivateVlan Remove-VDSwitchVMHost Remove-VDisk Remove-VICredentialStoreItem Remove-VIPermission Remove-VIProperty Remove-VIRole Remove-VM Remove-VMHost Remove-VMHostAccount Remove-VMHostNetworkAdapter Remove-VMHostNtpServer Remove-VMHostProfile Remove-VMHostProfileVmPortGroupConfiguration Remove-VMHostRoute Remove-VTpm Remove-VasaProvider Remove-VirtualPortGroup Remove-VirtualSwitch Remove-VirtualSwitchPhysicalNetworkAdapter Remove-VsanDisk Remove-VsanDiskGroup Remove-VsanFaultDomain Remove-VsanIscsiInitiatorGroup Remove-VsanIscsiInitiatorGroupTargetAssociation Remove-VsanIscsiLun Remove-VsanIscsiTarget Remove-vRABusinessGroup Remove-vRACustomForm Remove-vRAExternalNetworkProfile Remove-vRAGroupPrincipal Remove-vRAIcon Remove-vRANATNetworkProfile Remove-vRAPackage Remove-vRAPrincipalFromTenantRole Remove-vRAPropertyDefinition Remove-vRAPropertyGroup Remove-vRAReservation Remove-vRAReservationNetwork Remove-vRAReservationPolicy Remove-vRAReservationStorage Remove-vRARoutedNetworkProfile Remove-vRAService Remove-vRAStorageReservationPolicy Remove-vRATenant Remove-vRATenantDirectory Remove-vRAUserPrincipal Remove-vRNIApplication Remove-vRNIApplicationTier Remove-vRNIDataSource Repair-NsxEdge Repair-VsanObject Request-vRACatalogItem Request-vRAResourceAction Restart-CIVApp Restart-CIVAppGuest Restart-CIVM Restart-CIVMGuest Restart-VM Restart-VMGuest Restart-VMHost Restart-VMHostService Resume-HCXReplication Revoke-NsxSpoofguardNicApproval Save-Module Save-Package Save-Script Search-Cloud Set-AdvancedSetting Set-AlarmDefinition Set-Annotation Set-CDDrive Set-CIAccessControlRule Set-CINetworkAdapter Set-CIVApp Set-CIVAppNetwork Set-CIVAppStartRule Set-CIVAppTemplate Set-Cluster Set-CustomAttribute Set-Datacenter Set-Datastore Set-DatastoreCluster Set-DrsClusterGroup Set-DrsRule Set-DrsVMHostRule Set-FloppyDrive Set-Folder Set-HCXAppliance Set-HCXMigration Set-HCXReplication Set-HardDisk Set-IScsiHbaTarget Set-KeyManagementServer Set-KmsCluster Set-MarkdownOption Set-NetworkAdapter Set-NfsUser Set-NicTeamingPolicy Set-NodeExclusiveResources Set-NodeManager Set-NodeResourceSource Set-NodeResources Set-NsxEdge Set-NsxEdgeBgp Set-NsxEdgeFirewall Set-NsxEdgeInterface Set-NsxEdgeNat Set-NsxEdgeOspf Set-NsxEdgeRouting Set-NsxFirewallGlobalConfiguration Set-NsxFirewallRule Set-NsxFirewallSavedConfiguration Set-NsxFirewallThreshold Set-NsxLoadBalancer Set-NsxLoadBalancerPoolMember Set-NsxLogicalRouter Set-NsxLogicalRouterBgp Set-NsxLogicalRouterBridging Set-NsxLogicalRouterInterface Set-NsxLogicalRouterOspf Set-NsxLogicalRouterRouting Set-NsxManager Set-NsxManagerRole Set-NsxManagerTimeSettings Set-NsxSecurityPolicy Set-NsxSecurityPolicyFirewallRule Set-NsxSslVpn Set-OSCustomizationNicMapping Set-OSCustomizationSpec Set-Org Set-OrgNetwork Set-OrgVdc Set-OrgVdcNetwork Set-PSCurrentConfigurationNode Set-PSDefaultConfigurationDocument Set-PSMetaConfigDocInsProcessedBeforeMeta Set-PSMetaConfigVersionInfoV2 Set-PSReadLineKeyHandler Set-PSReadLineOption Set-PSRepository Set-PSTopConfigurationName Set-PackageSource Set-PowerCLIConfiguration Set-ResourcePool Set-ScsiController Set-ScsiLun Set-ScsiLunPath Set-SecurityPolicy Set-Snapshot Set-SpbmEntityConfiguration Set-SpbmStoragePolicy Set-StatInterval Set-Tag Set-TagCategory Set-Template Set-VAIOFilter Set-VApp Set-VDBlockedPolicy Set-VDPort Set-VDPortgroup Set-VDPortgroupOverridePolicy Set-VDSecurityPolicy Set-VDSwitch Set-VDTrafficShapingPolicy Set-VDUplinkLacpPolicy Set-VDUplinkTeamingPolicy Set-VDVlanConfiguration Set-VDisk Set-VIPermission Set-VIRole Set-VM Set-VMHost Set-VMHostAccount Set-VMHostAdvancedConfiguration Set-VMHostAuthentication Set-VMHostDiagnosticPartition Set-VMHostFirewallDefaultPolicy Set-VMHostFirewallException Set-VMHostFirmware Set-VMHostHba Set-VMHostModule Set-VMHostNetwork Set-VMHostNetworkAdapter Set-VMHostProfile Set-VMHostProfileImageCacheConfiguration Set-VMHostProfileStorageDeviceConfiguration Set-VMHostProfileUserConfiguration Set-VMHostProfileVmPortGroupConfiguration Set-VMHostRoute Set-VMHostService Set-VMHostSnmp Set-VMHostStartPolicy Set-VMHostStorage Set-VMHostSysLogServer Set-VMQuestion Set-VMResourceConfiguration Set-VMStartPolicy Set-VTpm Set-VirtualPortGroup Set-VirtualSwitch Set-VsanClusterConfiguration Set-VsanFaultDomain Set-VsanIscsiInitiatorGroup Set-VsanIscsiLun Set-VsanIscsiTarget Set-vRABusinessGroup Set-vRACatalogItem Set-vRACustomForm Set-vRAEntitlement Set-vRAExternalNetworkProfile Set-vRANATNetworkProfile Set-vRAReservation Set-vRAReservationNetwork Set-vRAReservationPolicy Set-vRAReservationStorage Set-vRARoutedNetworkProfile Set-vRAService Set-vRAStorageReservationPolicy Set-vRATenant Set-vRATenantDirectory Set-vRAUserPrincipal Set-vRNIDataSourceSNMPConfig Show-Markdown Start-CIVApp Start-CIVM Start-HCXMigration Start-HCXReplication Start-SpbmReplicationFailover Start-SpbmReplicationPrepareFailover Start-SpbmReplicationPromote Start-SpbmReplicationReverse Start-SpbmReplicationTestFailover Start-ThreadJob Start-VApp Start-VM Start-VMHost Start-VMHostService Start-VsanClusterDiskUpdate Start-VsanClusterRebalance Start-VsanEncryptionConfiguration Stop-CIVApp Stop-CIVAppGuest Stop-CIVM Stop-CIVMGuest Stop-SpbmReplicationTestFailover Stop-Task Stop-VApp Stop-VM Stop-VMGuest Stop-VMHost Stop-VMHostService Stop-VsanClusterRebalance Suspend-CIVApp Suspend-CIVM Suspend-HCXReplication Suspend-VM Suspend-VMGuest Suspend-VMHost Sync-SpbmReplicationGroup Test-ConflictingResources Test-HCXMigration Test-HCXReplication Test-Json Test-ModuleReloadRequired Test-MofInstanceText Test-NodeManager Test-NodeResourceSource Test-NodeResources 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diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem 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копироватьфайл краткоепредставлениеошибки лев макс местноевремя месяц мин минута монопольныйрежим найти найтинедопустимыесимволыxml найтиокнопонавигационнойссылке найтипомеченныенаудаление найтипоссылкам найтифайлы началогода началодня началоквартала началомесяца началоминуты началонедели началочаса начатьзапросразрешенияпользователя начатьзапускприложения начатькопированиефайла начатьперемещениефайла начатьподключениевнешнейкомпоненты начатьподключениерасширенияработыскриптографией начатьподключениерасширенияработысфайлами начатьпоискфайлов начатьполучениекаталогавременныхфайлов начатьполучениекаталогадокументов начатьполучениерабочегокаталогаданныхпользователя начатьполучениефайлов начатьпомещениефайла начатьпомещениефайлов начатьсозданиедвоичныхданныхизфайла начатьсозданиекаталога начатьтранзакцию начатьудалениефайлов начатьустановкувнешнейкомпоненты начатьустановкурасширенияработыскриптографией начатьустановкурасширенияработысфайлами неделягода необходимостьзавершениясоединения номерсеансаинформационнойбазы номерсоединенияинформационнойбазы нрег нстр обновитьинтерфейс обновитьнумерациюобъектов обновитьповторноиспользуемыезначения обработкапрерыванияпользователя объединитьфайлы окр описаниеошибки оповестить оповеститьобизменении отключитьобработчикзапросанастроекклиенталицензирования отключитьобработчикожидания отключитьобработчикоповещения открытьзначение открытьиндекссправки открытьсодержаниесправки открытьсправку открытьформу открытьформумодально отменитьтранзакцию очиститьжурналрегистрации очиститьнастройкипользователя очиститьсообщения параметрыдоступа перейтипонавигационнойссылке переместитьфайл подключитьвнешнююкомпоненту подключитьобработчикзапросанастроекклиенталицензирования подключитьобработчикожидания подключитьобработчикоповещения подключитьрасширениеработыскриптографией подключитьрасширениеработысфайлами подробноепредставлениеошибки показатьвводдаты показатьвводзначения показатьвводстроки показатьвводчисла показатьвопрос показатьзначение показатьинформациюобошибке показатьнакарте показатьоповещениепользователя показатьпредупреждение полноеимяпользователя получитьcomобъект получитьxmlтип получитьадреспоместоположению получитьблокировкусеансов получитьвремязавершенияспящегосеанса получитьвремязасыпанияпассивногосеанса получитьвремяожиданияблокировкиданных получитьданныевыбора получитьдополнительныйпараметрклиенталицензирования получитьдопустимыекодылокализации получитьдопустимыечасовыепояса получитьзаголовокклиентскогоприложения получитьзаголовоксистемы получитьзначенияотборажурналарегистрации получитьидентификаторконфигурации получитьизвременногохранилища получитьимявременногофайла получитьимяклиенталицензирования получитьинформациюэкрановклиента получитьиспользованиежурналарегистрации получитьиспользованиесобытияжурналарегистрации получитькраткийзаголовокприложения получитьмакетоформления получитьмаскувсефайлы получитьмаскувсефайлыклиента получитьмаскувсефайлысервера получитьместоположениепоадресу получитьминимальнуюдлинупаролейпользователей получитьнавигационнуюссылку получитьнавигационнуюссылкуинформационнойбазы получитьобновлениеконфигурациибазыданных получитьобновлениепредопределенныхданныхинформационнойбазы получитьобщиймакет получитьобщуюформу получитьокна получитьоперативнуюотметкувремени получитьотключениебезопасногорежима получитьпараметрыфункциональныхопцийинтерфейса получитьполноеимяпредопределенногозначения получитьпредставлениянавигационныхссылок получитьпроверкусложностипаролейпользователей получитьразделительпути получитьразделительпутиклиента получитьразделительпутисервера получитьсеансыинформационнойбазы получитьскоростьклиентскогосоединения получитьсоединенияинформационнойбазы получитьсообщенияпользователю получитьсоответствиеобъектаиформы получитьсоставстандартногоинтерфейсаodata получитьструктурухранениябазыданных получитьтекущийсеансинформационнойбазы получитьфайл получитьфайлы получитьформу получитьфункциональнуюопцию получитьфункциональнуюопциюинтерфейса 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стрразделить стрсоединить стрсравнить стрчисловхождений стрчислострок стршаблон текущаядата текущаядатасеанса текущаяуниверсальнаядата текущаяуниверсальнаядатавмиллисекундах текущийвариантинтерфейсаклиентскогоприложения текущийвариантосновногошрифтаклиентскогоприложения текущийкодлокализации текущийрежимзапуска текущийязык текущийязыксистемы тип типзнч транзакцияактивна трег удалитьданныеинформационнойбазы удалитьизвременногохранилища удалитьобъекты удалитьфайлы универсальноевремя установитьбезопасныйрежим установитьбезопасныйрежимразделенияданных установитьблокировкусеансов установитьвнешнююкомпоненту установитьвремязавершенияспящегосеанса установитьвремязасыпанияпассивногосеанса установитьвремяожиданияблокировкиданных установитьзаголовокклиентскогоприложения установитьзаголовоксистемы установитьиспользованиежурналарегистрации установитьиспользованиесобытияжурналарегистрации установитькраткийзаголовокприложения установитьминимальнуюдлинупаролейпользователей установитьмонопольныйрежим установитьнастройкиклиенталицензирования установитьобновлениепредопределенныхданныхинформационнойбазы установитьотключениебезопасногорежима установитьпараметрыфункциональныхопцийинтерфейса установитьпривилегированныйрежим установитьпроверкусложностипаролейпользователей установитьрасширениеработыскриптографией установитьрасширениеработысфайлами установитьсоединениесвнешнимисточникомданных установитьсоответствиеобъектаиформы установитьсоставстандартногоинтерфейсаodata установитьчасовойпоясинформационнойбазы установитьчасовойпояссеанса формат цел час часовойпояс часовойпояссеанса число числопрописью этоадресвременногохранилища wsссылки библиотекакартинок библиотекамакетовоформлениякомпоновкиданных библиотекастилей бизнеспроцессы внешниеисточникиданных внешниеобработки внешниеотчеты встроенныепокупки главныйинтерфейс главныйстиль документы доставляемыеуведомления журналыдокументов задачи информацияобинтернетсоединении использованиерабочейдаты историяработыпользователя константы критерииотбора метаданные обработки отображениерекламы отправкадоставляемыхуведомлений отчеты панельзадачос параметрзапуска параметрысеанса перечисления планывидоврасчета планывидовхарактеристик планыобмена планысчетов полнотекстовыйпоиск пользователиинформационнойбазы последовательности проверкавстроенныхпокупок рабочаядата расширенияконфигурации регистрыбухгалтерии регистрынакопления регистрырасчета регистрысведений регламентныезадания сериализаторxdto справочники средствагеопозиционирования средствакриптографии средствамультимедиа средстваотображениярекламы средствапочты средствателефонии фабрикаxdto файловыепотоки фоновыезадания хранилищанастроек хранилищевариантовотчетов хранилищенастроекданныхформ хранилищеобщихнастроек хранилищепользовательскихнастроекдинамическихсписков хранилищепользовательскихнастроекотчетов хранилищесистемныхнастроек ",class:"webцвета windowsцвета windowsшрифты библиотекакартинок рамкистиля символы цветастиля шрифтыстиля 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DeviceStreams DeviceWrite DeviceWriteBuffer DGaussianWavelet DiacriticalPositioning Diagonal DiagonalizableMatrixQ DiagonalMatrix DiagonalMatrixQ Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DictionaryWordQ DifferenceDelta DifferenceOrder DifferenceQuotient DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitalSignature DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralAngle DihedralGroup Dilation DimensionalCombinations DimensionalMeshComponents DimensionReduce DimensionReducerFunction DimensionReduction Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletBeta DirichletCharacter DirichletCondition DirichletConvolve DirichletDistribution DirichletEta DirichletL DirichletLambda DirichletTransform DirichletWindow DisableConsolePrintPacket DisableFormatting DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLimit DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscreteMaxLimit DiscreteMinLimit DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform DiscretizeGraphics DiscretizeRegion Discriminant DisjointQ Disjunction Disk DiskBox DiskMatrix DiskSegment Dispatch DispatchQ DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceMatrix DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers DivideSides Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentGenerator DocumentGeneratorInformation DocumentGeneratorInformationData DocumentGenerators DocumentNotebook DocumentWeightingRules Dodecahedron DomainRegistrationInformation DominantColors DOSTextFormat Dot DotDashed DotEqual DotLayer DotPlusLayer Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DropoutLayer DSolve DSolveValue Dt DualLinearProgramming DualPolyhedron DualSystemsModel DumpGet DumpSave DuplicateFreeQ Duration Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicGeoGraphics DynamicImage DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptionsE EarthImpactData EarthquakeData EccentricityCentrality Echo EchoFunction EclipseType EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeContract EdgeCost EdgeCount EdgeCoverQ EdgeCycleMatrix EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight EdgeWeightedGraphQ Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData ElementwiseLayer ElidedForms Eliminate EliminationOrder Ellipsoid EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmbedCode EmbeddedHTML EmbeddedService EmbeddingLayer EmbeddingObject EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EmptyRegion EnableConsolePrintPacket Enabled Encode Encrypt EncryptedObject EncryptFile End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfBuffer EndOfFile EndOfLine EndOfString EndPackage EngineEnvironment EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entity EntityClass EntityClassList EntityCopies EntityFunction EntityGroup EntityInstance EntityList EntityPrefetch EntityProperties EntityProperty EntityPropertyClass EntityRegister EntityStore EntityStores EntityTypeName EntityUnregister EntityValue Entropy EntropyFilter Environment Epilog EpilogFunction Equal EqualColumns EqualRows EqualTilde EqualTo EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EscapeRadius EstimatedBackground EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerAngles EulerCharacteristic EulerE EulerGamma EulerianGraphQ EulerMatrix EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluateScheduledTask EvaluationBox EvaluationCell EvaluationCompletionAction EvaluationData EvaluationElements EvaluationEnvironment EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels EventSeries ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludedLines ExcludedPhysicalQuantities ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog ExoplanetData Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi ExpirationDate Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportByteArray ExportForm ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpressionUUID ExpToTrig ExtendedEntityClass ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalBundle ExternalCall ExternalDataCharacterEncoding ExternalEvaluate ExternalFunction ExternalFunctionName ExternalObject ExternalOptions ExternalSessionObject ExternalSessions ExternalTypeSignature ExternalValue Extract ExtractArchive ExtractLayer ExtremeValueDistributionFaceForm FaceGrids FaceGridsStyle FacialFeatures Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail Failure FailureAction FailureDistribution FailureQ False FareySequence FARIMAProcess FeatureDistance FeatureExtract FeatureExtraction FeatureExtractor FeatureExtractorFunction FeatureNames FeatureNearest FeatureSpacePlot FeatureSpacePlot3D FeatureTypes FEDisableConsolePrintPacket FeedbackLinearize FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket FetalGrowthData Fibonacci Fibonorial FieldCompletionFunction FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileConvert FileDate FileExistsQ FileExtension FileFormat FileHandler FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameForms FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileSize FileSystemMap FileSystemScan FileTemplate FileTemplateApply FileType FilledCurve FilledCurveBox FilledCurveBoxOptions Filling FillingStyle FillingTransform FilteredEntityClass FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindAnomalies FindArgMax FindArgMin FindChannels FindClique FindClusters FindCookies FindCurvePath FindCycle FindDevices FindDistribution FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEdgeIndependentPaths FindEquationalProof FindEulerianCycle FindExternalEvaluators FindFaces FindFile FindFit FindFormula FindFundamentalCycles FindGeneratingFunction FindGeoLocation FindGeometricConjectures FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindHamiltonianPath FindHiddenMarkovStates FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMatchingColor FindMaximum FindMaximumFlow FindMaxValue FindMeshDefects FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindMoleculeSubstructure FindPath FindPeaks FindPermutation FindPostmanTour FindProcessParameters FindRepeat FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindSpanningTree FindSystemModelEquilibrium FindTextualAnswer FindThreshold FindTransientRepeat FindVertexCover FindVertexCut FindVertexIndependentPaths Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstCase FirstPassageTimeDistribution FirstPosition FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FitRegularization FittedModel FixedOrder FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlattenLayer FlatTopWindow FlipView Floor FlowPolynomial FlushPrintOutputPacket Fold FoldList FoldPair FoldPairList FollowRedirects Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FormControl FormFunction FormLayoutFunction FormObject FormPage FormTheme FormulaData FormulaLookup FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalGaussianNoiseProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameRate FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrenetSerretSystem FrequencySamplingFilterKernel FresnelC FresnelF FresnelG FresnelS Friday FrobeniusNumber FrobeniusSolve FromAbsoluteTime FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS FromEntity FromJulianDate FromLetterNumber FromPolarCoordinates FromRomanNumeral FromSphericalCoordinates FromUnixTime Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullInformationOutputRegulator FullOptions FullRegion FullSimplify Function FunctionCompile FunctionCompileExport FunctionCompileExportByteArray FunctionCompileExportLibrary FunctionCompileExportString FunctionDomain FunctionExpand FunctionInterpolation FunctionPeriod FunctionRange FunctionSpace FussellVeselyImportanceGaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins GalaxyData GalleryView Gamma GammaDistribution GammaRegularized GapPenalty GARCHProcess GatedRecurrentLayer Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianOrthogonalMatrixDistribution GaussianSymplecticMatrixDistribution GaussianUnitaryMatrixDistribution GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateAsymmetricKeyPair GenerateConditions GeneratedCell GeneratedDocumentBinding GenerateDerivedKey GenerateDigitalSignature GenerateDocument GeneratedParameters GeneratedQuantityMagnitudes GenerateHTTPResponse GenerateSecuredAuthenticationKey GenerateSymmetricKey GeneratingFunction GeneratorDescription GeneratorHistoryLength GeneratorOutputType Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeoAntipode GeoArea GeoArraySize GeoBackground GeoBoundingBox GeoBounds GeoBoundsRegion GeoBubbleChart GeoCenter GeoCircle GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDisk GeoDisplacement GeoDistance GeoDistanceList GeoElevationData GeoEntities GeoGraphics GeogravityModelData GeoGridDirectionDifference GeoGridLines GeoGridLinesStyle GeoGridPosition GeoGridRange GeoGridRangePadding GeoGridUnitArea GeoGridUnitDistance GeoGridVector GeoGroup GeoHemisphere GeoHemisphereBoundary GeoHistogram GeoIdentify GeoImage GeoLabels GeoLength GeoListPlot GeoLocation GeologicalPeriodData GeomagneticModelData GeoMarker GeometricAssertion GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricScene GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoModel GeoNearest GeoPath GeoPosition GeoPositionENU GeoPositionXYZ GeoProjection GeoProjectionData GeoRange GeoRangePadding GeoRegionValuePlot GeoResolution GeoScaleBar GeoServer GeoSmoothHistogram GeoStreamPlot GeoStyling GeoStylingImageFunction GeoVariant GeoVector GeoVectorENU GeoVectorPlot GeoVectorXYZ GeoVisibleRegion GeoVisibleRegionBoundary GeoWithinQ GeoZoomLevel GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenAngle GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter GrammarApply GrammarRules GrammarToken Graph Graph3D GraphAssortativity GraphAutomorphismGroup GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel Greater GreaterEqual GreaterEqualLess GreaterEqualThan GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterThan GreaterTilde Green GreenFunction Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupBy GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators Groupings GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain GroupTogetherGrouping GroupTogetherNestedGrouping GrowCutComponents Gudermannian GuidedFilter GumbelDistributionHaarWavelet HadamardMatrix HalfLine HalfNormalDistribution HalfPlane HalfSpace HamiltonianGraphQ HammingDistance HammingWindow HandlerFunctions HandlerFunctionsKeys HankelH1 HankelH2 HankelMatrix HankelTransform HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash Haversine HazardFunction Head HeadCompose HeaderLines Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings Here HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenMarkovProcess HiddenSurface Highlighted HighlightGraph HighlightImage HighlightMesh HighpassFilter HigmanSimsGroupHS HilbertCurve HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HistoricalPeriodData HitMissTransform HITSCentrality HjorthDistribution HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HostLookup HotellingTSquareDistribution HoytDistribution HTMLSave HTTPErrorResponse HTTPRedirect HTTPRequest HTTPRequestData HTTPResponse Hue HumanGrowthData HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyperplane Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestDataI IconData Iconize IconizedObject IconRules Icosahedron Identity IdentityMatrix If IgnoreCase IgnoreDiacritics IgnorePunctuation IgnoreSpellCheck IgnoringInactive Im Image Image3D Image3DProjection Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageApplyIndexed ImageAspectRatio ImageAssemble ImageAugmentationLayer ImageBoundingBoxes ImageCache ImageCacheValid ImageCapture ImageCaptureFunction ImageCases ImageChannels ImageClip ImageCollage ImageColorSpace ImageCompose ImageContainsQ ImageContents ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDisplacements ImageDistance ImageEffect ImageExposureCombine ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageFocusCombine ImageForestingComponents ImageFormattingWidth ImageForwardTransformation ImageGraphics ImageHistogram ImageIdentify ImageInstanceQ ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarker ImageMarkers ImageMeasurements ImageMesh ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImagePosition ImagePreviewFunction ImagePyramid ImagePyramidApply ImageQ ImageRangeCache ImageRecolor ImageReflect ImageRegion ImageResize ImageResolution ImageRestyle ImageRotate ImageRotated ImageSaliencyFilter ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions ImagingDevice ImplicitRegion Implies Import ImportAutoReplacements ImportByteArray ImportOptions ImportString ImprovementImportance In Inactivate Inactive IncidenceGraph IncidenceList IncidenceMatrix IncludeAromaticBonds IncludeConstantBasis IncludeDefinitions IncludeDirectories IncludeFileExtension IncludeGeneratorTasks IncludeHydrogens IncludeInflections IncludeMetaInformation IncludePods IncludeQuantities IncludeRelatedTables IncludeSingularTerm IncludeWindowTimes Increment IndefiniteMatrixQ Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentPhysicalQuantity IndependentUnit IndependentUnitDimension IndependentVertexSetQ Indeterminate IndeterminateThreshold IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers InfiniteLine InfinitePlane Infinity Infix InflationAdjust InflationMethod Information InformationData InformationDataGrid Inherited InheritScope InhomogeneousPoissonProcess InitialEvaluationHistory Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InitializationObjects InitializationValue Initialize InitialSeeding InlineCounterAssignments InlineCounterIncrements InlineRules Inner InnerPolygon InnerPolyhedron Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionFunction InsertionPointObject InsertLinebreaks InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Insphere Install InstallService InstanceNormalizationLayer InString Integer IntegerDigits IntegerExponent IntegerLength IntegerName IntegerPart IntegerPartitions IntegerQ IntegerReverse Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction Interpreter InterpretTemplate InterquartileRange Interrupt InterruptSettings IntersectingQ Intersection Interval IntervalIntersection IntervalMarkers IntervalMarkersStyle IntervalMemberQ IntervalSlider IntervalUnion Into Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHankelTransform InverseHaversine InverseImagePyramid InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InverseMellinTransform InversePermutation InverseRadon InverseRadonTransform InverseSeries InverseShortTimeFourier InverseSpectrogram InverseSurvivalFunction InverseTransformedRegion InverseWaveletTransform InverseWeierstrassP InverseWishartMatrixDistribution InverseZTransform Invisible InvisibleApplication InvisibleTimes IPAddress IrreduciblePolynomialQ IslandData IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemAspectRatio ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcessJaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join JoinAcross Joined JoinedCurve JoinedCurveBox JoinedCurveBoxOptions JoinForm JordanDecomposition JordanModelDecomposition JulianDate JuliaSetBoettcher JuliaSetIterationCount JuliaSetPlot JuliaSetPointsK KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KEdgeConnectedComponents KEdgeConnectedGraphQ KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelFunction KernelMixtureDistribution Kernels Ket Key KeyCollisionFunction KeyComplement KeyDrop KeyDropFrom KeyExistsQ KeyFreeQ KeyIntersection KeyMap KeyMemberQ KeypointStrength Keys KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Khinchin KillProcess KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnapsackSolve KnightTourGraph KnotData KnownUnitQ KochCurve KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter KVertexConnectedComponents KVertexConnectedGraphQLABColor Label Labeled LabeledSlider LabelingFunction LabelingSize LabelStyle LabelVisibility LaguerreL LakeData LambdaComponents LambertW LaminaData LanczosWindow LandauDistribution Language LanguageCategory LanguageData LanguageIdentify LanguageOptions LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCHColor LCM LeaderSize LeafCount LeapYearQ LearnDistribution LearnedDistribution LearningRate LearningRateMultipliers LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessEqualThan LessFullEqual LessGreater LessLess LessSlantEqual LessThan LessTilde LetterCharacter LetterCounts LetterNumber LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryDataType LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox Line3DBoxOptions LinearFilter LinearFractionalOptimization LinearFractionalTransform LinearGradientImage LinearizingTransformationData LinearLayer LinearModelFit LinearOffsetFunction LinearOptimization LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBoxOptions LineBreak LinebreakAdjustments LineBreakChart LinebreakSemicolonWeighting LineBreakWithin LineColor LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRankCentrality LinkRead LinkReadHeld LinkReadyQ Links LinkService LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot ListDensityPlot3D Listen ListFormat ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListSliceContourPlot3D ListSliceDensityPlot3D ListSliceVectorPlot3D ListStepPlot ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalAdaptiveBinarize LocalCache LocalClusteringCoefficient LocalizeDefinitions LocalizeVariables LocalObject LocalObjects LocalResponseNormalizationLayer LocalSubmit LocalSymbol LocalTime LocalTimeZone LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogisticSigmoid LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongestOrderedSequence LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow LongShortTermMemoryLayer Lookup Loopback LoopFreeGraphQ LossFunction LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowerTriangularMatrixQ LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LunarEclipse LUVColor LyapunovSolve LyonsGroupLyMachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MailAddressValidation MailExecute MailFolder MailItem MailReceiverFunction MailResponseFunction MailSearch MailServerConnect MailServerConnection MailSettings MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules ManagedLibraryExpressionID ManagedLibraryExpressionQ MandelbrotSetBoettcher MandelbrotSetDistance MandelbrotSetIterationCount MandelbrotSetMemberQ MandelbrotSetPlot MangoldtLambda ManhattanDistance Manipulate Manipulator MannedSpaceMissionData MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarchenkoPasturDistribution MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicalFunctionData MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixNormalDistribution MatrixPlot MatrixPower MatrixPropertyDistribution MatrixQ MatrixRank MatrixTDistribution Max MaxBend MaxCellMeasure MaxColorDistance MaxDetect MaxDuration MaxExtraBandwidths MaxExtraConditions MaxFeatureDisplacement MaxFeatures MaxFilter MaximalBy Maximize MaxItems MaxIterations MaxLimit MaxMemoryUsed MaxMixtureKernels MaxOverlapFraction MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxTrainingRounds MaxValue MaxwellDistribution MaxWordGap McLaughlinGroupMcL Mean MeanAbsoluteLossLayer MeanAround MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter MeanSquaredLossLayer Median MedianDeviation MedianFilter MedicalTestData Medium MeijerG MeijerGReduce MeixnerDistribution MellinConvolve MellinTransform MemberQ MemoryAvailable MemoryConstrained MemoryConstraint MemoryInUse MengerMesh Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuList MenuPacket MenuSortingValue MenuStyle MenuView Merge MergeDifferences MergingFunction MersennePrimeExponent MersennePrimeExponentQ Mesh MeshCellCentroid MeshCellCount MeshCellHighlight MeshCellIndex MeshCellLabel MeshCellMarker MeshCellMeasure MeshCellQuality MeshCells MeshCellShapeFunction MeshCellStyle MeshCoordinates MeshFunctions MeshPrimitives MeshQualityGoal MeshRange MeshRefinementFunction MeshRegion MeshRegionQ MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageObject MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation MeteorShowerData Method MethodOptions MexicanHatWavelet MeyerWavelet Midpoint Min MinColorDistance MinDetect MineralData MinFilter MinimalBy MinimalPolynomial MinimalStateSpaceModel Minimize MinimumTimeIncrement MinIntervalSize MinkowskiQuestionMark MinLimit MinMax MinorPlanetData Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingBehavior MissingDataMethod MissingDataRules MissingQ MissingString MissingStyle MissingValuePattern MittagLefflerE MixedFractionParts MixedGraphQ MixedMagnitude MixedRadix MixedRadixQuantity MixedUnit MixtureDistribution Mod Modal Mode Modular ModularInverse ModularLambda Module Modulus MoebiusMu Molecule MoleculeContainsQ MoleculeEquivalentQ MoleculeGraph MoleculeModify MoleculePattern MoleculePlot MoleculePlot3D MoleculeProperty MoleculeQ MoleculeValue Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction MomentOfInertia Monday Monitor MonomialList MonomialOrder MonsterGroupM MoonPhase MoonPosition MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform MortalityData Most MountainData MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovieData MovingAverage MovingMap MovingMedian MoyalDistribution Multicolumn MultiedgeStyle MultigraphQ MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity MultiplySides Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistributionN NakagamiDistribution NameQ Names NamespaceBox NamespaceBoxOptions Nand NArgMax NArgMin NBernoulliB NBodySimulation NBodySimulationData NCache NDEigensystem NDEigenvalues NDSolve NDSolveValue Nearest NearestFunction NearestNeighborGraph NearestTo NebulaData NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeDefiniteMatrixQ NegativeIntegers NegativeMultinomialDistribution NegativeRationals NegativeReals NegativeSemidefiniteMatrixQ NeighborhoodData NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestGraph NestList NestWhile NestWhileList NetAppend NetBidirectionalOperator NetChain NetDecoder NetDelete NetDrop NetEncoder NetEvaluationMode NetExtract NetFlatten NetFoldOperator NetGraph NetInformation NetInitialize NetInsert NetInsertSharedArrays NetJoin NetMapOperator NetMapThreadOperator NetMeasurements NetModel NetNestOperator NetPairEmbeddingOperator NetPort NetPortGradient NetPrepend NetRename NetReplace NetReplacePart NetSharedArray NetStateObject NetTake NetTrain NetTrainResultsObject NetworkPacketCapture NetworkPacketRecording NetworkPacketRecordingDuring NetworkPacketTrace NeumannValue NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextCell NextDate NextPrime NextScheduledTaskTime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NightHemisphere NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants NondimensionalizationTransform None NoneTrue NonlinearModelFit NonlinearStateSpaceModel NonlocalMeansFilter NonNegative NonNegativeIntegers NonNegativeRationals NonNegativeReals NonPositive NonPositiveIntegers NonPositiveRationals NonPositiveReals Nor NorlundB Norm Normal NormalDistribution NormalGrouping NormalizationLayer Normalize Normalized NormalizedSquaredEuclideanDistance NormalMatrixQ NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookImport NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookTemplate NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde Nothing NotHumpDownHump NotHumpEqual NotificationFunction NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar Now NoWhitespace NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms NuclearExplosionData NuclearReactorData Null NullRecords NullSpace NullWords Number NumberCompose NumberDecompose NumberExpand NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberLinePlot NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumeratorDenominator NumericalOrder NumericalSort NumericArray NumericArrayQ NumericArrayType NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlotO ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OceanData Octahedron OddQ Off Offset OLEData On ONanGroupON Once OneIdentity Opacity OpacityFunction OpacityFunctionScaling Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionalElement OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering OrderingBy OrderingLayer Orderless OrderlessPatternSequence OrnsteinUhlenbeckProcess Orthogonalize OrthogonalMatrixQ Out Outer OuterPolygon OuterPolyhedron OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OverwriteTarget OwenT OwnValuesPackage PackingMethod PaddedForm Padding PaddingLayer PaddingSize PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageTheme PageWidth Pagination PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath PalindromeQ Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo Parallelepiped ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds Parallelogram ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParametricRegion ParentBox ParentCell ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParentNotebook ParetoDistribution ParetoPickandsDistribution ParkData Part PartBehavior PartialCorrelationFunction PartialD ParticleAcceleratorData ParticleData Partition PartitionGranularity PartitionsP PartitionsQ PartLayer PartOfSpeech PartProtection ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteAutoQuoteCharacters PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PeakDetect PeanoCurve PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PercentForm PerfectNumber PerfectNumberQ PerformanceGoal Perimeter PeriodicBoundaryCondition PeriodicInterpolation Periodogram PeriodogramArray Permanent Permissions PermissionsGroup PermissionsGroupMemberQ PermissionsGroups PermissionsKey PermissionsKeys PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PerpendicularBisector PersistenceLocation PersistenceTime PersistentObject PersistentObjects PersistentValue PersonData PERTDistribution PetersenGraph PhaseMargins PhaseRange PhysicalSystemData Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest PingTime Pink PitchRecognize Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarAngle PlanarGraph PlanarGraphQ PlanckRadiationLaw PlaneCurveData PlanetaryMoonData PlanetData PlantData Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLabels PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangeClipPlanesStyle PlotRangePadding PlotRegion PlotStyle PlotTheme Pluralize Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox Point3DBoxOptions PointBox PointBoxOptions PointFigureChart PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonalNumber PolygonAngle PolygonBox PolygonBoxOptions PolygonCoordinates PolygonDecomposition PolygonHoleScale PolygonIntersections PolygonScale Polyhedron PolyhedronAngle PolyhedronCoordinates PolyhedronData PolyhedronDecomposition PolyhedronGenus PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PoolingLayer PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position PositionIndex Positive PositiveDefiniteMatrixQ PositiveIntegers PositiveRationals PositiveReals PositiveSemidefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerRange PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement Predict PredictionRoot PredictorFunction PredictorInformation PredictorMeasurements PredictorMeasurementsObject PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependLayer PrependTo PreprocessingRules PreserveColor PreserveImageOptions Previous PreviousCell PreviousDate PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitivePolynomialQ PrimitiveRoot PrimitiveRootList PrincipalComponents PrincipalValue Print PrintableASCIIQ PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment Printout3D Printout3DPreviewer PrintPrecision 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RangeSpecification RankedMax RankedMin RarerProbability Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadByteArray ReadLine ReadList ReadProtected ReadString Real RealAbs RealBlockDiagonalForm RealDigits RealExponent Reals RealSign Reap RecognitionPrior RecognitionThreshold Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RectangularRepeatingElement RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate Region RegionBinarize RegionBoundary RegionBounds RegionCentroid RegionDifference RegionDimension RegionDisjoint RegionDistance RegionDistanceFunction RegionEmbeddingDimension RegionEqual RegionFunction RegionImage RegionIntersection RegionMeasure RegionMember RegionMemberFunction RegionMoment RegionNearest RegionNearestFunction RegionPlot RegionPlot3D RegionProduct RegionQ RegionResize RegionSize RegionSymmetricDifference RegionUnion RegionWithin RegisterExternalEvaluator RegularExpression Regularization RegularlySampledQ RegularPolygon ReIm ReImLabels ReImPlot ReImStyle Reinstall RelationalDatabase RelationGraph Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot RemoteAuthorizationCaching RemoteConnect RemoteConnectionObject RemoteFile RemoteRun RemoteRunProcess Remove RemoveAlphaChannel RemoveAsynchronousTask RemoveAudioStream RemoveBackground RemoveChannelListener RemoveChannelSubscribers Removed RemoveDiacritics RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RemoveUsers RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart RepairMesh Repeated RepeatedNull RepeatedString RepeatedTiming RepeatingElement Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated ReplicateLayer RequiredPhysicalQuantities Resampling ResamplingAlgorithmData ResamplingMethod Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask ReshapeLayer Residue ResizeLayer Resolve ResourceAcquire ResourceData ResourceFunction ResourceObject ResourceRegister ResourceRemove ResourceSearch ResourceSubmissionObject ResourceSubmit ResourceSystemBase ResourceUpdate ResponseForm Rest RestartInterval Restricted Resultant ResumePacket Return ReturnEntersInput ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnReceiptFunction ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseSort ReverseSortBy ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ RiemannXi Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightComposition RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity RollPitchYawAngles RollPitchYawMatrix RomanNumeral Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RSolveValue RudinShapiro RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulePlot RulerUnits Run RunProcess RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilaritySameQ SameTest SampledEntityClass SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SASTriangle SatelliteData SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveConnection SaveDefinitions SavitzkyGolayMatrix SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTask ScheduledTaskActiveQ ScheduledTaskInformation ScheduledTaskInformationData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScientificNotationThreshold ScorerGi ScorerGiPrime ScorerHi ScorerHiPrime ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptForm ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition SearchAdjustment SearchIndexObject SearchIndices SearchQueryString SearchResultObject Sec Sech 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SequenceSplit Series SeriesCoefficient SeriesData ServiceConnect ServiceDisconnect ServiceExecute ServiceObject ServiceRequest ServiceResponse ServiceSubmit SessionSubmit SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetCloudDirectory SetCookies SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPermissions SetPrecision SetProperty SetSecuredAuthenticationKey SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemModel SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetUsers SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share SharingList Sharpen ShearingMatrix ShearingTransform ShellRegion ShenCastanMatrix ShiftedGompertzDistribution ShiftRegisterSequence Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow 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SkinStyle Skip SliceContourPlot3D SliceDensityPlot3D SliceDistribution SliceVectorPlot3D Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDecomposition SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SnDispersion Snippet SnubPolyhedron SocialMediaData Socket SocketConnect SocketListen SocketListener SocketObject SocketOpen SocketReadMessage SocketReadyQ Sockets SocketWaitAll SocketWaitNext SoftmaxLayer SokalSneathDissimilarity SolarEclipse SolarSystemFeatureData SolidAngle SolidData SolidRegionQ Solve SolveAlways SolveDelayed Sort SortBy SortedBy SortedEntityClass Sound SoundAndGraphics SoundNote SoundVolume SourceLink Sow Space SpaceCurveData SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution SpatialMedian SpatialTransformationLayer Speak SpeakTextPacket SpearmanRankTest SpearmanRho SpeciesData SpecificityGoal SpectralLineData Spectrogram SpectrogramArray Specularity SpeechRecognize SpeechSynthesize SpellingCorrection SpellingCorrectionList SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SpherePoints SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SphericalShell SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquareMatrixQ SquareRepeatingElement SquaresR SquareSubset 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WronskianXMLElement XMLObject XMLTemplate Xnor Xor XYZColorYellow Yesterday YuleDissimilarityZernikeR ZeroSymmetric ZeroTest ZeroWidthTimes Zeta ZetaZero ZIPCodeData ZipfDistribution ZoomCenter ZoomFactor ZTest ZTransform$Aborted $ActivationGroupID $ActivationKey $ActivationUserRegistered $AddOnsDirectory $AllowExternalChannelFunctions $AssertFunction $Assumptions $AsynchronousTask $AudioInputDevices $AudioOutputDevices $BaseDirectory $BatchInput $BatchOutput $BlockchainBase $BoxForms $ByteOrdering $CacheBaseDirectory $Canceled $ChannelBase $CharacterEncoding $CharacterEncodings $CloudBase $CloudConnected $CloudCreditsAvailable $CloudEvaluation $CloudExpressionBase $CloudObjectNameFormat $CloudObjectURLType $CloudRootDirectory $CloudSymbolBase $CloudUserID $CloudUserUUID $CloudVersion $CloudVersionNumber $CloudWolframEngineVersionNumber $CommandLine $CompilationTarget $ConditionHold $ConfiguredKernels $Context $ContextPath $ControlActiveSetting $Cookies $CookieStore $CreationDate $CurrentLink $CurrentTask $CurrentWebSession $DateStringFormat $DefaultAudioInputDevice $DefaultAudioOutputDevice $DefaultFont $DefaultFrontEnd $DefaultImagingDevice $DefaultLocalBase $DefaultMailbox $DefaultNetworkInterface $DefaultPath $Display $DisplayFunction $DistributedContexts $DynamicEvaluation $Echo $EmbedCodeEnvironments $EmbeddableServices $EntityStores $Epilog $EvaluationCloudBase $EvaluationCloudObject $EvaluationEnvironment $ExportFormats $Failed $FinancialDataSource $FontFamilies $FormatType $FrontEnd $FrontEndSession $GeoEntityTypes $GeoLocation $GeoLocationCity $GeoLocationCountry $GeoLocationPrecision $GeoLocationSource $HistoryLength $HomeDirectory $HTMLExportRules $HTTPCookies $HTTPRequest $IgnoreEOF $ImageFormattingWidth $ImagingDevice $ImagingDevices $ImportFormats $IncomingMailSettings $InitialDirectory $Initialization $InitializationContexts $Input $InputFileName $InputStreamMethods $Inspector $InstallationDate $InstallationDirectory $InterfaceEnvironment 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part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version timezone_local timezone_utc gamespeed_fps gamespeed_microseconds ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down 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= function(hljs) {\n var PARAMS = {\n className: 'params',\n begin: '\\\\(', end: '\\\\)'\n };\n\n var F_KEYWORDS = {\n literal: '.False. .True.',\n keyword: 'kind do while private call intrinsic where elsewhere ' +\n 'type endtype endmodule endselect endinterface end enddo endif if forall endforall only contains default return stop then ' +\n 'public subroutine|10 function program .and. .or. .not. .le. .eq. .ge. .gt. .lt. ' +\n 'goto save else use module select case ' +\n 'access blank direct exist file fmt form formatted iostat name named nextrec number opened rec recl sequential status unformatted unit ' +\n 'continue format pause cycle exit ' +\n 'c_null_char c_alert c_backspace c_form_feed flush wait decimal round iomsg ' +\n 'synchronous nopass non_overridable pass protected volatile abstract extends import ' +\n 'non_intrinsic value deferred generic final enumerator class associate bind enum ' +\n 'c_int c_short c_long c_long_long c_signed_char c_size_t c_int8_t c_int16_t c_int32_t c_int64_t c_int_least8_t c_int_least16_t ' +\n 'c_int_least32_t c_int_least64_t c_int_fast8_t c_int_fast16_t c_int_fast32_t c_int_fast64_t c_intmax_t C_intptr_t c_float c_double ' +\n 'c_long_double c_float_complex c_double_complex c_long_double_complex c_bool c_char c_null_ptr c_null_funptr ' +\n 'c_new_line c_carriage_return c_horizontal_tab c_vertical_tab iso_c_binding c_loc c_funloc c_associated c_f_pointer ' +\n 'c_ptr c_funptr iso_fortran_env character_storage_size error_unit file_storage_size input_unit iostat_end iostat_eor ' +\n 'numeric_storage_size output_unit c_f_procpointer ieee_arithmetic ieee_support_underflow_control ' +\n 'ieee_get_underflow_mode ieee_set_underflow_mode newunit contiguous recursive ' +\n 'pad position action delim readwrite eor advance nml interface procedure namelist include sequence elemental pure ' +\n 'integer real character complex logical dimension allocatable|10 parameter ' +\n 'external implicit|10 none double precision assign intent optional pointer ' +\n 'target in out common equivalence data ' +\n // IRPF90 special keywords\n 'begin_provider &begin_provider end_provider begin_shell end_shell begin_template end_template subst assert touch ' +\n 'soft_touch provide no_dep free irp_if irp_else irp_endif irp_write irp_read',\n built_in: 'alog alog10 amax0 amax1 amin0 amin1 amod cabs ccos cexp clog csin csqrt dabs dacos dasin datan datan2 dcos dcosh ddim dexp dint ' +\n 'dlog dlog10 dmax1 dmin1 dmod dnint dsign dsin dsinh dsqrt dtan dtanh float iabs idim idint idnint ifix isign max0 max1 min0 min1 sngl ' +\n 'algama cdabs cdcos cdexp cdlog cdsin cdsqrt cqabs cqcos cqexp cqlog cqsin cqsqrt dcmplx dconjg derf derfc dfloat dgamma dimag dlgama ' +\n 'iqint qabs qacos qasin qatan qatan2 qcmplx qconjg qcos qcosh qdim qerf qerfc qexp qgamma qimag qlgama qlog qlog10 qmax1 qmin1 qmod ' +\n 'qnint qsign qsin qsinh qsqrt qtan qtanh abs acos aimag aint anint asin atan atan2 char cmplx conjg cos cosh exp ichar index int log ' +\n 'log10 max min nint sign sin sinh sqrt tan tanh print write dim lge lgt lle llt mod nullify allocate deallocate ' +\n 'adjustl adjustr all allocated any associated bit_size btest ceiling count cshift date_and_time digits dot_product ' +\n 'eoshift epsilon exponent floor fraction huge iand ibclr ibits ibset ieor ior ishft ishftc lbound len_trim matmul ' +\n 'maxexponent maxloc maxval merge minexponent minloc minval modulo mvbits nearest pack present product ' +\n 'radix random_number random_seed range repeat reshape rrspacing scale scan selected_int_kind selected_real_kind ' +\n 'set_exponent shape size spacing spread sum system_clock tiny transpose trim ubound unpack verify achar iachar transfer ' +\n 'dble entry dprod cpu_time command_argument_count get_command get_command_argument get_environment_variable is_iostat_end ' +\n 'ieee_arithmetic ieee_support_underflow_control ieee_get_underflow_mode ieee_set_underflow_mode ' +\n 'is_iostat_eor move_alloc new_line selected_char_kind same_type_as extends_type_of' +\n 'acosh asinh atanh bessel_j0 bessel_j1 bessel_jn bessel_y0 bessel_y1 bessel_yn erf erfc erfc_scaled gamma log_gamma hypot norm2 ' +\n 'atomic_define atomic_ref execute_command_line leadz trailz storage_size merge_bits ' +\n 'bge bgt ble blt dshiftl dshiftr findloc iall iany iparity image_index lcobound ucobound maskl maskr ' +\n 'num_images parity popcnt poppar shifta shiftl shiftr this_image ' +\n 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float string vector matrix if else switch case default while do for in break continue global proc return about abs addAttr addAttributeEditorNodeHelp addDynamic addNewShelfTab addPP addPanelCategory addPrefixToName advanceToNextDrivenKey affectedNet affects aimConstraint air alias aliasAttr align alignCtx alignCurve alignSurface allViewFit ambientLight angle angleBetween animCone animCurveEditor animDisplay animView annotate appendStringArray applicationName applyAttrPreset applyTake arcLenDimContext arcLengthDimension arclen arrayMapper art3dPaintCtx artAttrCtx artAttrPaintVertexCtx artAttrSkinPaintCtx artAttrTool artBuildPaintMenu artFluidAttrCtx artPuttyCtx artSelectCtx artSetPaintCtx artUserPaintCtx assignCommand assignInputDevice assignViewportFactories attachCurve attachDeviceAttr attachSurface attrColorSliderGrp attrCompatibility attrControlGrp attrEnumOptionMenu attrEnumOptionMenuGrp attrFieldGrp attrFieldSliderGrp attrNavigationControlGrp attrPresetEditWin attributeExists 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collision color colorAtPoint colorEditor colorIndex colorIndexSliderGrp colorSliderButtonGrp colorSliderGrp columnLayout commandEcho commandLine commandPort compactHairSystem componentEditor compositingInterop computePolysetVolume condition cone confirmDialog connectAttr connectControl connectDynamic connectJoint connectionInfo constrain constrainValue constructionHistory container containsMultibyte contextInfo control convertFromOldLayers convertIffToPsd convertLightmap convertSolidTx convertTessellation convertUnit copyArray copyFlexor copyKey copySkinWeights cos cpButton cpCache cpClothSet cpCollision cpConstraint cpConvClothToMesh cpForces cpGetSolverAttr cpPanel cpProperty cpRigidCollisionFilter cpSeam cpSetEdit cpSetSolverAttr cpSolver cpSolverTypes cpTool cpUpdateClothUVs createDisplayLayer createDrawCtx createEditor createLayeredPsdFile createMotionField createNewShelf createNode createRenderLayer createSubdivRegion cross crossProduct ctxAbort ctxCompletion ctxEditMode ctxTraverse currentCtx currentTime currentTimeCtx currentUnit curve curveAddPtCtx curveCVCtx curveEPCtx curveEditorCtx curveIntersect curveMoveEPCtx curveOnSurface curveSketchCtx cutKey cycleCheck cylinder dagPose date defaultLightListCheckBox defaultNavigation defineDataServer defineVirtualDevice deformer deg_to_rad delete deleteAttr deleteShadingGroupsAndMaterials deleteShelfTab deleteUI deleteUnusedBrushes delrandstr detachCurve detachDeviceAttr detachSurface deviceEditor devicePanel dgInfo dgdirty dgeval dgtimer dimWhen directKeyCtx directionalLight dirmap dirname disable disconnectAttr disconnectJoint diskCache displacementToPoly displayAffected displayColor displayCull displayLevelOfDetail displayPref displayRGBColor displaySmoothness displayStats displayString displaySurface distanceDimContext distanceDimension doBlur dolly dollyCtx dopeSheetEditor dot dotProduct doubleProfileBirailSurface drag dragAttrContext draggerContext dropoffLocator duplicate duplicateCurve 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hsv_to_rgb hudButton hudSlider hudSliderButton hwReflectionMap hwRender hwRenderLoad hyperGraph hyperPanel hyperShade hypot iconTextButton iconTextCheckBox iconTextRadioButton iconTextRadioCollection iconTextScrollList iconTextStaticLabel ikHandle ikHandleCtx ikHandleDisplayScale ikSolver ikSplineHandleCtx ikSystem ikSystemInfo ikfkDisplayMethod illustratorCurves image imfPlugins inheritTransform insertJoint insertJointCtx insertKeyCtx insertKnotCurve insertKnotSurface instance instanceable instancer intField intFieldGrp intScrollBar intSlider intSliderGrp interToUI internalVar intersect iprEngine isAnimCurve isConnected isDirty isParentOf isSameObject isTrue isValidObjectName isValidString isValidUiName isolateSelect itemFilter itemFilterAttr itemFilterRender itemFilterType joint jointCluster jointCtx jointDisplayScale jointLattice keyTangent keyframe keyframeOutliner keyframeRegionCurrentTimeCtx keyframeRegionDirectKeyCtx keyframeRegionDollyCtx keyframeRegionInsertKeyCtx keyframeRegionMoveKeyCtx keyframeRegionScaleKeyCtx keyframeRegionSelectKeyCtx keyframeRegionSetKeyCtx keyframeRegionTrackCtx keyframeStats lassoContext lattice latticeDeformKeyCtx launch launchImageEditor layerButton layeredShaderPort layeredTexturePort layout layoutDialog lightList lightListEditor lightListPanel lightlink lineIntersection linearPrecision linstep listAnimatable listAttr listCameras listConnections listDeviceAttachments listHistory listInputDeviceAxes listInputDeviceButtons listInputDevices listMenuAnnotation listNodeTypes listPanelCategories listRelatives listSets listTransforms listUnselected listerEditor loadFluid loadNewShelf loadPlugin loadPluginLanguageResources loadPrefObjects localizedPanelLabel lockNode loft log longNameOf lookThru ls lsThroughFilter lsType lsUI Mayatomr mag makeIdentity makeLive makePaintable makeRoll makeSingleSurface makeTubeOn makebot manipMoveContext manipMoveLimitsCtx manipOptions manipRotateContext manipRotateLimitsCtx manipScaleContext manipScaleLimitsCtx marker match max memory menu menuBarLayout menuEditor menuItem menuItemToShelf menuSet menuSetPref messageLine min minimizeApp mirrorJoint modelCurrentTimeCtx modelEditor modelPanel mouse movIn movOut move moveIKtoFK moveKeyCtx moveVertexAlongDirection multiProfileBirailSurface mute nParticle nameCommand nameField namespace namespaceInfo newPanelItems newton nodeCast nodeIconButton nodeOutliner nodePreset nodeType noise nonLinear normalConstraint normalize nurbsBoolean nurbsCopyUVSet nurbsCube nurbsEditUV nurbsPlane nurbsSelect nurbsSquare nurbsToPoly nurbsToPolygonsPref nurbsToSubdiv nurbsToSubdivPref nurbsUVSet nurbsViewDirectionVector objExists objectCenter objectLayer objectType objectTypeUI obsoleteProc oceanNurbsPreviewPlane offsetCurve offsetCurveOnSurface offsetSurface openGLExtension openMayaPref optionMenu optionMenuGrp optionVar orbit orbitCtx orientConstraint outlinerEditor outlinerPanel overrideModifier paintEffectsDisplay pairBlend palettePort paneLayout panel panelConfiguration panelHistory paramDimContext paramDimension paramLocator parent parentConstraint particle particleExists particleInstancer particleRenderInfo partition pasteKey pathAnimation pause pclose percent performanceOptions pfxstrokes pickWalk picture pixelMove planarSrf plane play playbackOptions playblast plugAttr plugNode pluginInfo pluginResourceUtil pointConstraint pointCurveConstraint pointLight pointMatrixMult pointOnCurve pointOnSurface pointPosition poleVectorConstraint polyAppend polyAppendFacetCtx polyAppendVertex polyAutoProjection polyAverageNormal polyAverageVertex polyBevel polyBlendColor polyBlindData polyBoolOp polyBridgeEdge polyCacheMonitor polyCheck polyChipOff polyClipboard polyCloseBorder polyCollapseEdge polyCollapseFacet polyColorBlindData polyColorDel polyColorPerVertex polyColorSet polyCompare polyCone polyCopyUV polyCrease polyCreaseCtx polyCreateFacet polyCreateFacetCtx polyCube polyCut polyCutCtx polyCylinder polyCylindricalProjection polyDelEdge polyDelFacet polyDelVertex polyDuplicateAndConnect polyDuplicateEdge polyEditUV polyEditUVShell polyEvaluate polyExtrudeEdge polyExtrudeFacet polyExtrudeVertex polyFlipEdge polyFlipUV polyForceUV polyGeoSampler polyHelix polyInfo polyInstallAction polyLayoutUV polyListComponentConversion polyMapCut polyMapDel polyMapSew polyMapSewMove polyMergeEdge polyMergeEdgeCtx polyMergeFacet polyMergeFacetCtx polyMergeUV polyMergeVertex polyMirrorFace polyMoveEdge polyMoveFacet polyMoveFacetUV polyMoveUV polyMoveVertex polyNormal polyNormalPerVertex polyNormalizeUV polyOptUvs polyOptions polyOutput polyPipe polyPlanarProjection polyPlane polyPlatonicSolid polyPoke polyPrimitive polyPrism polyProjection polyPyramid polyQuad polyQueryBlindData polyReduce polySelect polySelectConstraint polySelectConstraintMonitor polySelectCtx polySelectEditCtx polySeparate polySetToFaceNormal polySewEdge polyShortestPathCtx polySmooth polySoftEdge polySphere 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selectKeyCtx selectKeyframeRegionCtx selectMode selectPref selectPriority selectType selectedNodes selectionConnection separator setAttr setAttrEnumResource setAttrMapping setAttrNiceNameResource setConstraintRestPosition setDefaultShadingGroup setDrivenKeyframe setDynamic setEditCtx setEditor setFluidAttr setFocus setInfinity setInputDeviceMapping setKeyCtx setKeyPath setKeyframe setKeyframeBlendshapeTargetWts setMenuMode setNodeNiceNameResource setNodeTypeFlag setParent setParticleAttr setPfxToPolyCamera setPluginResource setProject setStampDensity setStartupMessage setState setToolTo setUITemplate setXformManip sets shadingConnection shadingGeometryRelCtx shadingLightRelCtx shadingNetworkCompare shadingNode shapeCompare shelfButton shelfLayout shelfTabLayout shellField shortNameOf showHelp showHidden showManipCtx showSelectionInTitle showShadingGroupAttrEditor showWindow sign simplify sin singleProfileBirailSurface size sizeBytes skinCluster skinPercent smoothCurve smoothTangentSurface smoothstep snap2to2 snapKey snapMode snapTogetherCtx snapshot soft softMod softModCtx sort sound soundControl source spaceLocator sphere sphrand spotLight spotLightPreviewPort spreadSheetEditor spring sqrt squareSurface srtContext stackTrace startString startsWith stitchAndExplodeShell stitchSurface stitchSurfacePoints strcmp stringArrayCatenate stringArrayContains stringArrayCount stringArrayInsertAtIndex stringArrayIntersector stringArrayRemove stringArrayRemoveAtIndex stringArrayRemoveDuplicates stringArrayRemoveExact stringArrayToString stringToStringArray strip stripPrefixFromName stroke subdAutoProjection subdCleanTopology subdCollapse subdDuplicateAndConnect subdEditUV subdListComponentConversion subdMapCut subdMapSewMove subdMatchTopology subdMirror subdToBlind subdToPoly subdTransferUVsToCache subdiv subdivCrease subdivDisplaySmoothness substitute substituteAllString substituteGeometry substring surface surfaceSampler surfaceShaderList swatchDisplayPort 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createVehicleLocal crew ctAddHeader ctAddRow ctClear ctCurSel ctData ctFindHeaderRows ctFindRowHeader ctHeaderControls ctHeaderCount ctRemoveHeaders ctRemoveRows ctrlActivate ctrlAddEventHandler ctrlAngle ctrlAutoScrollDelay ctrlAutoScrollRewind ctrlAutoScrollSpeed ctrlChecked ctrlClassName ctrlCommit ctrlCommitted ctrlCreate ctrlDelete ctrlEnable ctrlEnabled ctrlFade ctrlHTMLLoaded ctrlIDC ctrlIDD ctrlMapAnimAdd ctrlMapAnimClear ctrlMapAnimCommit ctrlMapAnimDone ctrlMapCursor ctrlMapMouseOver ctrlMapScale ctrlMapScreenToWorld ctrlMapWorldToScreen ctrlModel ctrlModelDirAndUp ctrlModelScale ctrlParent ctrlParentControlsGroup ctrlPosition ctrlRemoveAllEventHandlers ctrlRemoveEventHandler ctrlScale ctrlSetActiveColor ctrlSetAngle ctrlSetAutoScrollDelay ctrlSetAutoScrollRewind ctrlSetAutoScrollSpeed ctrlSetBackgroundColor ctrlSetChecked ctrlSetEventHandler ctrlSetFade ctrlSetFocus ctrlSetFont ctrlSetFontH1 ctrlSetFontH1B ctrlSetFontH2 ctrlSetFontH2B ctrlSetFontH3 ctrlSetFontH3B ctrlSetFontH4 ctrlSetFontH4B ctrlSetFontH5 ctrlSetFontH5B ctrlSetFontH6 ctrlSetFontH6B ctrlSetFontHeight ctrlSetFontHeightH1 ctrlSetFontHeightH2 ctrlSetFontHeightH3 ctrlSetFontHeightH4 ctrlSetFontHeightH5 ctrlSetFontHeightH6 ctrlSetFontHeightSecondary ctrlSetFontP ctrlSetFontPB ctrlSetFontSecondary ctrlSetForegroundColor ctrlSetModel ctrlSetModelDirAndUp ctrlSetModelScale ctrlSetPixelPrecision ctrlSetPosition ctrlSetScale ctrlSetStructuredText ctrlSetText ctrlSetTextColor ctrlSetTooltip ctrlSetTooltipColorBox ctrlSetTooltipColorShade ctrlSetTooltipColorText ctrlShow ctrlShown ctrlText ctrlTextHeight ctrlTextWidth ctrlType ctrlVisible ctRowControls ctRowCount ctSetCurSel ctSetData ctSetHeaderTemplate ctSetRowTemplate ctSetValue ctValue curatorAddons curatorCamera curatorCameraArea curatorCameraAreaCeiling curatorCoef curatorEditableObjects curatorEditingArea curatorEditingAreaType curatorMouseOver curatorPoints curatorRegisteredObjects curatorSelected curatorWaypointCost current3DENOperation currentChannel currentCommand currentMagazine currentMagazineDetail currentMagazineDetailTurret currentMagazineTurret currentMuzzle currentNamespace currentTask currentTasks currentThrowable currentVisionMode currentWaypoint currentWeapon currentWeaponMode currentWeaponTurret currentZeroing cursorObject cursorTarget customChat customRadio cutFadeOut cutObj cutRsc cutText damage date dateToNumber daytime deActivateKey debriefingText debugFSM debugLog deg delete3DENEntities deleteAt deleteCenter deleteCollection deleteEditorObject deleteGroup deleteGroupWhenEmpty deleteIdentity deleteLocation deleteMarker deleteMarkerLocal deleteRange deleteResources deleteSite deleteStatus deleteTeam deleteVehicle deleteVehicleCrew deleteWaypoint detach detectedMines diag_activeMissionFSMs diag_activeScripts diag_activeSQFScripts diag_activeSQSScripts diag_captureFrame diag_captureFrameToFile diag_captureSlowFrame diag_codePerformance diag_drawMode diag_enable diag_enabled diag_fps diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem unlockAchievement unregisterTask updateDrawIcon updateMenuItem updateObjectTree useAISteeringComponent useAudioTimeForMoves userInputDisabled vectorAdd vectorCos vectorCrossProduct vectorDiff vectorDir vectorDirVisual vectorDistance vectorDistanceSqr vectorDotProduct vectorFromTo vectorMagnitude vectorMagnitudeSqr vectorModelToWorld vectorModelToWorldVisual vectorMultiply vectorNormalized vectorUp vectorUpVisual vectorWorldToModel vectorWorldToModelVisual vehicle vehicleCargoEnabled vehicleChat vehicleRadio vehicleReceiveRemoteTargets vehicleReportOwnPosition vehicleReportRemoteTargets vehicles vehicleVarName velocity velocityModelSpace verifySignature vest vestContainer vestItems vestMagazines viewDistance visibleCompass visibleGPS visibleMap visiblePosition visiblePositionASL visibleScoretable visibleWatch waves waypointAttachedObject waypointAttachedVehicle waypointAttachObject waypointAttachVehicle waypointBehaviour waypointCombatMode waypointCompletionRadius waypointDescription 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CodeAssistOptions Coefficient CoefficientArrays CoefficientDomain CoefficientList CoefficientRules CoifletWavelet Collect Colon ColonForm ColorBalance ColorCombine ColorConvert ColorCoverage ColorData ColorDataFunction ColorDetect ColorDistance ColorFunction ColorFunctionScaling Colorize ColorNegate ColorOutput ColorProfileData ColorQ ColorQuantize ColorReplace ColorRules ColorSelectorSettings ColorSeparate ColorSetter ColorSetterBox ColorSetterBoxOptions ColorSlider ColorsNear ColorSpace ColorToneMapping Column ColumnAlignments ColumnBackgrounds ColumnForm ColumnLines ColumnsEqual ColumnSpacings ColumnWidths CombinedEntityClass CombinerFunction CometData CommonDefaultFormatTypes Commonest CommonestFilter CommonName CommonUnits CommunityBoundaryStyle CommunityGraphPlot CommunityLabels CommunityRegionStyle CompanyData CompatibleUnitQ CompilationOptions CompilationTarget Compile Compiled CompiledCodeFunction CompiledFunction CompilerOptions Complement CompleteGraph CompleteGraphQ CompleteKaryTree CompletionsListPacket Complex Complexes ComplexExpand ComplexInfinity ComplexityFunction ComplexListPlot ComplexPlot ComplexPlot3D ComponentMeasurements ComponentwiseContextMenu Compose ComposeList ComposeSeries CompositeQ Composition CompoundElement CompoundExpression CompoundPoissonDistribution CompoundPoissonProcess CompoundRenewalProcess Compress CompressedData ComputeUncertainty Condition ConditionalExpression Conditioned Cone ConeBox ConfidenceLevel ConfidenceRange ConfidenceTransform ConfigurationPath ConformAudio ConformImages Congruent ConicHullRegion ConicHullRegion3DBox ConicHullRegionBox ConicOptimization Conjugate ConjugateTranspose Conjunction Connect ConnectedComponents ConnectedGraphComponents ConnectedGraphQ ConnectedMeshComponents ConnectedMoleculeComponents ConnectedMoleculeQ ConnectionSettings ConnectLibraryCallbackFunction ConnectSystemModelComponents ConnesWindow ConoverTest ConsoleMessage ConsoleMessagePacket ConsolePrint Constant ConstantArray ConstantArrayLayer ConstantImage ConstantPlusLayer ConstantRegionQ Constants ConstantTimesLayer ConstellationData ConstrainedMax ConstrainedMin Construct Containing ContainsAll ContainsAny ContainsExactly ContainsNone ContainsOnly ContentFieldOptions ContentLocationFunction ContentObject ContentPadding ContentsBoundingBox ContentSelectable ContentSize Context ContextMenu Contexts ContextToFileName Continuation Continue ContinuedFraction ContinuedFractionK ContinuousAction ContinuousMarkovProcess ContinuousTask ContinuousTimeModelQ ContinuousWaveletData ContinuousWaveletTransform ContourDetect ContourGraphics ContourIntegral ContourLabels ContourLines ContourPlot ContourPlot3D Contours ContourShading ContourSmoothing ContourStyle ContraharmonicMean ContrastiveLossLayer Control ControlActive ControlAlignment ControlGroupContentsBox ControllabilityGramian ControllabilityMatrix ControllableDecomposition ControllableModelQ ControllerDuration ControllerInformation ControllerInformationData ControllerLinking ControllerManipulate ControllerMethod ControllerPath ControllerState ControlPlacement ControlsRendering ControlType Convergents ConversionOptions ConversionRules ConvertToBitmapPacket ConvertToPostScript ConvertToPostScriptPacket ConvexHullMesh ConvexPolygonQ ConvexPolyhedronQ ConvolutionLayer Convolve ConwayGroupCo1 ConwayGroupCo2 ConwayGroupCo3 CookieFunction Cookies CoordinateBoundingBox CoordinateBoundingBoxArray CoordinateBounds CoordinateBoundsArray CoordinateChartData CoordinatesToolOptions CoordinateTransform CoordinateTransformData CoprimeQ Coproduct CopulaDistribution Copyable CopyDatabin CopyDirectory CopyFile CopyTag CopyToClipboard CornerFilter CornerNeighbors Correlation CorrelationDistance CorrelationFunction CorrelationTest Cos Cosh CoshIntegral CosineDistance CosineWindow CosIntegral Cot Coth Count CountDistinct CountDistinctBy CounterAssignments CounterBox CounterBoxOptions CounterClockwiseContourIntegral CounterEvaluator CounterFunction CounterIncrements CounterStyle CounterStyleMenuListing CountRoots CountryData Counts CountsBy Covariance CovarianceEstimatorFunction CovarianceFunction CoxianDistribution CoxIngersollRossProcess CoxModel CoxModelFit CramerVonMisesTest CreateArchive CreateCellID CreateChannel CreateCloudExpression CreateDatabin CreateDataSystemModel CreateDialog CreateDirectory CreateDocument CreateFile CreateIntermediateDirectories CreateManagedLibraryExpression CreateNotebook CreatePalette CreatePalettePacket CreatePermissionsGroup CreateScheduledTask CreateSearchIndex CreateSystemModel CreateTemporary CreateUUID CreateWindow CriterionFunction CriticalityFailureImportance CriticalitySuccessImportance CriticalSection Cross CrossEntropyLossLayer CrossingCount CrossingDetect CrossingPolygon CrossMatrix Csc Csch CTCLossLayer Cube CubeRoot Cubics Cuboid CuboidBox Cumulant CumulantGeneratingFunction Cup CupCap Curl CurlyDoubleQuote CurlyQuote CurrencyConvert CurrentDate CurrentImage CurrentlySpeakingPacket CurrentNotebookImage CurrentScreenImage CurrentValue Curry CurvatureFlowFilter CurveClosed Cyan CycleGraph CycleIndexPolynomial Cycles CyclicGroup Cyclotomic Cylinder CylinderBox CylindricalDecompositionD DagumDistribution DamData DamerauLevenshteinDistance DampingFactor Darker Dashed Dashing DatabaseConnect DatabaseDisconnect DatabaseReference Databin DatabinAdd DatabinRemove Databins DatabinUpload DataCompression DataDistribution DataRange DataReversed Dataset Date DateBounds Dated DateDelimiters DateDifference DatedUnit DateFormat DateFunction DateHistogram DateList DateListLogPlot DateListPlot DateListStepPlot DateObject DateObjectQ DateOverlapsQ DatePattern DatePlus DateRange DateReduction DateString DateTicksFormat DateValue DateWithinQ DaubechiesWavelet DavisDistribution DawsonF DayCount DayCountConvention DayHemisphere DaylightQ DayMatchQ DayName DayNightTerminator DayPlus DayRange DayRound DeBruijnGraph DeBruijnSequence Debug DebugTag Decapitalize Decimal DecimalForm DeclareKnownSymbols DeclarePackage Decompose DeconvolutionLayer Decrement Decrypt DecryptFile DedekindEta DeepSpaceProbeData Default DefaultAxesStyle DefaultBaseStyle DefaultBoxStyle DefaultButton DefaultColor DefaultControlPlacement DefaultDuplicateCellStyle DefaultDuration DefaultElement DefaultFaceGridsStyle DefaultFieldHintStyle DefaultFont DefaultFontProperties DefaultFormatType DefaultFormatTypeForStyle DefaultFrameStyle DefaultFrameTicksStyle DefaultGridLinesStyle DefaultInlineFormatType DefaultInputFormatType DefaultLabelStyle DefaultMenuStyle DefaultNaturalLanguage DefaultNewCellStyle DefaultNewInlineCellStyle DefaultNotebook DefaultOptions DefaultOutputFormatType DefaultPrintPrecision DefaultStyle DefaultStyleDefinitions DefaultTextFormatType DefaultTextInlineFormatType DefaultTicksStyle DefaultTooltipStyle DefaultValue DefaultValues Defer DefineExternal DefineInputStreamMethod DefineOutputStreamMethod DefineResourceFunction Definition Degree DegreeCentrality DegreeGraphDistribution DegreeLexicographic DegreeReverseLexicographic DEigensystem DEigenvalues Deinitialization Del DelaunayMesh Delayed Deletable Delete DeleteAnomalies DeleteBorderComponents DeleteCases DeleteChannel DeleteCloudExpression DeleteContents DeleteDirectory DeleteDuplicates DeleteDuplicatesBy DeleteFile DeleteMissing DeleteObject DeletePermissionsKey DeleteSearchIndex DeleteSmallComponents DeleteStopwords DeleteWithContents DeletionWarning DelimitedArray DelimitedSequence Delimiter DelimiterFlashTime DelimiterMatching Delimiters DeliveryFunction Dendrogram Denominator DensityGraphics DensityHistogram DensityPlot DensityPlot3D DependentVariables Deploy Deployed Depth DepthFirstScan Derivative DerivativeFilter DerivedKey DescriptorStateSpace DesignMatrix DestroyAfterEvaluation Det DeviceClose DeviceConfigure DeviceExecute DeviceExecuteAsynchronous DeviceObject DeviceOpen DeviceOpenQ DeviceRead DeviceReadBuffer DeviceReadLatest DeviceReadList DeviceReadTimeSeries Devices DeviceStreams DeviceWrite DeviceWriteBuffer DGaussianWavelet DiacriticalPositioning Diagonal DiagonalizableMatrixQ DiagonalMatrix DiagonalMatrixQ Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DictionaryWordQ DifferenceDelta DifferenceOrder DifferenceQuotient DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitalSignature DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralAngle DihedralGroup Dilation DimensionalCombinations DimensionalMeshComponents DimensionReduce DimensionReducerFunction DimensionReduction Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletBeta DirichletCharacter DirichletCondition DirichletConvolve DirichletDistribution DirichletEta DirichletL DirichletLambda DirichletTransform DirichletWindow DisableConsolePrintPacket DisableFormatting DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLimit DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscreteMaxLimit DiscreteMinLimit DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform DiscretizeGraphics DiscretizeRegion Discriminant DisjointQ Disjunction Disk DiskBox DiskMatrix DiskSegment Dispatch DispatchQ DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceMatrix DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers DivideSides Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentGenerator DocumentGeneratorInformation DocumentGeneratorInformationData DocumentGenerators DocumentNotebook DocumentWeightingRules Dodecahedron DomainRegistrationInformation DominantColors DOSTextFormat Dot DotDashed DotEqual DotLayer DotPlusLayer Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DropoutLayer DSolve DSolveValue Dt DualLinearProgramming DualPolyhedron DualSystemsModel DumpGet DumpSave DuplicateFreeQ Duration Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicGeoGraphics DynamicImage DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptionsE EarthImpactData EarthquakeData EccentricityCentrality Echo EchoFunction EclipseType EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeContract EdgeCost EdgeCount EdgeCoverQ EdgeCycleMatrix EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight EdgeWeightedGraphQ Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData ElementwiseLayer ElidedForms Eliminate EliminationOrder Ellipsoid EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmbedCode EmbeddedHTML EmbeddedService EmbeddingLayer EmbeddingObject EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EmptyRegion EnableConsolePrintPacket Enabled Encode Encrypt EncryptedObject EncryptFile End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfBuffer EndOfFile EndOfLine EndOfString EndPackage EngineEnvironment EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entity EntityClass EntityClassList EntityCopies EntityFunction EntityGroup EntityInstance EntityList EntityPrefetch EntityProperties EntityProperty EntityPropertyClass EntityRegister EntityStore EntityStores EntityTypeName EntityUnregister EntityValue Entropy EntropyFilter Environment Epilog EpilogFunction Equal EqualColumns EqualRows EqualTilde EqualTo EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EscapeRadius EstimatedBackground EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerAngles EulerCharacteristic EulerE EulerGamma EulerianGraphQ EulerMatrix EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluateScheduledTask EvaluationBox EvaluationCell EvaluationCompletionAction EvaluationData EvaluationElements EvaluationEnvironment EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels EventSeries ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludedLines ExcludedPhysicalQuantities ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog ExoplanetData Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi ExpirationDate Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportByteArray ExportForm ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpressionUUID ExpToTrig ExtendedEntityClass ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalBundle ExternalCall ExternalDataCharacterEncoding ExternalEvaluate ExternalFunction ExternalFunctionName ExternalObject ExternalOptions ExternalSessionObject ExternalSessions ExternalTypeSignature ExternalValue Extract ExtractArchive ExtractLayer ExtremeValueDistributionFaceForm FaceGrids FaceGridsStyle FacialFeatures Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail Failure FailureAction FailureDistribution FailureQ False FareySequence FARIMAProcess FeatureDistance FeatureExtract FeatureExtraction FeatureExtractor FeatureExtractorFunction FeatureNames FeatureNearest FeatureSpacePlot FeatureSpacePlot3D FeatureTypes FEDisableConsolePrintPacket FeedbackLinearize FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket FetalGrowthData Fibonacci Fibonorial FieldCompletionFunction FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileConvert FileDate FileExistsQ FileExtension FileFormat FileHandler FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameForms FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileSize FileSystemMap FileSystemScan FileTemplate FileTemplateApply FileType FilledCurve FilledCurveBox FilledCurveBoxOptions Filling FillingStyle FillingTransform FilteredEntityClass FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindAnomalies FindArgMax FindArgMin FindChannels FindClique FindClusters FindCookies FindCurvePath FindCycle FindDevices FindDistribution FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEdgeIndependentPaths FindEquationalProof FindEulerianCycle FindExternalEvaluators FindFaces FindFile FindFit FindFormula FindFundamentalCycles FindGeneratingFunction FindGeoLocation FindGeometricConjectures FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindHamiltonianPath FindHiddenMarkovStates FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMatchingColor FindMaximum FindMaximumFlow FindMaxValue FindMeshDefects FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindMoleculeSubstructure FindPath FindPeaks FindPermutation FindPostmanTour FindProcessParameters FindRepeat FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindSpanningTree FindSystemModelEquilibrium FindTextualAnswer FindThreshold FindTransientRepeat FindVertexCover FindVertexCut FindVertexIndependentPaths Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstCase FirstPassageTimeDistribution FirstPosition FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FitRegularization FittedModel FixedOrder FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlattenLayer FlatTopWindow FlipView Floor FlowPolynomial FlushPrintOutputPacket Fold FoldList FoldPair FoldPairList FollowRedirects Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FormControl FormFunction FormLayoutFunction FormObject FormPage FormTheme FormulaData FormulaLookup FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalGaussianNoiseProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameRate FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrenetSerretSystem FrequencySamplingFilterKernel FresnelC FresnelF FresnelG FresnelS Friday FrobeniusNumber FrobeniusSolve FromAbsoluteTime FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS FromEntity FromJulianDate FromLetterNumber FromPolarCoordinates FromRomanNumeral FromSphericalCoordinates FromUnixTime Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullInformationOutputRegulator FullOptions FullRegion FullSimplify Function FunctionCompile FunctionCompileExport FunctionCompileExportByteArray FunctionCompileExportLibrary FunctionCompileExportString FunctionDomain FunctionExpand FunctionInterpolation FunctionPeriod FunctionRange FunctionSpace FussellVeselyImportanceGaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins GalaxyData GalleryView Gamma GammaDistribution GammaRegularized GapPenalty GARCHProcess GatedRecurrentLayer Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianOrthogonalMatrixDistribution GaussianSymplecticMatrixDistribution GaussianUnitaryMatrixDistribution GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateAsymmetricKeyPair GenerateConditions GeneratedCell GeneratedDocumentBinding GenerateDerivedKey GenerateDigitalSignature GenerateDocument GeneratedParameters GeneratedQuantityMagnitudes GenerateHTTPResponse GenerateSecuredAuthenticationKey GenerateSymmetricKey GeneratingFunction GeneratorDescription GeneratorHistoryLength GeneratorOutputType Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeoAntipode GeoArea GeoArraySize GeoBackground GeoBoundingBox GeoBounds GeoBoundsRegion GeoBubbleChart GeoCenter GeoCircle GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDisk GeoDisplacement GeoDistance GeoDistanceList GeoElevationData GeoEntities GeoGraphics GeogravityModelData GeoGridDirectionDifference GeoGridLines GeoGridLinesStyle GeoGridPosition GeoGridRange GeoGridRangePadding GeoGridUnitArea GeoGridUnitDistance GeoGridVector GeoGroup GeoHemisphere GeoHemisphereBoundary GeoHistogram GeoIdentify GeoImage GeoLabels GeoLength GeoListPlot GeoLocation GeologicalPeriodData GeomagneticModelData GeoMarker GeometricAssertion GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricScene GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoModel GeoNearest GeoPath GeoPosition GeoPositionENU GeoPositionXYZ GeoProjection GeoProjectionData GeoRange GeoRangePadding GeoRegionValuePlot GeoResolution GeoScaleBar GeoServer GeoSmoothHistogram GeoStreamPlot GeoStyling GeoStylingImageFunction GeoVariant GeoVector GeoVectorENU GeoVectorPlot GeoVectorXYZ GeoVisibleRegion GeoVisibleRegionBoundary GeoWithinQ GeoZoomLevel GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenAngle GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter GrammarApply GrammarRules GrammarToken Graph Graph3D GraphAssortativity GraphAutomorphismGroup GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel Greater GreaterEqual GreaterEqualLess GreaterEqualThan GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterThan GreaterTilde Green GreenFunction Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupBy GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators Groupings GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain GroupTogetherGrouping GroupTogetherNestedGrouping GrowCutComponents Gudermannian GuidedFilter GumbelDistributionHaarWavelet HadamardMatrix HalfLine HalfNormalDistribution HalfPlane HalfSpace HamiltonianGraphQ HammingDistance HammingWindow HandlerFunctions HandlerFunctionsKeys HankelH1 HankelH2 HankelMatrix HankelTransform HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash Haversine HazardFunction Head HeadCompose HeaderLines Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings Here HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenMarkovProcess HiddenSurface Highlighted HighlightGraph HighlightImage HighlightMesh HighpassFilter HigmanSimsGroupHS HilbertCurve HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HistoricalPeriodData HitMissTransform HITSCentrality HjorthDistribution HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HostLookup HotellingTSquareDistribution HoytDistribution HTMLSave HTTPErrorResponse HTTPRedirect HTTPRequest HTTPRequestData HTTPResponse Hue HumanGrowthData HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyperplane Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestDataI IconData Iconize IconizedObject IconRules Icosahedron Identity IdentityMatrix If IgnoreCase IgnoreDiacritics IgnorePunctuation IgnoreSpellCheck IgnoringInactive Im Image Image3D Image3DProjection Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageApplyIndexed ImageAspectRatio ImageAssemble ImageAugmentationLayer ImageBoundingBoxes ImageCache ImageCacheValid ImageCapture ImageCaptureFunction ImageCases ImageChannels ImageClip ImageCollage ImageColorSpace ImageCompose ImageContainsQ ImageContents ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDisplacements ImageDistance ImageEffect ImageExposureCombine ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageFocusCombine ImageForestingComponents ImageFormattingWidth ImageForwardTransformation ImageGraphics ImageHistogram ImageIdentify ImageInstanceQ ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarker ImageMarkers ImageMeasurements ImageMesh ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImagePosition ImagePreviewFunction ImagePyramid ImagePyramidApply ImageQ ImageRangeCache ImageRecolor ImageReflect ImageRegion ImageResize ImageResolution ImageRestyle ImageRotate ImageRotated ImageSaliencyFilter ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions ImagingDevice ImplicitRegion Implies Import ImportAutoReplacements ImportByteArray ImportOptions ImportString ImprovementImportance In Inactivate Inactive IncidenceGraph IncidenceList IncidenceMatrix IncludeAromaticBonds IncludeConstantBasis IncludeDefinitions IncludeDirectories IncludeFileExtension IncludeGeneratorTasks IncludeHydrogens IncludeInflections IncludeMetaInformation IncludePods IncludeQuantities IncludeRelatedTables IncludeSingularTerm IncludeWindowTimes Increment IndefiniteMatrixQ Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentPhysicalQuantity IndependentUnit IndependentUnitDimension IndependentVertexSetQ Indeterminate IndeterminateThreshold IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers InfiniteLine InfinitePlane Infinity Infix InflationAdjust InflationMethod Information InformationData InformationDataGrid Inherited InheritScope InhomogeneousPoissonProcess InitialEvaluationHistory Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InitializationObjects InitializationValue Initialize InitialSeeding InlineCounterAssignments InlineCounterIncrements InlineRules Inner InnerPolygon InnerPolyhedron Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionFunction InsertionPointObject InsertLinebreaks InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Insphere Install InstallService InstanceNormalizationLayer InString Integer IntegerDigits IntegerExponent IntegerLength IntegerName IntegerPart IntegerPartitions IntegerQ IntegerReverse Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction Interpreter InterpretTemplate InterquartileRange Interrupt InterruptSettings IntersectingQ Intersection Interval IntervalIntersection IntervalMarkers IntervalMarkersStyle IntervalMemberQ IntervalSlider IntervalUnion Into Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHankelTransform InverseHaversine InverseImagePyramid InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InverseMellinTransform InversePermutation InverseRadon InverseRadonTransform InverseSeries InverseShortTimeFourier InverseSpectrogram InverseSurvivalFunction InverseTransformedRegion InverseWaveletTransform InverseWeierstrassP InverseWishartMatrixDistribution InverseZTransform Invisible InvisibleApplication InvisibleTimes IPAddress IrreduciblePolynomialQ IslandData IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemAspectRatio ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcessJaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join JoinAcross Joined JoinedCurve JoinedCurveBox JoinedCurveBoxOptions JoinForm JordanDecomposition JordanModelDecomposition JulianDate JuliaSetBoettcher JuliaSetIterationCount JuliaSetPlot JuliaSetPointsK KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KEdgeConnectedComponents KEdgeConnectedGraphQ KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelFunction KernelMixtureDistribution Kernels Ket Key KeyCollisionFunction KeyComplement KeyDrop KeyDropFrom KeyExistsQ KeyFreeQ KeyIntersection KeyMap KeyMemberQ KeypointStrength Keys KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Khinchin KillProcess KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnapsackSolve KnightTourGraph KnotData KnownUnitQ KochCurve KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter KVertexConnectedComponents KVertexConnectedGraphQLABColor Label Labeled LabeledSlider LabelingFunction LabelingSize LabelStyle LabelVisibility LaguerreL LakeData LambdaComponents LambertW LaminaData LanczosWindow LandauDistribution Language LanguageCategory LanguageData LanguageIdentify LanguageOptions LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCHColor LCM LeaderSize LeafCount LeapYearQ LearnDistribution LearnedDistribution LearningRate LearningRateMultipliers LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessEqualThan LessFullEqual LessGreater LessLess LessSlantEqual LessThan LessTilde LetterCharacter LetterCounts LetterNumber LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryDataType LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox Line3DBoxOptions LinearFilter LinearFractionalOptimization LinearFractionalTransform LinearGradientImage LinearizingTransformationData LinearLayer LinearModelFit LinearOffsetFunction LinearOptimization LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBoxOptions LineBreak LinebreakAdjustments LineBreakChart LinebreakSemicolonWeighting LineBreakWithin LineColor LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRankCentrality LinkRead LinkReadHeld LinkReadyQ Links LinkService LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot ListDensityPlot3D Listen ListFormat ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListSliceContourPlot3D ListSliceDensityPlot3D ListSliceVectorPlot3D ListStepPlot ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalAdaptiveBinarize LocalCache LocalClusteringCoefficient LocalizeDefinitions LocalizeVariables LocalObject LocalObjects LocalResponseNormalizationLayer LocalSubmit LocalSymbol LocalTime LocalTimeZone LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogisticSigmoid LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongestOrderedSequence LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow LongShortTermMemoryLayer Lookup Loopback LoopFreeGraphQ LossFunction LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowerTriangularMatrixQ LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LunarEclipse LUVColor LyapunovSolve LyonsGroupLyMachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MailAddressValidation MailExecute MailFolder MailItem MailReceiverFunction MailResponseFunction MailSearch MailServerConnect MailServerConnection MailSettings MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules ManagedLibraryExpressionID ManagedLibraryExpressionQ MandelbrotSetBoettcher MandelbrotSetDistance MandelbrotSetIterationCount MandelbrotSetMemberQ MandelbrotSetPlot MangoldtLambda ManhattanDistance Manipulate Manipulator MannedSpaceMissionData MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarchenkoPasturDistribution MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicalFunctionData MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixNormalDistribution MatrixPlot MatrixPower MatrixPropertyDistribution MatrixQ MatrixRank MatrixTDistribution Max MaxBend MaxCellMeasure MaxColorDistance MaxDetect MaxDuration MaxExtraBandwidths MaxExtraConditions MaxFeatureDisplacement MaxFeatures MaxFilter MaximalBy Maximize MaxItems MaxIterations MaxLimit MaxMemoryUsed MaxMixtureKernels MaxOverlapFraction MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxTrainingRounds MaxValue MaxwellDistribution MaxWordGap McLaughlinGroupMcL Mean MeanAbsoluteLossLayer MeanAround MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter MeanSquaredLossLayer Median MedianDeviation MedianFilter MedicalTestData Medium MeijerG MeijerGReduce MeixnerDistribution MellinConvolve MellinTransform MemberQ MemoryAvailable MemoryConstrained MemoryConstraint MemoryInUse MengerMesh Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuList MenuPacket MenuSortingValue MenuStyle MenuView Merge MergeDifferences MergingFunction MersennePrimeExponent MersennePrimeExponentQ Mesh MeshCellCentroid MeshCellCount MeshCellHighlight MeshCellIndex MeshCellLabel MeshCellMarker MeshCellMeasure MeshCellQuality MeshCells MeshCellShapeFunction MeshCellStyle MeshCoordinates MeshFunctions MeshPrimitives MeshQualityGoal MeshRange MeshRefinementFunction MeshRegion MeshRegionQ MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageObject MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation MeteorShowerData Method MethodOptions MexicanHatWavelet MeyerWavelet Midpoint Min MinColorDistance MinDetect MineralData MinFilter MinimalBy MinimalPolynomial MinimalStateSpaceModel Minimize MinimumTimeIncrement MinIntervalSize MinkowskiQuestionMark MinLimit MinMax MinorPlanetData Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingBehavior MissingDataMethod MissingDataRules MissingQ MissingString MissingStyle MissingValuePattern MittagLefflerE MixedFractionParts MixedGraphQ MixedMagnitude MixedRadix MixedRadixQuantity MixedUnit MixtureDistribution Mod Modal Mode Modular ModularInverse ModularLambda Module Modulus MoebiusMu Molecule MoleculeContainsQ MoleculeEquivalentQ MoleculeGraph MoleculeModify MoleculePattern MoleculePlot MoleculePlot3D MoleculeProperty MoleculeQ MoleculeValue Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction MomentOfInertia Monday Monitor MonomialList MonomialOrder MonsterGroupM MoonPhase MoonPosition MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform MortalityData Most MountainData MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovieData MovingAverage MovingMap MovingMedian MoyalDistribution Multicolumn MultiedgeStyle MultigraphQ MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity MultiplySides Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistributionN NakagamiDistribution NameQ Names NamespaceBox NamespaceBoxOptions Nand NArgMax NArgMin NBernoulliB NBodySimulation NBodySimulationData NCache NDEigensystem NDEigenvalues NDSolve NDSolveValue Nearest NearestFunction NearestNeighborGraph NearestTo NebulaData NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeDefiniteMatrixQ NegativeIntegers NegativeMultinomialDistribution NegativeRationals NegativeReals NegativeSemidefiniteMatrixQ NeighborhoodData NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestGraph NestList NestWhile NestWhileList NetAppend NetBidirectionalOperator NetChain NetDecoder NetDelete NetDrop NetEncoder NetEvaluationMode NetExtract NetFlatten NetFoldOperator NetGraph NetInformation NetInitialize NetInsert NetInsertSharedArrays NetJoin NetMapOperator NetMapThreadOperator NetMeasurements NetModel NetNestOperator NetPairEmbeddingOperator NetPort NetPortGradient NetPrepend NetRename NetReplace NetReplacePart NetSharedArray NetStateObject NetTake NetTrain NetTrainResultsObject NetworkPacketCapture NetworkPacketRecording NetworkPacketRecordingDuring NetworkPacketTrace NeumannValue NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextCell NextDate NextPrime NextScheduledTaskTime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NightHemisphere NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants NondimensionalizationTransform None NoneTrue NonlinearModelFit NonlinearStateSpaceModel NonlocalMeansFilter NonNegative NonNegativeIntegers NonNegativeRationals NonNegativeReals NonPositive NonPositiveIntegers NonPositiveRationals NonPositiveReals Nor NorlundB Norm Normal NormalDistribution NormalGrouping NormalizationLayer Normalize Normalized NormalizedSquaredEuclideanDistance NormalMatrixQ NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookImport NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookTemplate NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde Nothing NotHumpDownHump NotHumpEqual NotificationFunction NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar Now NoWhitespace NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms NuclearExplosionData NuclearReactorData Null NullRecords NullSpace NullWords Number NumberCompose NumberDecompose NumberExpand NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberLinePlot NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumeratorDenominator NumericalOrder NumericalSort NumericArray NumericArrayQ NumericArrayType NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlotO ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OceanData Octahedron OddQ Off Offset OLEData On ONanGroupON Once OneIdentity Opacity OpacityFunction OpacityFunctionScaling Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionalElement OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering OrderingBy OrderingLayer Orderless OrderlessPatternSequence OrnsteinUhlenbeckProcess Orthogonalize OrthogonalMatrixQ Out Outer OuterPolygon OuterPolyhedron OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OverwriteTarget OwenT OwnValuesPackage PackingMethod PaddedForm Padding PaddingLayer PaddingSize PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageTheme PageWidth Pagination PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath PalindromeQ Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo Parallelepiped ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds Parallelogram ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParametricRegion ParentBox ParentCell ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParentNotebook ParetoDistribution ParetoPickandsDistribution ParkData Part PartBehavior PartialCorrelationFunction PartialD ParticleAcceleratorData ParticleData Partition PartitionGranularity PartitionsP PartitionsQ PartLayer PartOfSpeech PartProtection ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteAutoQuoteCharacters PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PeakDetect PeanoCurve PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PercentForm PerfectNumber PerfectNumberQ PerformanceGoal Perimeter PeriodicBoundaryCondition PeriodicInterpolation Periodogram PeriodogramArray Permanent Permissions PermissionsGroup PermissionsGroupMemberQ PermissionsGroups PermissionsKey PermissionsKeys PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PerpendicularBisector PersistenceLocation PersistenceTime PersistentObject PersistentObjects PersistentValue PersonData PERTDistribution PetersenGraph PhaseMargins PhaseRange PhysicalSystemData Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest PingTime Pink PitchRecognize Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarAngle PlanarGraph PlanarGraphQ PlanckRadiationLaw PlaneCurveData PlanetaryMoonData PlanetData PlantData Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLabels PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangeClipPlanesStyle PlotRangePadding PlotRegion PlotStyle PlotTheme Pluralize Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox Point3DBoxOptions PointBox PointBoxOptions PointFigureChart PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonalNumber PolygonAngle PolygonBox PolygonBoxOptions PolygonCoordinates PolygonDecomposition PolygonHoleScale PolygonIntersections PolygonScale Polyhedron PolyhedronAngle PolyhedronCoordinates PolyhedronData PolyhedronDecomposition PolyhedronGenus PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PoolingLayer PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position PositionIndex Positive PositiveDefiniteMatrixQ PositiveIntegers PositiveRationals PositiveReals PositiveSemidefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerRange PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement Predict PredictionRoot PredictorFunction PredictorInformation PredictorMeasurements PredictorMeasurementsObject PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependLayer PrependTo PreprocessingRules PreserveColor PreserveImageOptions Previous PreviousCell PreviousDate PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitivePolynomialQ PrimitiveRoot PrimitiveRootList PrincipalComponents PrincipalValue Print PrintableASCIIQ PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment Printout3D Printout3DPreviewer PrintPrecision PrintTemporary Prism PrismBox PrismBoxOptions PrivateCellOptions PrivateEvaluationOptions PrivateFontOptions PrivateFrontEndOptions PrivateKey PrivateNotebookOptions PrivatePaths Probability ProbabilityDistribution ProbabilityPlot ProbabilityPr ProbabilityScalePlot ProbitModelFit ProcessConnection ProcessDirectory ProcessEnvironment Processes ProcessEstimator ProcessInformation ProcessObject ProcessParameterAssumptions ProcessParameterQ ProcessStateDomain ProcessStatus ProcessTimeDomain Product ProductDistribution ProductLog ProgressIndicator ProgressIndicatorBox ProgressIndicatorBoxOptions Projection Prolog PromptForm ProofObject Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse PsychrometricPropertyData PublicKey PublisherID PulsarData PunctuationCharacter Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptionsQBinomial QFactorial QGamma QHypergeometricPFQ QnDispersion QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ QuadraticOptimization Quantile QuantilePlot Quantity QuantityArray QuantityDistribution QuantityForm QuantityMagnitude QuantityQ QuantityUnit QuantityVariable QuantityVariableCanonicalUnit QuantityVariableDimensions QuantityVariableIdentifier QuantityVariablePhysicalQuantity Quartics QuartileDeviation Quartiles QuartileSkewness Query QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainderRadialGradientImage RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RadonTransform RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Ramp Random RandomChoice RandomColor RandomComplex RandomEntity RandomFunction RandomGeoPosition RandomGraph RandomImage RandomInstance RandomInteger RandomPermutation RandomPoint RandomPolygon RandomPolyhedron RandomPrime RandomReal RandomSample RandomSeed RandomSeeding RandomVariate RandomWalkProcess RandomWord Range RangeFilter RangeSpecification RankedMax RankedMin RarerProbability Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadByteArray ReadLine ReadList ReadProtected ReadString Real RealAbs RealBlockDiagonalForm RealDigits RealExponent Reals RealSign Reap RecognitionPrior RecognitionThreshold Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RectangularRepeatingElement RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate Region RegionBinarize RegionBoundary RegionBounds RegionCentroid RegionDifference RegionDimension RegionDisjoint RegionDistance RegionDistanceFunction RegionEmbeddingDimension RegionEqual RegionFunction RegionImage RegionIntersection RegionMeasure RegionMember RegionMemberFunction RegionMoment RegionNearest RegionNearestFunction RegionPlot RegionPlot3D RegionProduct RegionQ RegionResize RegionSize RegionSymmetricDifference RegionUnion RegionWithin RegisterExternalEvaluator RegularExpression Regularization RegularlySampledQ RegularPolygon ReIm ReImLabels ReImPlot ReImStyle Reinstall RelationalDatabase RelationGraph Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot RemoteAuthorizationCaching RemoteConnect RemoteConnectionObject RemoteFile RemoteRun RemoteRunProcess Remove RemoveAlphaChannel RemoveAsynchronousTask RemoveAudioStream RemoveBackground RemoveChannelListener RemoveChannelSubscribers Removed RemoveDiacritics RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RemoveUsers RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart RepairMesh Repeated RepeatedNull RepeatedString RepeatedTiming RepeatingElement Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated ReplicateLayer RequiredPhysicalQuantities Resampling ResamplingAlgorithmData ResamplingMethod Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask ReshapeLayer Residue ResizeLayer Resolve ResourceAcquire ResourceData ResourceFunction ResourceObject ResourceRegister ResourceRemove ResourceSearch ResourceSubmissionObject ResourceSubmit ResourceSystemBase ResourceUpdate ResponseForm Rest RestartInterval Restricted Resultant ResumePacket Return ReturnEntersInput ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnReceiptFunction ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseSort ReverseSortBy ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ RiemannXi Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightComposition RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity RollPitchYawAngles RollPitchYawMatrix RomanNumeral Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RSolveValue RudinShapiro RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulePlot RulerUnits Run RunProcess RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilaritySameQ SameTest SampledEntityClass SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SASTriangle SatelliteData SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveConnection SaveDefinitions SavitzkyGolayMatrix SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTask ScheduledTaskActiveQ ScheduledTaskInformation ScheduledTaskInformationData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScientificNotationThreshold ScorerGi ScorerGiPrime ScorerHi ScorerHiPrime ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptForm ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition SearchAdjustment SearchIndexObject SearchIndices SearchQueryString SearchResultObject Sec Sech SechDistribution SecondOrderConeOptimization SectionGrouping SectorChart SectorChart3D SectorOrigin SectorSpacing SecuredAuthenticationKey SecuredAuthenticationKeys SeedRandom Select Selectable SelectComponents SelectedCells SelectedNotebook SelectFirst Selection SelectionAnimate SelectionCell SelectionCellCreateCell SelectionCellDefaultStyle SelectionCellParentStyle SelectionCreateCell SelectionDebuggerTag SelectionDuplicateCell SelectionEvaluate SelectionEvaluateCreateCell SelectionMove SelectionPlaceholder SelectionSetStyle SelectWithContents SelfLoops SelfLoopStyle SemanticImport SemanticImportString SemanticInterpretation SemialgebraicComponentInstances SemidefiniteOptimization SendMail SendMessage Sequence SequenceAlignment SequenceAttentionLayer SequenceCases SequenceCount SequenceFold SequenceFoldList SequenceForm SequenceHold SequenceLastLayer SequenceMostLayer SequencePosition SequencePredict SequencePredictorFunction SequenceReplace SequenceRestLayer SequenceReverseLayer SequenceSplit Series SeriesCoefficient SeriesData ServiceConnect ServiceDisconnect ServiceExecute ServiceObject ServiceRequest ServiceResponse ServiceSubmit SessionSubmit SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetCloudDirectory SetCookies SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPermissions SetPrecision SetProperty SetSecuredAuthenticationKey SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemModel SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetUsers SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share SharingList Sharpen ShearingMatrix ShearingTransform ShellRegion ShenCastanMatrix ShiftedGompertzDistribution ShiftRegisterSequence Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortTimeFourier ShortTimeFourierData ShortUpArrow Show ShowAutoConvert ShowAutoSpellCheck ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowCodeAssist ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiderealTime SiegelTheta SiegelTukeyTest SierpinskiCurve SierpinskiMesh Sign Signature SignedRankTest SignedRegionDistance SignificanceLevel SignPadding SignTest SimilarityRules SimpleGraph SimpleGraphQ SimplePolygonQ SimplePolyhedronQ Simplex Simplify Sin Sinc SinghMaddalaDistribution SingleEvaluation SingleLetterItalics SingleLetterStyle SingularValueDecomposition SingularValueList SingularValuePlot SingularValues Sinh SinhIntegral SinIntegral SixJSymbol Skeleton SkeletonTransform SkellamDistribution Skewness SkewNormalDistribution SkinStyle Skip SliceContourPlot3D SliceDensityPlot3D SliceDistribution SliceVectorPlot3D Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDecomposition SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SnDispersion Snippet SnubPolyhedron SocialMediaData Socket SocketConnect SocketListen SocketListener SocketObject SocketOpen SocketReadMessage SocketReadyQ Sockets SocketWaitAll SocketWaitNext SoftmaxLayer SokalSneathDissimilarity SolarEclipse SolarSystemFeatureData SolidAngle SolidData SolidRegionQ Solve SolveAlways SolveDelayed Sort SortBy SortedBy SortedEntityClass Sound SoundAndGraphics SoundNote SoundVolume SourceLink Sow Space SpaceCurveData SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution SpatialMedian SpatialTransformationLayer Speak SpeakTextPacket SpearmanRankTest SpearmanRho SpeciesData SpecificityGoal SpectralLineData Spectrogram SpectrogramArray Specularity SpeechRecognize SpeechSynthesize SpellingCorrection SpellingCorrectionList SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SpherePoints SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SphericalShell SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquareMatrixQ SquareRepeatingElement SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave SSSTriangle StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackedDateListPlot StackedListPlot StackInhibit StadiumShape StandardAtmosphereData StandardDeviation StandardDeviationFilter StandardForm Standardize Standardized StandardOceanData StandbyDistribution Star StarClusterData StarData StarGraph StartAsynchronousTask StartExternalSession StartingStepSize StartOfLine StartOfString StartProcess StartScheduledTask StartupSound StartWebSession StateDimensions StateFeedbackGains StateOutputEstimator StateResponse StateSpaceModel StateSpaceRealization StateSpaceTransform StateTransformationLinearize StationaryDistribution StationaryWaveletPacketTransform StationaryWaveletTransform StatusArea StatusCentrality StepMonitor StereochemistryElements StieltjesGamma StirlingS1 StirlingS2 StopAsynchronousTask StoppingPowerData StopScheduledTask StrataVariables StratonovichProcess StreamColorFunction StreamColorFunctionScaling StreamDensityPlot StreamMarkers StreamPlot StreamPoints StreamPosition Streams StreamScale StreamStyle String StringBreak StringByteCount StringCases StringContainsQ StringCount StringDelete StringDrop StringEndsQ StringExpression StringExtract StringForm StringFormat StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPadLeft StringPadRight StringPart StringPartition StringPosition StringQ StringRepeat StringReplace StringReplaceList StringReplacePart StringReverse StringRiffle StringRotateLeft StringRotateRight StringSkeleton StringSplit StringStartsQ StringTake StringTemplate StringToByteArray StringToStream StringTrim StripBoxes StripOnInput StripWrapperBoxes StrokeForm StructuralImportance StructuredArray StructuredSelection StruveH StruveL Stub StudentTDistribution Style StyleBox StyleBoxAutoDelete StyleData StyleDefinitions StyleForm StyleHints StyleKeyMapping StyleMenuListing StyleNameDialogSettings StyleNames StylePrint StyleSheetPath Subdivide Subfactorial Subgraph SubMinus SubPlus SubresultantPolynomialRemainders SubresultantPolynomials Subresultants Subscript SubscriptBox SubscriptBoxOptions Subscripted Subsequences Subset SubsetEqual SubsetMap SubsetQ Subsets SubStar SubstitutionSystem Subsuperscript SubsuperscriptBox SubsuperscriptBoxOptions Subtract SubtractFrom SubtractSides SubValues Succeeds SucceedsEqual SucceedsSlantEqual SucceedsTilde Success SuchThat Sum SumConvergence SummationLayer Sunday SunPosition Sunrise Sunset SuperDagger SuperMinus SupernovaData SuperPlus Superscript SuperscriptBox SuperscriptBoxOptions Superset SupersetEqual SuperStar Surd SurdForm SurfaceArea SurfaceColor SurfaceData SurfaceGraphics SurvivalDistribution SurvivalFunction SurvivalModel SurvivalModelFit SuspendPacket SuzukiDistribution SuzukiGroupSuz SwatchLegend Switch Symbol SymbolName SymletWavelet Symmetric SymmetricGroup SymmetricKey SymmetricMatrixQ SymmetricPolynomial SymmetricReduction Symmetrize SymmetrizedArray SymmetrizedArrayRules SymmetrizedDependentComponents SymmetrizedIndependentComponents SymmetrizedReplacePart SynchronousInitialization SynchronousUpdating Synonyms Syntax SyntaxForm SyntaxInformation SyntaxLength SyntaxPacket SyntaxQ SynthesizeMissingValues SystemDialogInput SystemException SystemGet SystemHelpPath SystemInformation SystemInformationData SystemInstall SystemModel SystemModeler SystemModelExamples SystemModelLinearize SystemModelParametricSimulate SystemModelPlot SystemModelProgressReporting SystemModelReliability SystemModels SystemModelSimulate SystemModelSimulateSensitivity SystemModelSimulationData SystemOpen SystemOptions SystemProcessData SystemProcesses SystemsConnectionsModel SystemsModelDelay SystemsModelDelayApproximate SystemsModelDelete SystemsModelDimensions SystemsModelExtract SystemsModelFeedbackConnect SystemsModelLabels SystemsModelLinearity SystemsModelMerge SystemsModelOrder SystemsModelParallelConnect SystemsModelSeriesConnect SystemsModelStateFeedbackConnect SystemsModelVectorRelativeOrders SystemStub SystemTestTab TabFilling Table TableAlignments TableDepth TableDirections TableForm TableHeadings TableSpacing TableView TableViewBox TableViewBoxBackground TableViewBoxOptions TabSpacings TabView TabViewBox TabViewBoxOptions TagBox TagBoxNote TagBoxOptions TaggingRules TagSet TagSetDelayed TagStyle TagUnset Take TakeDrop TakeLargest TakeLargestBy TakeList TakeSmallest TakeSmallestBy TakeWhile Tally Tan Tanh TargetDevice TargetFunctions TargetSystem TargetUnits TaskAbort TaskExecute TaskObject TaskRemove TaskResume Tasks TaskSuspend TaskWait TautologyQ TelegraphProcess TemplateApply TemplateArgBox TemplateBox TemplateBoxOptions TemplateEvaluate TemplateExpression TemplateIf TemplateObject TemplateSequence TemplateSlot TemplateSlotSequence TemplateUnevaluated TemplateVerbatim TemplateWith TemporalData TemporalRegularity Temporary TemporaryVariable TensorContract TensorDimensions TensorExpand TensorProduct TensorQ TensorRank TensorReduce TensorSymmetry TensorTranspose TensorWedge TestID TestReport TestReportObject TestResultObject Tetrahedron TetrahedronBox TetrahedronBoxOptions TeXForm TeXSave Text Text3DBox Text3DBoxOptions TextAlignment TextBand TextBoundingBox TextBox TextCases TextCell TextClipboardType TextContents TextData TextElement TextForm TextGrid TextJustification TextLine TextPacket TextParagraph TextPosition TextRecognize TextSearch TextSearchReport TextSentences TextString TextStructure TextStyle TextTranslation Texture TextureCoordinateFunction TextureCoordinateScaling TextWords Therefore ThermodynamicData ThermometerGauge Thick Thickness Thin Thinning ThisLink ThompsonGroupTh Thread ThreadingLayer ThreeJSymbol Threshold Through Throw ThueMorse Thumbnail Thursday Ticks TicksStyle TideData Tilde TildeEqual TildeFullEqual TildeTilde TimeConstrained TimeConstraint TimeDirection TimeFormat TimeGoal TimelinePlot TimeObject TimeObjectQ Times TimesBy TimeSeries 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Trace TraceAbove TraceAction TraceBackward TraceDepth TraceDialog TraceForward TraceInternal TraceLevel TraceOff TraceOn TraceOriginal TracePrint TraceScan TrackedSymbols TrackingFunction TracyWidomDistribution TradingChart TraditionalForm TraditionalFunctionNotation TraditionalNotation TraditionalOrder TrainingProgressCheckpointing TrainingProgressFunction TrainingProgressMeasurements TrainingProgressReporting TrainingStoppingCriterion TransferFunctionCancel TransferFunctionExpand TransferFunctionFactor TransferFunctionModel TransferFunctionPoles TransferFunctionTransform TransferFunctionZeros TransformationClass TransformationFunction TransformationFunctions TransformationMatrix TransformedDistribution TransformedField TransformedProcess TransformedRegion TransitionDirection TransitionDuration TransitionEffect TransitiveClosureGraph TransitiveReductionGraph Translate TranslationOptions TranslationTransform Transliterate Transparent TransparentColor Transpose TransposeLayer 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clickable_add clickable_add_ext clickable_change clickable_change_ext clickable_delete clickable_exists clickable_set_style show_question show_question_async get_integer get_string get_integer_async get_string_async get_login_async get_open_filename get_save_filename get_open_filename_ext get_save_filename_ext show_error highscore_clear highscore_add highscore_value highscore_name draw_highscore sprite_exists sprite_get_name sprite_get_number sprite_get_width sprite_get_height sprite_get_xoffset sprite_get_yoffset sprite_get_bbox_left sprite_get_bbox_right sprite_get_bbox_top sprite_get_bbox_bottom sprite_save sprite_save_strip sprite_set_cache_size sprite_set_cache_size_ext sprite_get_tpe sprite_prefetch sprite_prefetch_multi sprite_flush sprite_flush_multi sprite_set_speed sprite_get_speed_type sprite_get_speed font_exists font_get_name font_get_fontname font_get_bold font_get_italic font_get_first font_get_last font_get_size font_set_cache_size path_exists path_get_name path_get_length path_get_time path_get_kind path_get_closed path_get_precision path_get_number path_get_point_x path_get_point_y path_get_point_speed path_get_x path_get_y path_get_speed script_exists script_get_name timeline_add timeline_delete timeline_clear timeline_exists timeline_get_name timeline_moment_clear timeline_moment_add_script timeline_size timeline_max_moment object_exists object_get_name object_get_sprite object_get_solid object_get_visible object_get_persistent object_get_mask object_get_parent object_get_physics object_is_ancestor room_exists room_get_name sprite_set_offset sprite_duplicate sprite_assign sprite_merge sprite_add sprite_replace sprite_create_from_surface sprite_add_from_surface sprite_delete sprite_set_alpha_from_sprite sprite_collision_mask font_add_enable_aa font_add_get_enable_aa font_add font_add_sprite font_add_sprite_ext font_replace font_replace_sprite font_replace_sprite_ext font_delete path_set_kind path_set_closed path_set_precision path_add path_assign path_duplicate path_append path_delete path_add_point path_insert_point path_change_point path_delete_point path_clear_points path_reverse path_mirror path_flip path_rotate path_rescale path_shift script_execute object_set_sprite object_set_solid object_set_visible object_set_persistent object_set_mask room_set_width room_set_height room_set_persistent room_set_background_colour room_set_background_color room_set_view room_set_viewport room_get_viewport room_set_view_enabled room_add room_duplicate room_assign room_instance_add room_instance_clear room_get_camera room_set_camera asset_get_index asset_get_type file_text_open_from_string file_text_open_read file_text_open_write file_text_open_append file_text_close file_text_write_string file_text_write_real file_text_writeln file_text_read_string file_text_read_real file_text_readln file_text_eof file_text_eoln file_exists file_delete file_rename file_copy directory_exists directory_create directory_destroy file_find_first file_find_next file_find_close file_attributes filename_name filename_path filename_dir filename_drive filename_ext filename_change_ext file_bin_open file_bin_rewrite file_bin_close file_bin_position file_bin_size file_bin_seek file_bin_write_byte file_bin_read_byte parameter_count parameter_string environment_get_variable ini_open_from_string ini_open ini_close ini_read_string ini_read_real ini_write_string ini_write_real ini_key_exists ini_section_exists ini_key_delete ini_section_delete ds_set_precision ds_exists ds_stack_create ds_stack_destroy ds_stack_clear ds_stack_copy ds_stack_size ds_stack_empty ds_stack_push ds_stack_pop ds_stack_top ds_stack_write ds_stack_read ds_queue_create ds_queue_destroy ds_queue_clear ds_queue_copy ds_queue_size ds_queue_empty ds_queue_enqueue ds_queue_dequeue ds_queue_head ds_queue_tail ds_queue_write ds_queue_read ds_list_create ds_list_destroy ds_list_clear ds_list_copy ds_list_size ds_list_empty ds_list_add ds_list_insert ds_list_replace ds_list_delete ds_list_find_index ds_list_find_value ds_list_mark_as_list ds_list_mark_as_map ds_list_sort ds_list_shuffle ds_list_write ds_list_read ds_list_set ds_map_create ds_map_destroy ds_map_clear ds_map_copy ds_map_size ds_map_empty ds_map_add ds_map_add_list ds_map_add_map ds_map_replace ds_map_replace_map ds_map_replace_list ds_map_delete ds_map_exists ds_map_find_value ds_map_find_previous ds_map_find_next ds_map_find_first ds_map_find_last ds_map_write ds_map_read ds_map_secure_save ds_map_secure_load ds_map_secure_load_buffer ds_map_secure_save_buffer ds_map_set ds_priority_create ds_priority_destroy ds_priority_clear ds_priority_copy ds_priority_size ds_priority_empty ds_priority_add ds_priority_change_priority ds_priority_find_priority ds_priority_delete_value ds_priority_delete_min ds_priority_find_min ds_priority_delete_max ds_priority_find_max ds_priority_write ds_priority_read ds_grid_create ds_grid_destroy ds_grid_copy ds_grid_resize ds_grid_width ds_grid_height ds_grid_clear ds_grid_set ds_grid_add ds_grid_multiply ds_grid_set_region ds_grid_add_region ds_grid_multiply_region ds_grid_set_disk ds_grid_add_disk ds_grid_multiply_disk ds_grid_set_grid_region ds_grid_add_grid_region ds_grid_multiply_grid_region ds_grid_get ds_grid_get_sum ds_grid_get_max ds_grid_get_min ds_grid_get_mean ds_grid_get_disk_sum ds_grid_get_disk_min ds_grid_get_disk_max ds_grid_get_disk_mean ds_grid_value_exists ds_grid_value_x ds_grid_value_y ds_grid_value_disk_exists ds_grid_value_disk_x ds_grid_value_disk_y ds_grid_shuffle ds_grid_write ds_grid_read ds_grid_sort ds_grid_set ds_grid_get effect_create_below effect_create_above effect_clear part_type_create part_type_destroy part_type_exists part_type_clear part_type_shape part_type_sprite part_type_size part_type_scale part_type_orientation part_type_life part_type_step part_type_death part_type_speed part_type_direction part_type_gravity part_type_colour1 part_type_colour2 part_type_colour3 part_type_colour_mix part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists 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= function(hljs) {\n var PARAMS = {\n className: 'params',\n begin: '\\\\(', end: '\\\\)'\n };\n\n var F_KEYWORDS = {\n literal: '.False. .True.',\n keyword: 'kind do while private call intrinsic where elsewhere ' +\n 'type endtype endmodule endselect endinterface end enddo endif if forall endforall only contains default return stop then ' +\n 'public subroutine|10 function program .and. .or. .not. .le. .eq. .ge. .gt. .lt. ' +\n 'goto save else use module select case ' +\n 'access blank direct exist file fmt form formatted iostat name named nextrec number opened rec recl sequential status unformatted unit ' +\n 'continue format pause cycle exit ' +\n 'c_null_char c_alert c_backspace c_form_feed flush wait decimal round iomsg ' +\n 'synchronous nopass non_overridable pass protected volatile abstract extends import ' +\n 'non_intrinsic value deferred generic final enumerator class associate bind enum ' +\n 'c_int c_short c_long c_long_long c_signed_char c_size_t c_int8_t c_int16_t c_int32_t c_int64_t c_int_least8_t c_int_least16_t ' +\n 'c_int_least32_t c_int_least64_t c_int_fast8_t c_int_fast16_t c_int_fast32_t c_int_fast64_t c_intmax_t C_intptr_t c_float c_double ' +\n 'c_long_double c_float_complex c_double_complex c_long_double_complex c_bool c_char c_null_ptr c_null_funptr ' +\n 'c_new_line c_carriage_return c_horizontal_tab c_vertical_tab iso_c_binding c_loc c_funloc c_associated c_f_pointer ' +\n 'c_ptr c_funptr iso_fortran_env character_storage_size error_unit file_storage_size input_unit iostat_end iostat_eor ' +\n 'numeric_storage_size output_unit c_f_procpointer ieee_arithmetic ieee_support_underflow_control ' +\n 'ieee_get_underflow_mode ieee_set_underflow_mode newunit contiguous recursive ' +\n 'pad position action delim readwrite eor advance nml interface procedure namelist include sequence elemental pure ' +\n 'integer real character complex logical dimension allocatable|10 parameter ' +\n 'external implicit|10 none double precision assign intent optional pointer ' +\n 'target in out common equivalence data ' +\n // IRPF90 special keywords\n 'begin_provider &begin_provider end_provider begin_shell end_shell begin_template end_template subst assert touch ' +\n 'soft_touch provide no_dep free irp_if irp_else irp_endif irp_write irp_read',\n built_in: 'alog alog10 amax0 amax1 amin0 amin1 amod cabs ccos cexp clog csin csqrt dabs dacos dasin datan datan2 dcos dcosh ddim dexp dint ' +\n 'dlog dlog10 dmax1 dmin1 dmod dnint dsign dsin dsinh dsqrt dtan dtanh float iabs idim idint idnint ifix isign max0 max1 min0 min1 sngl ' +\n 'algama cdabs cdcos cdexp cdlog cdsin cdsqrt cqabs cqcos cqexp cqlog cqsin cqsqrt dcmplx dconjg derf derfc dfloat dgamma dimag dlgama ' +\n 'iqint qabs qacos qasin qatan qatan2 qcmplx qconjg qcos qcosh qdim qerf qerfc qexp qgamma qimag qlgama qlog qlog10 qmax1 qmin1 qmod ' +\n 'qnint qsign qsin qsinh qsqrt qtan qtanh abs acos aimag aint anint asin atan atan2 char cmplx conjg cos cosh exp ichar index int log ' +\n 'log10 max min nint sign sin sinh sqrt tan tanh print write dim lge lgt lle llt mod nullify allocate deallocate ' +\n 'adjustl adjustr all allocated any associated bit_size btest ceiling count cshift date_and_time digits dot_product ' +\n 'eoshift epsilon exponent floor fraction huge iand ibclr ibits ibset ieor ior ishft ishftc lbound len_trim matmul ' +\n 'maxexponent maxloc maxval merge minexponent minloc minval modulo mvbits nearest pack present product ' +\n 'radix random_number random_seed range repeat reshape rrspacing scale scan selected_int_kind selected_real_kind ' +\n 'set_exponent shape size spacing spread sum system_clock tiny transpose trim ubound unpack verify achar iachar transfer ' +\n 'dble entry dprod cpu_time command_argument_count get_command get_command_argument get_environment_variable is_iostat_end ' +\n 'ieee_arithmetic ieee_support_underflow_control ieee_get_underflow_mode ieee_set_underflow_mode ' +\n 'is_iostat_eor move_alloc new_line selected_char_kind same_type_as extends_type_of' +\n 'acosh asinh atanh bessel_j0 bessel_j1 bessel_jn bessel_y0 bessel_y1 bessel_yn erf erfc erfc_scaled gamma log_gamma hypot norm2 ' +\n 'atomic_define atomic_ref execute_command_line leadz trailz storage_size merge_bits ' +\n 'bge bgt ble blt dshiftl dshiftr findloc iall iany iparity image_index lcobound ucobound maskl maskr ' +\n 'num_images parity popcnt poppar shifta shiftl shiftr this_image ' +\n 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float string vector matrix if else switch case default while do for in break continue global proc return about abs addAttr addAttributeEditorNodeHelp addDynamic addNewShelfTab addPP addPanelCategory addPrefixToName advanceToNextDrivenKey affectedNet affects aimConstraint air alias aliasAttr align alignCtx alignCurve alignSurface allViewFit ambientLight angle angleBetween animCone animCurveEditor animDisplay animView annotate appendStringArray applicationName applyAttrPreset applyTake arcLenDimContext arcLengthDimension arclen arrayMapper art3dPaintCtx artAttrCtx artAttrPaintVertexCtx artAttrSkinPaintCtx artAttrTool artBuildPaintMenu artFluidAttrCtx artPuttyCtx artSelectCtx artSetPaintCtx artUserPaintCtx assignCommand assignInputDevice assignViewportFactories attachCurve attachDeviceAttr attachSurface attrColorSliderGrp attrCompatibility attrControlGrp attrEnumOptionMenu attrEnumOptionMenuGrp attrFieldGrp attrFieldSliderGrp attrNavigationControlGrp attrPresetEditWin attributeExists 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collision color colorAtPoint colorEditor colorIndex colorIndexSliderGrp colorSliderButtonGrp colorSliderGrp columnLayout commandEcho commandLine commandPort compactHairSystem componentEditor compositingInterop computePolysetVolume condition cone confirmDialog connectAttr connectControl connectDynamic connectJoint connectionInfo constrain constrainValue constructionHistory container containsMultibyte contextInfo control convertFromOldLayers convertIffToPsd convertLightmap convertSolidTx convertTessellation convertUnit copyArray copyFlexor copyKey copySkinWeights cos cpButton cpCache cpClothSet cpCollision cpConstraint cpConvClothToMesh cpForces cpGetSolverAttr cpPanel cpProperty cpRigidCollisionFilter cpSeam cpSetEdit cpSetSolverAttr cpSolver cpSolverTypes cpTool cpUpdateClothUVs createDisplayLayer createDrawCtx createEditor createLayeredPsdFile createMotionField createNewShelf createNode createRenderLayer createSubdivRegion cross crossProduct ctxAbort ctxCompletion ctxEditMode ctxTraverse currentCtx currentTime currentTimeCtx currentUnit curve curveAddPtCtx curveCVCtx curveEPCtx curveEditorCtx curveIntersect curveMoveEPCtx curveOnSurface curveSketchCtx cutKey cycleCheck cylinder dagPose date defaultLightListCheckBox defaultNavigation defineDataServer defineVirtualDevice deformer deg_to_rad delete deleteAttr deleteShadingGroupsAndMaterials deleteShelfTab deleteUI deleteUnusedBrushes delrandstr detachCurve detachDeviceAttr detachSurface deviceEditor devicePanel dgInfo dgdirty dgeval dgtimer dimWhen directKeyCtx directionalLight dirmap dirname disable disconnectAttr disconnectJoint diskCache displacementToPoly displayAffected displayColor displayCull displayLevelOfDetail displayPref displayRGBColor displaySmoothness displayStats displayString displaySurface distanceDimContext distanceDimension doBlur dolly dollyCtx dopeSheetEditor dot dotProduct doubleProfileBirailSurface drag dragAttrContext draggerContext dropoffLocator duplicate duplicateCurve 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hsv_to_rgb hudButton hudSlider hudSliderButton hwReflectionMap hwRender hwRenderLoad hyperGraph hyperPanel hyperShade hypot iconTextButton iconTextCheckBox iconTextRadioButton iconTextRadioCollection iconTextScrollList iconTextStaticLabel ikHandle ikHandleCtx ikHandleDisplayScale ikSolver ikSplineHandleCtx ikSystem ikSystemInfo ikfkDisplayMethod illustratorCurves image imfPlugins inheritTransform insertJoint insertJointCtx insertKeyCtx insertKnotCurve insertKnotSurface instance instanceable instancer intField intFieldGrp intScrollBar intSlider intSliderGrp interToUI internalVar intersect iprEngine isAnimCurve isConnected isDirty isParentOf isSameObject isTrue isValidObjectName isValidString isValidUiName isolateSelect itemFilter itemFilterAttr itemFilterRender itemFilterType joint jointCluster jointCtx jointDisplayScale jointLattice keyTangent keyframe keyframeOutliner keyframeRegionCurrentTimeCtx keyframeRegionDirectKeyCtx keyframeRegionDollyCtx keyframeRegionInsertKeyCtx keyframeRegionMoveKeyCtx keyframeRegionScaleKeyCtx keyframeRegionSelectKeyCtx keyframeRegionSetKeyCtx keyframeRegionTrackCtx keyframeStats lassoContext lattice latticeDeformKeyCtx launch launchImageEditor layerButton layeredShaderPort layeredTexturePort layout layoutDialog lightList lightListEditor lightListPanel lightlink lineIntersection linearPrecision linstep listAnimatable listAttr listCameras listConnections listDeviceAttachments listHistory listInputDeviceAxes listInputDeviceButtons listInputDevices listMenuAnnotation listNodeTypes listPanelCategories listRelatives listSets listTransforms listUnselected listerEditor loadFluid loadNewShelf loadPlugin loadPluginLanguageResources loadPrefObjects localizedPanelLabel lockNode loft log longNameOf lookThru ls lsThroughFilter lsType lsUI Mayatomr mag makeIdentity makeLive makePaintable makeRoll makeSingleSurface makeTubeOn makebot manipMoveContext manipMoveLimitsCtx manipOptions manipRotateContext manipRotateLimitsCtx manipScaleContext manipScaleLimitsCtx marker match max memory menu menuBarLayout menuEditor menuItem menuItemToShelf menuSet menuSetPref messageLine min minimizeApp mirrorJoint modelCurrentTimeCtx modelEditor modelPanel mouse movIn movOut move moveIKtoFK moveKeyCtx moveVertexAlongDirection multiProfileBirailSurface mute nParticle nameCommand nameField namespace namespaceInfo newPanelItems newton nodeCast nodeIconButton nodeOutliner nodePreset nodeType noise nonLinear normalConstraint normalize nurbsBoolean nurbsCopyUVSet nurbsCube nurbsEditUV nurbsPlane nurbsSelect nurbsSquare nurbsToPoly nurbsToPolygonsPref nurbsToSubdiv nurbsToSubdivPref nurbsUVSet nurbsViewDirectionVector objExists objectCenter objectLayer objectType objectTypeUI obsoleteProc oceanNurbsPreviewPlane offsetCurve offsetCurveOnSurface offsetSurface openGLExtension openMayaPref optionMenu optionMenuGrp optionVar orbit orbitCtx orientConstraint outlinerEditor outlinerPanel overrideModifier paintEffectsDisplay pairBlend palettePort paneLayout panel panelConfiguration panelHistory paramDimContext paramDimension paramLocator parent parentConstraint particle particleExists particleInstancer particleRenderInfo partition pasteKey pathAnimation pause pclose percent performanceOptions pfxstrokes pickWalk picture pixelMove planarSrf plane play playbackOptions playblast plugAttr plugNode pluginInfo pluginResourceUtil pointConstraint pointCurveConstraint pointLight pointMatrixMult pointOnCurve pointOnSurface pointPosition poleVectorConstraint polyAppend polyAppendFacetCtx polyAppendVertex polyAutoProjection polyAverageNormal polyAverageVertex polyBevel polyBlendColor polyBlindData polyBoolOp polyBridgeEdge polyCacheMonitor polyCheck polyChipOff polyClipboard polyCloseBorder polyCollapseEdge polyCollapseFacet polyColorBlindData polyColorDel polyColorPerVertex polyColorSet polyCompare polyCone polyCopyUV polyCrease polyCreaseCtx polyCreateFacet polyCreateFacetCtx polyCube polyCut polyCutCtx polyCylinder polyCylindricalProjection polyDelEdge polyDelFacet polyDelVertex polyDuplicateAndConnect polyDuplicateEdge polyEditUV polyEditUVShell polyEvaluate polyExtrudeEdge polyExtrudeFacet polyExtrudeVertex polyFlipEdge polyFlipUV polyForceUV polyGeoSampler polyHelix polyInfo polyInstallAction polyLayoutUV polyListComponentConversion polyMapCut polyMapDel polyMapSew polyMapSewMove polyMergeEdge polyMergeEdgeCtx polyMergeFacet polyMergeFacetCtx polyMergeUV polyMergeVertex polyMirrorFace polyMoveEdge polyMoveFacet polyMoveFacetUV polyMoveUV polyMoveVertex polyNormal polyNormalPerVertex polyNormalizeUV polyOptUvs polyOptions polyOutput polyPipe polyPlanarProjection polyPlane polyPlatonicSolid polyPoke polyPrimitive polyPrism polyProjection polyPyramid polyQuad polyQueryBlindData polyReduce polySelect polySelectConstraint polySelectConstraintMonitor polySelectCtx polySelectEditCtx polySeparate polySetToFaceNormal polySewEdge polyShortestPathCtx polySmooth polySoftEdge polySphere polySphericalProjection polySplit polySplitCtx polySplitEdge polySplitRing polySplitVertex polyStraightenUVBorder polySubdivideEdge polySubdivideFacet polyToSubdiv polyTorus polyTransfer polyTriangulate polyUVSet polyUnite polyWedgeFace popen popupMenu pose pow preloadRefEd print progressBar progressWindow projFileViewer projectCurve projectTangent projectionContext projectionManip promptDialog propModCtx propMove psdChannelOutliner psdEditTextureFile psdExport psdTextureFile putenv pwd python querySubdiv quit rad_to_deg radial radioButton radioButtonGrp radioCollection radioMenuItemCollection rampColorPort rand randomizeFollicles randstate rangeControl readTake rebuildCurve rebuildSurface recordAttr recordDevice redo reference referenceEdit referenceQuery refineSubdivSelectionList refresh refreshAE registerPluginResource rehash reloadImage removeJoint removeMultiInstance removePanelCategory rename renameAttr renameSelectionList renameUI render renderGlobalsNode renderInfo 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selectKeyCtx selectKeyframeRegionCtx selectMode selectPref selectPriority selectType selectedNodes selectionConnection separator setAttr setAttrEnumResource setAttrMapping setAttrNiceNameResource setConstraintRestPosition setDefaultShadingGroup setDrivenKeyframe setDynamic setEditCtx setEditor setFluidAttr setFocus setInfinity setInputDeviceMapping setKeyCtx setKeyPath setKeyframe setKeyframeBlendshapeTargetWts setMenuMode setNodeNiceNameResource setNodeTypeFlag setParent setParticleAttr setPfxToPolyCamera setPluginResource setProject setStampDensity setStartupMessage setState setToolTo setUITemplate setXformManip sets shadingConnection shadingGeometryRelCtx shadingLightRelCtx shadingNetworkCompare shadingNode shapeCompare shelfButton shelfLayout shelfTabLayout shellField shortNameOf showHelp showHidden showManipCtx showSelectionInTitle showShadingGroupAttrEditor showWindow sign simplify sin singleProfileBirailSurface size sizeBytes skinCluster skinPercent smoothCurve smoothTangentSurface smoothstep snap2to2 snapKey snapMode snapTogetherCtx snapshot soft softMod softModCtx sort sound soundControl source spaceLocator sphere sphrand spotLight spotLightPreviewPort spreadSheetEditor spring sqrt squareSurface srtContext stackTrace startString startsWith stitchAndExplodeShell stitchSurface stitchSurfacePoints strcmp stringArrayCatenate stringArrayContains stringArrayCount stringArrayInsertAtIndex stringArrayIntersector stringArrayRemove stringArrayRemoveAtIndex stringArrayRemoveDuplicates stringArrayRemoveExact stringArrayToString stringToStringArray strip stripPrefixFromName stroke subdAutoProjection subdCleanTopology subdCollapse subdDuplicateAndConnect subdEditUV subdListComponentConversion subdMapCut subdMapSewMove subdMatchTopology subdMirror subdToBlind subdToPoly subdTransferUVsToCache subdiv subdivCrease subdivDisplaySmoothness substitute substituteAllString substituteGeometry substring surface surfaceSampler surfaceShaderList swatchDisplayPort 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createVehicleLocal crew ctAddHeader ctAddRow ctClear ctCurSel ctData ctFindHeaderRows ctFindRowHeader ctHeaderControls ctHeaderCount ctRemoveHeaders ctRemoveRows ctrlActivate ctrlAddEventHandler ctrlAngle ctrlAutoScrollDelay ctrlAutoScrollRewind ctrlAutoScrollSpeed ctrlChecked ctrlClassName ctrlCommit ctrlCommitted ctrlCreate ctrlDelete ctrlEnable ctrlEnabled ctrlFade ctrlHTMLLoaded ctrlIDC ctrlIDD ctrlMapAnimAdd ctrlMapAnimClear ctrlMapAnimCommit ctrlMapAnimDone ctrlMapCursor ctrlMapMouseOver ctrlMapScale ctrlMapScreenToWorld ctrlMapWorldToScreen ctrlModel ctrlModelDirAndUp ctrlModelScale ctrlParent ctrlParentControlsGroup ctrlPosition ctrlRemoveAllEventHandlers ctrlRemoveEventHandler ctrlScale ctrlSetActiveColor ctrlSetAngle ctrlSetAutoScrollDelay ctrlSetAutoScrollRewind ctrlSetAutoScrollSpeed ctrlSetBackgroundColor ctrlSetChecked ctrlSetEventHandler ctrlSetFade ctrlSetFocus ctrlSetFont ctrlSetFontH1 ctrlSetFontH1B ctrlSetFontH2 ctrlSetFontH2B ctrlSetFontH3 ctrlSetFontH3B ctrlSetFontH4 ctrlSetFontH4B ctrlSetFontH5 ctrlSetFontH5B ctrlSetFontH6 ctrlSetFontH6B ctrlSetFontHeight ctrlSetFontHeightH1 ctrlSetFontHeightH2 ctrlSetFontHeightH3 ctrlSetFontHeightH4 ctrlSetFontHeightH5 ctrlSetFontHeightH6 ctrlSetFontHeightSecondary ctrlSetFontP ctrlSetFontPB ctrlSetFontSecondary ctrlSetForegroundColor ctrlSetModel ctrlSetModelDirAndUp ctrlSetModelScale ctrlSetPixelPrecision ctrlSetPosition ctrlSetScale ctrlSetStructuredText ctrlSetText ctrlSetTextColor ctrlSetTooltip ctrlSetTooltipColorBox ctrlSetTooltipColorShade ctrlSetTooltipColorText ctrlShow ctrlShown ctrlText ctrlTextHeight ctrlTextWidth ctrlType ctrlVisible ctRowControls ctRowCount ctSetCurSel ctSetData ctSetHeaderTemplate ctSetRowTemplate ctSetValue ctValue curatorAddons curatorCamera curatorCameraArea curatorCameraAreaCeiling curatorCoef curatorEditableObjects curatorEditingArea curatorEditingAreaType curatorMouseOver curatorPoints curatorRegisteredObjects curatorSelected curatorWaypointCost current3DENOperation currentChannel currentCommand currentMagazine currentMagazineDetail currentMagazineDetailTurret currentMagazineTurret currentMuzzle currentNamespace currentTask currentTasks currentThrowable currentVisionMode currentWaypoint currentWeapon currentWeaponMode currentWeaponTurret currentZeroing cursorObject cursorTarget customChat customRadio cutFadeOut cutObj cutRsc cutText damage date dateToNumber daytime deActivateKey debriefingText debugFSM debugLog deg delete3DENEntities deleteAt deleteCenter deleteCollection deleteEditorObject deleteGroup deleteGroupWhenEmpty deleteIdentity deleteLocation deleteMarker deleteMarkerLocal deleteRange deleteResources deleteSite deleteStatus deleteTeam deleteVehicle deleteVehicleCrew deleteWaypoint detach detectedMines diag_activeMissionFSMs diag_activeScripts diag_activeSQFScripts diag_activeSQSScripts diag_captureFrame diag_captureFrameToFile diag_captureSlowFrame diag_codePerformance diag_drawMode diag_enable diag_enabled diag_fps diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem unlockAchievement unregisterTask updateDrawIcon updateMenuItem updateObjectTree useAISteeringComponent useAudioTimeForMoves userInputDisabled vectorAdd vectorCos vectorCrossProduct vectorDiff vectorDir vectorDirVisual vectorDistance vectorDistanceSqr vectorDotProduct vectorFromTo vectorMagnitude vectorMagnitudeSqr vectorModelToWorld vectorModelToWorldVisual vectorMultiply vectorNormalized vectorUp vectorUpVisual vectorWorldToModel vectorWorldToModelVisual vehicle vehicleCargoEnabled vehicleChat vehicleRadio vehicleReceiveRemoteTargets vehicleReportOwnPosition vehicleReportRemoteTargets vehicles vehicleVarName velocity velocityModelSpace verifySignature vest vestContainer vestItems vestMagazines viewDistance visibleCompass visibleGPS visibleMap visiblePosition visiblePositionASL visibleScoretable visibleWatch waves waypointAttachedObject waypointAttachedVehicle waypointAttachObject waypointAttachVehicle waypointBehaviour waypointCombatMode waypointCompletionRadius waypointDescription 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BinomialDistribution BinomialProcess BinormalDistribution BiorthogonalSplineWavelet BipartiteGraphQ BiquadraticFilterModel BirnbaumImportance BirnbaumSaundersDistribution BitAnd BitClear BitGet BitLength BitNot BitOr BitSet BitShiftLeft BitShiftRight BitXor BiweightLocation BiweightMidvariance Black BlackmanHarrisWindow BlackmanNuttallWindow BlackmanWindow Blank BlankForm BlankNullSequence BlankSequence Blend Block BlockchainAddressData BlockchainBase BlockchainBlockData BlockchainContractValue BlockchainData BlockchainGet BlockchainKeyEncode BlockchainPut BlockchainTokenData BlockchainTransaction BlockchainTransactionData BlockchainTransactionSign BlockchainTransactionSubmit BlockMap BlockRandom BlomqvistBeta BlomqvistBetaTest Blue Blur BodePlot BohmanWindow Bold Bond BondCount BondList BondQ Bookmarks Boole BooleanConsecutiveFunction BooleanConvert BooleanCountingFunction BooleanFunction BooleanGraph BooleanMaxterms BooleanMinimize BooleanMinterms BooleanQ BooleanRegion Booleans BooleanStrings BooleanTable BooleanVariables BorderDimensions BorelTannerDistribution Bottom BottomHatTransform BoundaryDiscretizeGraphics BoundaryDiscretizeRegion BoundaryMesh BoundaryMeshRegion BoundaryMeshRegionQ BoundaryStyle BoundedRegionQ BoundingRegion Bounds Box BoxBaselineShift BoxData BoxDimensions Boxed Boxes BoxForm BoxFormFormatTypes BoxFrame BoxID BoxMargins BoxMatrix BoxObject BoxRatios BoxRotation BoxRotationPoint BoxStyle BoxWhiskerChart Bra BracketingBar BraKet BrayCurtisDistance BreadthFirstScan Break BridgeData BrightnessEqualize BroadcastStationData Brown BrownForsytheTest BrownianBridgeProcess BrowserCategory BSplineBasis BSplineCurve BSplineCurve3DBox BSplineCurve3DBoxOptions BSplineCurveBox BSplineCurveBoxOptions BSplineFunction BSplineSurface BSplineSurface3DBox BSplineSurface3DBoxOptions BubbleChart BubbleChart3D BubbleScale BubbleSizes BuildingData BulletGauge BusinessDayQ ButterflyGraph ButterworthFilterModel Button ButtonBar ButtonBox ButtonBoxOptions ButtonCell ButtonContents ButtonData ButtonEvaluator ButtonExpandable ButtonFrame ButtonFunction ButtonMargins ButtonMinHeight ButtonNote ButtonNotebook ButtonSource ButtonStyle ButtonStyleMenuListing Byte ByteArray ByteArrayFormat ByteArrayQ ByteArrayToString ByteCount ByteOrderingC CachedValue CacheGraphics CachePersistence CalendarConvert CalendarData CalendarType Callout CalloutMarker CalloutStyle CallPacket CanberraDistance Cancel CancelButton CandlestickChart CanonicalGraph CanonicalizePolygon CanonicalizePolyhedron CanonicalName CanonicalWarpingCorrespondence CanonicalWarpingDistance CantorMesh CantorStaircase Cap CapForm CapitalDifferentialD Capitalize CapsuleShape CaptureRunning CardinalBSplineBasis CarlemanLinearize CarmichaelLambda CaseOrdering Cases CaseSensitive Cashflow Casoratian Catalan CatalanNumber Catch Catenate CatenateLayer CauchyDistribution CauchyWindow CayleyGraph CDF CDFDeploy CDFInformation CDFWavelet Ceiling CelestialSystem Cell CellAutoOverwrite CellBaseline CellBoundingBox CellBracketOptions CellChangeTimes CellContents CellContext CellDingbat CellDynamicExpression CellEditDuplicate CellElementsBoundingBox CellElementSpacings CellEpilog CellEvaluationDuplicate CellEvaluationFunction CellEvaluationLanguage CellEventActions CellFrame CellFrameColor CellFrameLabelMargins CellFrameLabels CellFrameMargins CellGroup CellGroupData CellGrouping CellGroupingRules CellHorizontalScrolling CellID CellLabel CellLabelAutoDelete CellLabelMargins CellLabelPositioning CellLabelStyle CellLabelTemplate CellMargins CellObject CellOpen CellPrint CellProlog Cells CellSize CellStyle CellTags CellularAutomaton CensoredDistribution Censoring Center CenterArray CenterDot CentralFeature CentralMoment CentralMomentGeneratingFunction Cepstrogram CepstrogramArray CepstrumArray CForm ChampernowneNumber ChangeOptions ChannelBase ChannelBrokerAction ChannelDatabin ChannelHistoryLength ChannelListen ChannelListener ChannelListeners ChannelListenerWait ChannelObject ChannelPreSendFunction ChannelReceiverFunction ChannelSend ChannelSubscribers ChanVeseBinarize Character CharacterCounts CharacterEncoding CharacterEncodingsPath CharacteristicFunction CharacteristicPolynomial CharacterName CharacterRange Characters ChartBaseStyle ChartElementData ChartElementDataFunction ChartElementFunction ChartElements ChartLabels ChartLayout ChartLegends ChartStyle Chebyshev1FilterModel Chebyshev2FilterModel ChebyshevDistance ChebyshevT ChebyshevU Check CheckAbort CheckAll Checkbox CheckboxBar CheckboxBox CheckboxBoxOptions ChemicalData ChessboardDistance ChiDistribution ChineseRemainder ChiSquareDistribution ChoiceButtons ChoiceDialog CholeskyDecomposition Chop ChromaticityPlot ChromaticityPlot3D ChromaticPolynomial Circle CircleBox CircleDot CircleMinus CirclePlus CirclePoints CircleThrough CircleTimes CirculantGraph CircularOrthogonalMatrixDistribution CircularQuaternionMatrixDistribution CircularRealMatrixDistribution CircularSymplecticMatrixDistribution CircularUnitaryMatrixDistribution Circumsphere CityData ClassifierFunction ClassifierInformation ClassifierMeasurements ClassifierMeasurementsObject Classify ClassPriors Clear ClearAll ClearAttributes ClearCookies ClearPermissions ClearSystemCache ClebschGordan ClickPane Clip ClipboardNotebook ClipFill ClippingStyle ClipPlanes ClipPlanesStyle ClipRange Clock ClockGauge ClockwiseContourIntegral Close Closed CloseKernels ClosenessCentrality Closing ClosingAutoSave ClosingEvent CloudAccountData CloudBase CloudConnect CloudDeploy CloudDirectory CloudDisconnect CloudEvaluate CloudExport CloudExpression CloudExpressions CloudFunction CloudGet CloudImport CloudLoggingData CloudObject CloudObjectInformation CloudObjectInformationData CloudObjectNameFormat CloudObjects CloudObjectURLType CloudPublish CloudPut CloudRenderingMethod CloudSave CloudShare CloudSubmit CloudSymbol CloudUnshare ClusterClassify ClusterDissimilarityFunction ClusteringComponents ClusteringTree CMYKColor Coarse CodeAssistOptions Coefficient CoefficientArrays CoefficientDomain CoefficientList CoefficientRules CoifletWavelet Collect Colon ColonForm ColorBalance ColorCombine ColorConvert ColorCoverage ColorData ColorDataFunction ColorDetect ColorDistance ColorFunction ColorFunctionScaling Colorize ColorNegate ColorOutput ColorProfileData ColorQ ColorQuantize ColorReplace ColorRules ColorSelectorSettings ColorSeparate ColorSetter ColorSetterBox ColorSetterBoxOptions ColorSlider ColorsNear ColorSpace ColorToneMapping Column ColumnAlignments ColumnBackgrounds ColumnForm ColumnLines ColumnsEqual ColumnSpacings ColumnWidths CombinedEntityClass CombinerFunction CometData CommonDefaultFormatTypes Commonest CommonestFilter CommonName CommonUnits CommunityBoundaryStyle CommunityGraphPlot CommunityLabels CommunityRegionStyle CompanyData CompatibleUnitQ CompilationOptions CompilationTarget Compile Compiled CompiledCodeFunction CompiledFunction CompilerOptions Complement CompleteGraph CompleteGraphQ CompleteKaryTree CompletionsListPacket Complex Complexes ComplexExpand ComplexInfinity ComplexityFunction ComplexListPlot ComplexPlot ComplexPlot3D ComponentMeasurements ComponentwiseContextMenu Compose ComposeList ComposeSeries CompositeQ Composition CompoundElement CompoundExpression CompoundPoissonDistribution CompoundPoissonProcess CompoundRenewalProcess Compress CompressedData ComputeUncertainty Condition ConditionalExpression Conditioned Cone ConeBox ConfidenceLevel ConfidenceRange ConfidenceTransform ConfigurationPath ConformAudio ConformImages Congruent ConicHullRegion ConicHullRegion3DBox ConicHullRegionBox ConicOptimization Conjugate ConjugateTranspose Conjunction Connect ConnectedComponents ConnectedGraphComponents ConnectedGraphQ ConnectedMeshComponents ConnectedMoleculeComponents ConnectedMoleculeQ ConnectionSettings ConnectLibraryCallbackFunction ConnectSystemModelComponents ConnesWindow ConoverTest ConsoleMessage ConsoleMessagePacket ConsolePrint Constant ConstantArray ConstantArrayLayer ConstantImage ConstantPlusLayer ConstantRegionQ Constants ConstantTimesLayer ConstellationData ConstrainedMax ConstrainedMin Construct Containing ContainsAll ContainsAny ContainsExactly ContainsNone ContainsOnly ContentFieldOptions ContentLocationFunction ContentObject ContentPadding ContentsBoundingBox ContentSelectable ContentSize Context ContextMenu Contexts ContextToFileName Continuation Continue ContinuedFraction ContinuedFractionK ContinuousAction ContinuousMarkovProcess ContinuousTask ContinuousTimeModelQ ContinuousWaveletData ContinuousWaveletTransform ContourDetect ContourGraphics ContourIntegral ContourLabels ContourLines ContourPlot ContourPlot3D Contours ContourShading ContourSmoothing ContourStyle ContraharmonicMean ContrastiveLossLayer Control ControlActive ControlAlignment ControlGroupContentsBox ControllabilityGramian ControllabilityMatrix ControllableDecomposition ControllableModelQ ControllerDuration ControllerInformation ControllerInformationData ControllerLinking ControllerManipulate ControllerMethod ControllerPath ControllerState ControlPlacement ControlsRendering ControlType Convergents ConversionOptions ConversionRules ConvertToBitmapPacket ConvertToPostScript ConvertToPostScriptPacket ConvexHullMesh ConvexPolygonQ ConvexPolyhedronQ ConvolutionLayer Convolve ConwayGroupCo1 ConwayGroupCo2 ConwayGroupCo3 CookieFunction Cookies CoordinateBoundingBox CoordinateBoundingBoxArray CoordinateBounds CoordinateBoundsArray CoordinateChartData CoordinatesToolOptions CoordinateTransform CoordinateTransformData CoprimeQ Coproduct CopulaDistribution Copyable CopyDatabin CopyDirectory CopyFile CopyTag CopyToClipboard CornerFilter CornerNeighbors Correlation CorrelationDistance CorrelationFunction CorrelationTest Cos Cosh CoshIntegral CosineDistance CosineWindow CosIntegral Cot Coth Count CountDistinct CountDistinctBy CounterAssignments CounterBox CounterBoxOptions CounterClockwiseContourIntegral CounterEvaluator CounterFunction CounterIncrements CounterStyle CounterStyleMenuListing CountRoots CountryData Counts CountsBy Covariance CovarianceEstimatorFunction CovarianceFunction CoxianDistribution CoxIngersollRossProcess CoxModel CoxModelFit CramerVonMisesTest CreateArchive CreateCellID CreateChannel CreateCloudExpression CreateDatabin CreateDataSystemModel CreateDialog CreateDirectory CreateDocument CreateFile CreateIntermediateDirectories CreateManagedLibraryExpression CreateNotebook CreatePalette CreatePalettePacket CreatePermissionsGroup CreateScheduledTask CreateSearchIndex CreateSystemModel CreateTemporary CreateUUID CreateWindow CriterionFunction CriticalityFailureImportance CriticalitySuccessImportance CriticalSection Cross CrossEntropyLossLayer CrossingCount CrossingDetect CrossingPolygon CrossMatrix Csc Csch CTCLossLayer Cube CubeRoot Cubics Cuboid CuboidBox Cumulant CumulantGeneratingFunction Cup CupCap Curl CurlyDoubleQuote CurlyQuote CurrencyConvert CurrentDate CurrentImage CurrentlySpeakingPacket CurrentNotebookImage CurrentScreenImage CurrentValue Curry CurvatureFlowFilter CurveClosed Cyan CycleGraph CycleIndexPolynomial Cycles CyclicGroup Cyclotomic Cylinder CylinderBox CylindricalDecompositionD DagumDistribution DamData DamerauLevenshteinDistance DampingFactor Darker Dashed Dashing DatabaseConnect DatabaseDisconnect DatabaseReference Databin DatabinAdd DatabinRemove Databins DatabinUpload DataCompression DataDistribution DataRange DataReversed Dataset Date DateBounds Dated DateDelimiters DateDifference DatedUnit DateFormat DateFunction DateHistogram DateList DateListLogPlot DateListPlot DateListStepPlot DateObject DateObjectQ DateOverlapsQ DatePattern DatePlus DateRange DateReduction DateString DateTicksFormat DateValue DateWithinQ DaubechiesWavelet DavisDistribution DawsonF DayCount DayCountConvention DayHemisphere DaylightQ DayMatchQ DayName DayNightTerminator DayPlus DayRange DayRound DeBruijnGraph DeBruijnSequence Debug DebugTag Decapitalize Decimal DecimalForm DeclareKnownSymbols DeclarePackage Decompose DeconvolutionLayer Decrement Decrypt DecryptFile DedekindEta DeepSpaceProbeData Default DefaultAxesStyle DefaultBaseStyle DefaultBoxStyle DefaultButton DefaultColor DefaultControlPlacement DefaultDuplicateCellStyle DefaultDuration DefaultElement DefaultFaceGridsStyle DefaultFieldHintStyle DefaultFont DefaultFontProperties DefaultFormatType DefaultFormatTypeForStyle DefaultFrameStyle DefaultFrameTicksStyle DefaultGridLinesStyle DefaultInlineFormatType DefaultInputFormatType DefaultLabelStyle DefaultMenuStyle DefaultNaturalLanguage DefaultNewCellStyle DefaultNewInlineCellStyle DefaultNotebook DefaultOptions DefaultOutputFormatType DefaultPrintPrecision DefaultStyle DefaultStyleDefinitions DefaultTextFormatType DefaultTextInlineFormatType DefaultTicksStyle DefaultTooltipStyle DefaultValue DefaultValues Defer DefineExternal DefineInputStreamMethod DefineOutputStreamMethod DefineResourceFunction Definition Degree DegreeCentrality DegreeGraphDistribution DegreeLexicographic DegreeReverseLexicographic DEigensystem DEigenvalues Deinitialization Del DelaunayMesh Delayed Deletable Delete DeleteAnomalies DeleteBorderComponents DeleteCases DeleteChannel DeleteCloudExpression DeleteContents DeleteDirectory DeleteDuplicates DeleteDuplicatesBy DeleteFile DeleteMissing DeleteObject DeletePermissionsKey DeleteSearchIndex DeleteSmallComponents DeleteStopwords DeleteWithContents DeletionWarning DelimitedArray DelimitedSequence Delimiter DelimiterFlashTime DelimiterMatching Delimiters DeliveryFunction Dendrogram Denominator DensityGraphics DensityHistogram DensityPlot DensityPlot3D DependentVariables Deploy Deployed Depth DepthFirstScan Derivative DerivativeFilter DerivedKey DescriptorStateSpace DesignMatrix DestroyAfterEvaluation Det DeviceClose DeviceConfigure DeviceExecute DeviceExecuteAsynchronous DeviceObject DeviceOpen DeviceOpenQ DeviceRead DeviceReadBuffer DeviceReadLatest DeviceReadList DeviceReadTimeSeries Devices DeviceStreams DeviceWrite DeviceWriteBuffer DGaussianWavelet DiacriticalPositioning Diagonal DiagonalizableMatrixQ DiagonalMatrix DiagonalMatrixQ Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DictionaryWordQ DifferenceDelta DifferenceOrder DifferenceQuotient DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitalSignature DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralAngle DihedralGroup Dilation DimensionalCombinations DimensionalMeshComponents DimensionReduce DimensionReducerFunction DimensionReduction Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletBeta DirichletCharacter DirichletCondition DirichletConvolve DirichletDistribution DirichletEta DirichletL DirichletLambda DirichletTransform DirichletWindow DisableConsolePrintPacket DisableFormatting DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLimit DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscreteMaxLimit DiscreteMinLimit DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform DiscretizeGraphics DiscretizeRegion Discriminant DisjointQ Disjunction Disk DiskBox DiskMatrix DiskSegment Dispatch DispatchQ DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceMatrix DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers DivideSides Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentGenerator DocumentGeneratorInformation DocumentGeneratorInformationData DocumentGenerators DocumentNotebook DocumentWeightingRules Dodecahedron DomainRegistrationInformation DominantColors DOSTextFormat Dot DotDashed DotEqual DotLayer DotPlusLayer Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DropoutLayer DSolve DSolveValue Dt DualLinearProgramming DualPolyhedron DualSystemsModel DumpGet DumpSave DuplicateFreeQ Duration Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicGeoGraphics DynamicImage DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptionsE EarthImpactData EarthquakeData EccentricityCentrality Echo EchoFunction EclipseType EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeContract EdgeCost EdgeCount EdgeCoverQ EdgeCycleMatrix EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight EdgeWeightedGraphQ Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData ElementwiseLayer ElidedForms Eliminate EliminationOrder Ellipsoid EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmbedCode EmbeddedHTML EmbeddedService EmbeddingLayer EmbeddingObject EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EmptyRegion EnableConsolePrintPacket Enabled Encode Encrypt EncryptedObject EncryptFile End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfBuffer EndOfFile EndOfLine EndOfString EndPackage EngineEnvironment EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entity EntityClass EntityClassList EntityCopies EntityFunction EntityGroup EntityInstance EntityList EntityPrefetch EntityProperties EntityProperty EntityPropertyClass EntityRegister EntityStore EntityStores EntityTypeName EntityUnregister EntityValue Entropy EntropyFilter Environment Epilog EpilogFunction Equal EqualColumns EqualRows EqualTilde EqualTo EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EscapeRadius EstimatedBackground EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerAngles EulerCharacteristic EulerE EulerGamma EulerianGraphQ EulerMatrix EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluateScheduledTask EvaluationBox EvaluationCell EvaluationCompletionAction EvaluationData EvaluationElements EvaluationEnvironment EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels EventSeries ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludedLines ExcludedPhysicalQuantities ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog ExoplanetData Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi ExpirationDate Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportByteArray ExportForm ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpressionUUID ExpToTrig ExtendedEntityClass ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalBundle ExternalCall ExternalDataCharacterEncoding ExternalEvaluate ExternalFunction ExternalFunctionName ExternalObject ExternalOptions ExternalSessionObject ExternalSessions ExternalTypeSignature ExternalValue Extract ExtractArchive ExtractLayer ExtremeValueDistributionFaceForm FaceGrids FaceGridsStyle FacialFeatures Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail Failure FailureAction FailureDistribution FailureQ False FareySequence FARIMAProcess FeatureDistance FeatureExtract FeatureExtraction FeatureExtractor FeatureExtractorFunction FeatureNames FeatureNearest FeatureSpacePlot FeatureSpacePlot3D FeatureTypes FEDisableConsolePrintPacket FeedbackLinearize FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket FetalGrowthData Fibonacci Fibonorial FieldCompletionFunction FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileConvert FileDate FileExistsQ FileExtension FileFormat FileHandler FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameForms FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileSize FileSystemMap FileSystemScan FileTemplate FileTemplateApply FileType FilledCurve FilledCurveBox FilledCurveBoxOptions Filling FillingStyle FillingTransform FilteredEntityClass FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindAnomalies FindArgMax FindArgMin FindChannels FindClique FindClusters FindCookies FindCurvePath FindCycle FindDevices FindDistribution FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEdgeIndependentPaths FindEquationalProof FindEulerianCycle FindExternalEvaluators FindFaces FindFile FindFit FindFormula FindFundamentalCycles FindGeneratingFunction FindGeoLocation FindGeometricConjectures FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindHamiltonianPath FindHiddenMarkovStates FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMatchingColor FindMaximum FindMaximumFlow FindMaxValue FindMeshDefects FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindMoleculeSubstructure FindPath FindPeaks FindPermutation FindPostmanTour FindProcessParameters FindRepeat FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindSpanningTree FindSystemModelEquilibrium FindTextualAnswer FindThreshold FindTransientRepeat FindVertexCover FindVertexCut FindVertexIndependentPaths Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstCase FirstPassageTimeDistribution FirstPosition FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FitRegularization FittedModel FixedOrder FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlattenLayer FlatTopWindow FlipView Floor FlowPolynomial FlushPrintOutputPacket Fold FoldList FoldPair FoldPairList FollowRedirects Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FormControl FormFunction FormLayoutFunction FormObject FormPage FormTheme FormulaData FormulaLookup FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalGaussianNoiseProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameRate FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrenetSerretSystem FrequencySamplingFilterKernel FresnelC FresnelF FresnelG FresnelS Friday FrobeniusNumber FrobeniusSolve FromAbsoluteTime FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS FromEntity FromJulianDate FromLetterNumber FromPolarCoordinates FromRomanNumeral FromSphericalCoordinates FromUnixTime Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullInformationOutputRegulator FullOptions FullRegion FullSimplify Function FunctionCompile FunctionCompileExport FunctionCompileExportByteArray FunctionCompileExportLibrary FunctionCompileExportString FunctionDomain FunctionExpand FunctionInterpolation FunctionPeriod FunctionRange FunctionSpace FussellVeselyImportanceGaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins GalaxyData GalleryView Gamma GammaDistribution GammaRegularized GapPenalty GARCHProcess GatedRecurrentLayer Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianOrthogonalMatrixDistribution GaussianSymplecticMatrixDistribution GaussianUnitaryMatrixDistribution GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateAsymmetricKeyPair GenerateConditions GeneratedCell GeneratedDocumentBinding GenerateDerivedKey GenerateDigitalSignature GenerateDocument GeneratedParameters GeneratedQuantityMagnitudes GenerateHTTPResponse GenerateSecuredAuthenticationKey GenerateSymmetricKey GeneratingFunction GeneratorDescription GeneratorHistoryLength GeneratorOutputType Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeoAntipode GeoArea GeoArraySize GeoBackground GeoBoundingBox GeoBounds GeoBoundsRegion GeoBubbleChart GeoCenter GeoCircle GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDisk GeoDisplacement GeoDistance GeoDistanceList GeoElevationData GeoEntities GeoGraphics GeogravityModelData GeoGridDirectionDifference GeoGridLines GeoGridLinesStyle GeoGridPosition GeoGridRange GeoGridRangePadding GeoGridUnitArea GeoGridUnitDistance GeoGridVector GeoGroup GeoHemisphere GeoHemisphereBoundary GeoHistogram GeoIdentify GeoImage GeoLabels GeoLength GeoListPlot GeoLocation GeologicalPeriodData GeomagneticModelData GeoMarker GeometricAssertion GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricScene GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoModel GeoNearest GeoPath GeoPosition GeoPositionENU GeoPositionXYZ GeoProjection GeoProjectionData GeoRange GeoRangePadding GeoRegionValuePlot GeoResolution GeoScaleBar GeoServer GeoSmoothHistogram GeoStreamPlot GeoStyling GeoStylingImageFunction GeoVariant GeoVector GeoVectorENU GeoVectorPlot GeoVectorXYZ GeoVisibleRegion GeoVisibleRegionBoundary GeoWithinQ GeoZoomLevel GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenAngle GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter GrammarApply GrammarRules GrammarToken Graph Graph3D GraphAssortativity GraphAutomorphismGroup GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel Greater GreaterEqual GreaterEqualLess GreaterEqualThan GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterThan GreaterTilde Green GreenFunction Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupBy GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators Groupings GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain GroupTogetherGrouping GroupTogetherNestedGrouping GrowCutComponents Gudermannian GuidedFilter GumbelDistributionHaarWavelet HadamardMatrix HalfLine HalfNormalDistribution HalfPlane HalfSpace HamiltonianGraphQ HammingDistance HammingWindow HandlerFunctions HandlerFunctionsKeys HankelH1 HankelH2 HankelMatrix HankelTransform HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash Haversine HazardFunction Head HeadCompose HeaderLines Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings Here HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenMarkovProcess HiddenSurface Highlighted HighlightGraph HighlightImage HighlightMesh HighpassFilter HigmanSimsGroupHS HilbertCurve HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HistoricalPeriodData HitMissTransform HITSCentrality HjorthDistribution HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HostLookup HotellingTSquareDistribution HoytDistribution HTMLSave HTTPErrorResponse HTTPRedirect HTTPRequest HTTPRequestData HTTPResponse Hue HumanGrowthData HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyperplane Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestDataI IconData Iconize IconizedObject IconRules Icosahedron Identity IdentityMatrix If IgnoreCase IgnoreDiacritics IgnorePunctuation IgnoreSpellCheck IgnoringInactive Im Image Image3D Image3DProjection Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageApplyIndexed ImageAspectRatio ImageAssemble ImageAugmentationLayer ImageBoundingBoxes ImageCache ImageCacheValid ImageCapture ImageCaptureFunction ImageCases ImageChannels ImageClip ImageCollage ImageColorSpace ImageCompose ImageContainsQ ImageContents ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDisplacements ImageDistance ImageEffect ImageExposureCombine ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageFocusCombine ImageForestingComponents ImageFormattingWidth ImageForwardTransformation ImageGraphics ImageHistogram ImageIdentify ImageInstanceQ ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarker ImageMarkers ImageMeasurements ImageMesh ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImagePosition ImagePreviewFunction ImagePyramid ImagePyramidApply ImageQ ImageRangeCache ImageRecolor ImageReflect ImageRegion ImageResize ImageResolution ImageRestyle ImageRotate ImageRotated ImageSaliencyFilter ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions ImagingDevice ImplicitRegion Implies Import ImportAutoReplacements ImportByteArray ImportOptions ImportString ImprovementImportance In Inactivate Inactive IncidenceGraph IncidenceList IncidenceMatrix IncludeAromaticBonds IncludeConstantBasis IncludeDefinitions IncludeDirectories IncludeFileExtension IncludeGeneratorTasks IncludeHydrogens IncludeInflections IncludeMetaInformation IncludePods IncludeQuantities IncludeRelatedTables IncludeSingularTerm IncludeWindowTimes Increment IndefiniteMatrixQ Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentPhysicalQuantity IndependentUnit IndependentUnitDimension IndependentVertexSetQ Indeterminate IndeterminateThreshold IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers InfiniteLine InfinitePlane Infinity Infix InflationAdjust InflationMethod Information InformationData InformationDataGrid Inherited InheritScope InhomogeneousPoissonProcess InitialEvaluationHistory Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InitializationObjects InitializationValue Initialize InitialSeeding InlineCounterAssignments InlineCounterIncrements InlineRules Inner InnerPolygon InnerPolyhedron Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionFunction InsertionPointObject InsertLinebreaks InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Insphere Install InstallService InstanceNormalizationLayer InString Integer IntegerDigits IntegerExponent IntegerLength IntegerName IntegerPart IntegerPartitions IntegerQ IntegerReverse Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction Interpreter InterpretTemplate InterquartileRange Interrupt InterruptSettings IntersectingQ Intersection Interval IntervalIntersection IntervalMarkers IntervalMarkersStyle IntervalMemberQ IntervalSlider IntervalUnion Into Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHankelTransform InverseHaversine InverseImagePyramid InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InverseMellinTransform InversePermutation InverseRadon InverseRadonTransform InverseSeries InverseShortTimeFourier InverseSpectrogram InverseSurvivalFunction InverseTransformedRegion InverseWaveletTransform InverseWeierstrassP InverseWishartMatrixDistribution InverseZTransform Invisible InvisibleApplication InvisibleTimes IPAddress IrreduciblePolynomialQ IslandData IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemAspectRatio ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcessJaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join JoinAcross Joined JoinedCurve JoinedCurveBox JoinedCurveBoxOptions JoinForm JordanDecomposition JordanModelDecomposition JulianDate JuliaSetBoettcher JuliaSetIterationCount JuliaSetPlot JuliaSetPointsK KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KEdgeConnectedComponents KEdgeConnectedGraphQ KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelFunction KernelMixtureDistribution Kernels Ket Key KeyCollisionFunction KeyComplement KeyDrop KeyDropFrom KeyExistsQ KeyFreeQ KeyIntersection KeyMap KeyMemberQ KeypointStrength Keys KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Khinchin KillProcess KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnapsackSolve KnightTourGraph KnotData KnownUnitQ KochCurve KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter KVertexConnectedComponents KVertexConnectedGraphQLABColor Label Labeled LabeledSlider LabelingFunction LabelingSize LabelStyle LabelVisibility LaguerreL LakeData LambdaComponents LambertW LaminaData LanczosWindow LandauDistribution Language LanguageCategory LanguageData LanguageIdentify LanguageOptions LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCHColor LCM LeaderSize LeafCount LeapYearQ LearnDistribution LearnedDistribution LearningRate LearningRateMultipliers LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessEqualThan LessFullEqual LessGreater LessLess LessSlantEqual LessThan LessTilde LetterCharacter LetterCounts LetterNumber LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryDataType LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox Line3DBoxOptions LinearFilter LinearFractionalOptimization LinearFractionalTransform LinearGradientImage LinearizingTransformationData LinearLayer LinearModelFit LinearOffsetFunction LinearOptimization LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBoxOptions LineBreak LinebreakAdjustments LineBreakChart LinebreakSemicolonWeighting LineBreakWithin LineColor LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRankCentrality LinkRead LinkReadHeld LinkReadyQ Links LinkService LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot ListDensityPlot3D Listen ListFormat ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListSliceContourPlot3D ListSliceDensityPlot3D ListSliceVectorPlot3D ListStepPlot ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalAdaptiveBinarize LocalCache LocalClusteringCoefficient LocalizeDefinitions LocalizeVariables LocalObject LocalObjects LocalResponseNormalizationLayer LocalSubmit LocalSymbol LocalTime LocalTimeZone LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogisticSigmoid LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongestOrderedSequence LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow LongShortTermMemoryLayer Lookup Loopback LoopFreeGraphQ LossFunction LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowerTriangularMatrixQ LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LunarEclipse LUVColor LyapunovSolve LyonsGroupLyMachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MailAddressValidation MailExecute MailFolder MailItem MailReceiverFunction MailResponseFunction MailSearch MailServerConnect MailServerConnection MailSettings MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules ManagedLibraryExpressionID ManagedLibraryExpressionQ MandelbrotSetBoettcher MandelbrotSetDistance MandelbrotSetIterationCount MandelbrotSetMemberQ MandelbrotSetPlot MangoldtLambda ManhattanDistance Manipulate Manipulator MannedSpaceMissionData MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarchenkoPasturDistribution MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicalFunctionData MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixNormalDistribution MatrixPlot MatrixPower MatrixPropertyDistribution MatrixQ MatrixRank MatrixTDistribution Max MaxBend MaxCellMeasure MaxColorDistance MaxDetect MaxDuration MaxExtraBandwidths MaxExtraConditions MaxFeatureDisplacement MaxFeatures MaxFilter MaximalBy Maximize MaxItems MaxIterations MaxLimit MaxMemoryUsed MaxMixtureKernels MaxOverlapFraction MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxTrainingRounds MaxValue MaxwellDistribution MaxWordGap McLaughlinGroupMcL Mean MeanAbsoluteLossLayer MeanAround MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter MeanSquaredLossLayer Median MedianDeviation MedianFilter MedicalTestData Medium MeijerG MeijerGReduce MeixnerDistribution MellinConvolve MellinTransform MemberQ MemoryAvailable MemoryConstrained MemoryConstraint MemoryInUse MengerMesh Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuList MenuPacket MenuSortingValue MenuStyle MenuView Merge MergeDifferences MergingFunction MersennePrimeExponent MersennePrimeExponentQ Mesh MeshCellCentroid MeshCellCount MeshCellHighlight MeshCellIndex MeshCellLabel MeshCellMarker MeshCellMeasure MeshCellQuality MeshCells MeshCellShapeFunction MeshCellStyle MeshCoordinates MeshFunctions MeshPrimitives MeshQualityGoal MeshRange MeshRefinementFunction MeshRegion MeshRegionQ MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageObject MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation MeteorShowerData Method MethodOptions MexicanHatWavelet MeyerWavelet Midpoint Min MinColorDistance MinDetect MineralData MinFilter MinimalBy MinimalPolynomial MinimalStateSpaceModel Minimize MinimumTimeIncrement MinIntervalSize MinkowskiQuestionMark MinLimit MinMax MinorPlanetData Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingBehavior MissingDataMethod MissingDataRules MissingQ MissingString MissingStyle MissingValuePattern MittagLefflerE MixedFractionParts MixedGraphQ MixedMagnitude MixedRadix MixedRadixQuantity MixedUnit MixtureDistribution Mod Modal Mode Modular ModularInverse ModularLambda Module Modulus MoebiusMu Molecule MoleculeContainsQ MoleculeEquivalentQ MoleculeGraph MoleculeModify MoleculePattern MoleculePlot MoleculePlot3D MoleculeProperty MoleculeQ MoleculeValue Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction MomentOfInertia Monday Monitor MonomialList MonomialOrder MonsterGroupM MoonPhase MoonPosition MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform MortalityData Most MountainData MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovieData MovingAverage MovingMap MovingMedian MoyalDistribution Multicolumn MultiedgeStyle MultigraphQ MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity MultiplySides Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistributionN NakagamiDistribution NameQ Names NamespaceBox NamespaceBoxOptions Nand NArgMax NArgMin NBernoulliB NBodySimulation NBodySimulationData NCache NDEigensystem NDEigenvalues NDSolve NDSolveValue Nearest NearestFunction NearestNeighborGraph NearestTo NebulaData NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeDefiniteMatrixQ NegativeIntegers NegativeMultinomialDistribution NegativeRationals NegativeReals NegativeSemidefiniteMatrixQ NeighborhoodData NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestGraph NestList NestWhile NestWhileList NetAppend NetBidirectionalOperator NetChain NetDecoder NetDelete NetDrop NetEncoder NetEvaluationMode NetExtract NetFlatten NetFoldOperator NetGraph NetInformation NetInitialize NetInsert NetInsertSharedArrays NetJoin NetMapOperator NetMapThreadOperator NetMeasurements NetModel NetNestOperator NetPairEmbeddingOperator NetPort NetPortGradient NetPrepend NetRename NetReplace NetReplacePart NetSharedArray NetStateObject NetTake NetTrain NetTrainResultsObject NetworkPacketCapture NetworkPacketRecording NetworkPacketRecordingDuring NetworkPacketTrace NeumannValue NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextCell NextDate NextPrime NextScheduledTaskTime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NightHemisphere NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants NondimensionalizationTransform None NoneTrue NonlinearModelFit NonlinearStateSpaceModel NonlocalMeansFilter NonNegative NonNegativeIntegers NonNegativeRationals NonNegativeReals NonPositive NonPositiveIntegers NonPositiveRationals NonPositiveReals Nor NorlundB Norm Normal NormalDistribution NormalGrouping NormalizationLayer Normalize Normalized NormalizedSquaredEuclideanDistance NormalMatrixQ NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookImport NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookTemplate NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde Nothing NotHumpDownHump NotHumpEqual NotificationFunction NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar Now NoWhitespace NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms NuclearExplosionData NuclearReactorData Null NullRecords NullSpace NullWords Number NumberCompose NumberDecompose NumberExpand NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberLinePlot NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumeratorDenominator NumericalOrder NumericalSort NumericArray NumericArrayQ NumericArrayType NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlotO ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OceanData Octahedron OddQ Off Offset OLEData On ONanGroupON Once OneIdentity Opacity OpacityFunction OpacityFunctionScaling Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionalElement OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering OrderingBy OrderingLayer Orderless OrderlessPatternSequence OrnsteinUhlenbeckProcess Orthogonalize OrthogonalMatrixQ Out Outer OuterPolygon OuterPolyhedron OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OverwriteTarget OwenT OwnValuesPackage PackingMethod PaddedForm Padding PaddingLayer PaddingSize PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageTheme PageWidth Pagination PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath PalindromeQ Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo Parallelepiped ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds Parallelogram ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParametricRegion ParentBox ParentCell ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParentNotebook ParetoDistribution ParetoPickandsDistribution ParkData Part PartBehavior PartialCorrelationFunction PartialD ParticleAcceleratorData ParticleData Partition PartitionGranularity PartitionsP PartitionsQ PartLayer PartOfSpeech PartProtection ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteAutoQuoteCharacters PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PeakDetect PeanoCurve PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PercentForm PerfectNumber PerfectNumberQ PerformanceGoal Perimeter PeriodicBoundaryCondition PeriodicInterpolation Periodogram PeriodogramArray Permanent Permissions PermissionsGroup PermissionsGroupMemberQ PermissionsGroups PermissionsKey PermissionsKeys PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PerpendicularBisector PersistenceLocation PersistenceTime PersistentObject PersistentObjects PersistentValue PersonData PERTDistribution PetersenGraph PhaseMargins PhaseRange PhysicalSystemData Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest PingTime Pink PitchRecognize Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarAngle PlanarGraph PlanarGraphQ PlanckRadiationLaw PlaneCurveData PlanetaryMoonData PlanetData PlantData Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLabels PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangeClipPlanesStyle PlotRangePadding PlotRegion PlotStyle PlotTheme Pluralize Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox Point3DBoxOptions PointBox PointBoxOptions PointFigureChart PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonalNumber PolygonAngle PolygonBox PolygonBoxOptions PolygonCoordinates PolygonDecomposition PolygonHoleScale PolygonIntersections PolygonScale Polyhedron PolyhedronAngle PolyhedronCoordinates PolyhedronData PolyhedronDecomposition PolyhedronGenus PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PoolingLayer PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position PositionIndex Positive PositiveDefiniteMatrixQ PositiveIntegers PositiveRationals PositiveReals PositiveSemidefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerRange PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement Predict PredictionRoot PredictorFunction PredictorInformation PredictorMeasurements PredictorMeasurementsObject PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependLayer PrependTo PreprocessingRules PreserveColor PreserveImageOptions Previous PreviousCell PreviousDate PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitivePolynomialQ PrimitiveRoot PrimitiveRootList PrincipalComponents PrincipalValue Print PrintableASCIIQ PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment Printout3D Printout3DPreviewer PrintPrecision PrintTemporary Prism PrismBox PrismBoxOptions PrivateCellOptions PrivateEvaluationOptions PrivateFontOptions PrivateFrontEndOptions PrivateKey PrivateNotebookOptions PrivatePaths Probability ProbabilityDistribution ProbabilityPlot ProbabilityPr ProbabilityScalePlot ProbitModelFit ProcessConnection ProcessDirectory ProcessEnvironment Processes ProcessEstimator ProcessInformation ProcessObject ProcessParameterAssumptions ProcessParameterQ ProcessStateDomain ProcessStatus ProcessTimeDomain Product ProductDistribution ProductLog ProgressIndicator ProgressIndicatorBox ProgressIndicatorBoxOptions Projection Prolog PromptForm ProofObject Properties Property PropertyList PropertyValue Proportion Proportional Protect Protected ProteinData Pruning PseudoInverse PsychrometricPropertyData PublicKey PublisherID PulsarData PunctuationCharacter Purple Put PutAppend Pyramid PyramidBox PyramidBoxOptionsQBinomial QFactorial QGamma QHypergeometricPFQ QnDispersion QPochhammer QPolyGamma QRDecomposition QuadraticIrrationalQ QuadraticOptimization Quantile QuantilePlot Quantity QuantityArray QuantityDistribution QuantityForm QuantityMagnitude QuantityQ QuantityUnit QuantityVariable QuantityVariableCanonicalUnit QuantityVariableDimensions QuantityVariableIdentifier QuantityVariablePhysicalQuantity Quartics QuartileDeviation Quartiles QuartileSkewness Query QueueingNetworkProcess QueueingProcess QueueProperties Quiet Quit Quotient QuotientRemainderRadialGradientImage RadialityCentrality RadicalBox RadicalBoxOptions RadioButton RadioButtonBar RadioButtonBox RadioButtonBoxOptions Radon RadonTransform RamanujanTau RamanujanTauL RamanujanTauTheta RamanujanTauZ Ramp Random RandomChoice RandomColor RandomComplex RandomEntity RandomFunction RandomGeoPosition RandomGraph RandomImage RandomInstance RandomInteger RandomPermutation RandomPoint RandomPolygon RandomPolyhedron RandomPrime RandomReal RandomSample RandomSeed RandomSeeding RandomVariate RandomWalkProcess RandomWord Range RangeFilter RangeSpecification RankedMax RankedMin RarerProbability Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadByteArray ReadLine ReadList ReadProtected ReadString Real RealAbs RealBlockDiagonalForm RealDigits RealExponent Reals RealSign Reap RecognitionPrior RecognitionThreshold Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RectangularRepeatingElement RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate Region RegionBinarize RegionBoundary RegionBounds RegionCentroid RegionDifference RegionDimension RegionDisjoint RegionDistance RegionDistanceFunction RegionEmbeddingDimension RegionEqual RegionFunction RegionImage RegionIntersection RegionMeasure RegionMember RegionMemberFunction RegionMoment RegionNearest RegionNearestFunction RegionPlot RegionPlot3D RegionProduct RegionQ RegionResize RegionSize RegionSymmetricDifference RegionUnion RegionWithin RegisterExternalEvaluator RegularExpression Regularization RegularlySampledQ RegularPolygon ReIm ReImLabels ReImPlot ReImStyle Reinstall RelationalDatabase RelationGraph Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot RemoteAuthorizationCaching RemoteConnect RemoteConnectionObject RemoteFile RemoteRun RemoteRunProcess Remove RemoveAlphaChannel RemoveAsynchronousTask RemoveAudioStream RemoveBackground RemoveChannelListener RemoveChannelSubscribers Removed RemoveDiacritics RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RemoveUsers RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart RepairMesh Repeated RepeatedNull RepeatedString RepeatedTiming RepeatingElement Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated ReplicateLayer RequiredPhysicalQuantities Resampling ResamplingAlgorithmData ResamplingMethod Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask ReshapeLayer Residue ResizeLayer Resolve ResourceAcquire ResourceData ResourceFunction ResourceObject ResourceRegister ResourceRemove ResourceSearch ResourceSubmissionObject ResourceSubmit ResourceSystemBase ResourceUpdate ResponseForm Rest RestartInterval Restricted Resultant ResumePacket Return ReturnEntersInput ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnReceiptFunction ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseSort ReverseSortBy ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ RiemannXi Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightComposition RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity RollPitchYawAngles RollPitchYawMatrix RomanNumeral Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RSolveValue RudinShapiro RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulePlot RulerUnits Run RunProcess RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilaritySameQ SameTest SampledEntityClass SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SASTriangle SatelliteData SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveConnection SaveDefinitions SavitzkyGolayMatrix SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTask ScheduledTaskActiveQ ScheduledTaskInformation ScheduledTaskInformationData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScientificNotationThreshold ScorerGi ScorerGiPrime ScorerHi ScorerHiPrime ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptForm ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition SearchAdjustment SearchIndexObject SearchIndices SearchQueryString SearchResultObject Sec Sech SechDistribution SecondOrderConeOptimization SectionGrouping SectorChart SectorChart3D SectorOrigin SectorSpacing SecuredAuthenticationKey SecuredAuthenticationKeys SeedRandom Select Selectable SelectComponents SelectedCells SelectedNotebook SelectFirst Selection SelectionAnimate SelectionCell SelectionCellCreateCell SelectionCellDefaultStyle SelectionCellParentStyle SelectionCreateCell SelectionDebuggerTag SelectionDuplicateCell SelectionEvaluate SelectionEvaluateCreateCell SelectionMove SelectionPlaceholder SelectionSetStyle SelectWithContents SelfLoops SelfLoopStyle SemanticImport SemanticImportString SemanticInterpretation SemialgebraicComponentInstances SemidefiniteOptimization SendMail SendMessage Sequence SequenceAlignment SequenceAttentionLayer SequenceCases SequenceCount SequenceFold SequenceFoldList SequenceForm SequenceHold SequenceLastLayer SequenceMostLayer SequencePosition SequencePredict SequencePredictorFunction SequenceReplace SequenceRestLayer SequenceReverseLayer SequenceSplit Series SeriesCoefficient SeriesData ServiceConnect ServiceDisconnect ServiceExecute ServiceObject ServiceRequest ServiceResponse ServiceSubmit SessionSubmit SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetCloudDirectory SetCookies SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPermissions SetPrecision SetProperty SetSecuredAuthenticationKey SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemModel SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetUsers SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share SharingList Sharpen ShearingMatrix ShearingTransform ShellRegion ShenCastanMatrix ShiftedGompertzDistribution ShiftRegisterSequence Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow ShortTimeFourier ShortTimeFourierData ShortUpArrow Show ShowAutoConvert ShowAutoSpellCheck ShowAutoStyles ShowCellBracket ShowCellLabel ShowCellTags ShowClosedCellArea ShowCodeAssist ShowContents ShowControls ShowCursorTracker ShowGroupOpenCloseIcon ShowGroupOpener ShowInvisibleCharacters ShowPageBreaks ShowPredictiveInterface ShowSelection ShowShortBoxForm ShowSpecialCharacters ShowStringCharacters ShowSyntaxStyles ShrinkingDelay ShrinkWrapBoundingBox SiderealTime SiegelTheta SiegelTukeyTest SierpinskiCurve SierpinskiMesh Sign Signature SignedRankTest SignedRegionDistance SignificanceLevel SignPadding SignTest SimilarityRules SimpleGraph SimpleGraphQ SimplePolygonQ SimplePolyhedronQ Simplex Simplify Sin Sinc SinghMaddalaDistribution SingleEvaluation SingleLetterItalics SingleLetterStyle SingularValueDecomposition SingularValueList SingularValuePlot SingularValues Sinh SinhIntegral SinIntegral SixJSymbol Skeleton SkeletonTransform SkellamDistribution Skewness SkewNormalDistribution SkinStyle Skip SliceContourPlot3D SliceDensityPlot3D SliceDistribution SliceVectorPlot3D Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDecomposition SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SnDispersion Snippet SnubPolyhedron SocialMediaData Socket SocketConnect SocketListen SocketListener SocketObject SocketOpen SocketReadMessage SocketReadyQ Sockets SocketWaitAll SocketWaitNext SoftmaxLayer SokalSneathDissimilarity SolarEclipse SolarSystemFeatureData SolidAngle SolidData SolidRegionQ Solve SolveAlways SolveDelayed Sort SortBy SortedBy SortedEntityClass Sound SoundAndGraphics SoundNote SoundVolume SourceLink Sow Space SpaceCurveData SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution SpatialMedian SpatialTransformationLayer Speak SpeakTextPacket SpearmanRankTest SpearmanRho SpeciesData SpecificityGoal SpectralLineData Spectrogram SpectrogramArray Specularity SpeechRecognize SpeechSynthesize SpellingCorrection SpellingCorrectionList SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SpherePoints SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SphericalShell SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquareMatrixQ SquareRepeatingElement SquaresR SquareSubset SquareSubsetEqual SquareSuperset SquareSupersetEqual SquareUnion SquareWave SSSTriangle StabilityMargins StabilityMarginsStyle StableDistribution Stack StackBegin StackComplete StackedDateListPlot StackedListPlot StackInhibit StadiumShape StandardAtmosphereData StandardDeviation StandardDeviationFilter StandardForm Standardize Standardized StandardOceanData StandbyDistribution Star StarClusterData StarData StarGraph StartAsynchronousTask StartExternalSession StartingStepSize StartOfLine StartOfString StartProcess StartScheduledTask StartupSound StartWebSession StateDimensions StateFeedbackGains StateOutputEstimator StateResponse StateSpaceModel StateSpaceRealization StateSpaceTransform StateTransformationLinearize StationaryDistribution StationaryWaveletPacketTransform StationaryWaveletTransform StatusArea StatusCentrality StepMonitor StereochemistryElements StieltjesGamma StirlingS1 StirlingS2 StopAsynchronousTask StoppingPowerData StopScheduledTask StrataVariables StratonovichProcess StreamColorFunction StreamColorFunctionScaling StreamDensityPlot StreamMarkers StreamPlot StreamPoints StreamPosition Streams StreamScale StreamStyle String StringBreak StringByteCount StringCases StringContainsQ StringCount StringDelete StringDrop StringEndsQ StringExpression StringExtract StringForm StringFormat StringFreeQ StringInsert StringJoin StringLength StringMatchQ StringPadLeft StringPadRight StringPart StringPartition StringPosition StringQ StringRepeat StringReplace StringReplaceList StringReplacePart StringReverse StringRiffle StringRotateLeft StringRotateRight StringSkeleton StringSplit StringStartsQ StringTake StringTemplate StringToByteArray StringToStream StringTrim StripBoxes StripOnInput StripWrapperBoxes StrokeForm StructuralImportance StructuredArray StructuredSelection StruveH StruveL Stub StudentTDistribution Style StyleBox StyleBoxAutoDelete StyleData StyleDefinitions StyleForm StyleHints StyleKeyMapping StyleMenuListing StyleNameDialogSettings StyleNames StylePrint StyleSheetPath Subdivide Subfactorial Subgraph SubMinus SubPlus SubresultantPolynomialRemainders SubresultantPolynomials Subresultants Subscript SubscriptBox SubscriptBoxOptions Subscripted Subsequences Subset SubsetEqual SubsetMap SubsetQ Subsets SubStar SubstitutionSystem Subsuperscript SubsuperscriptBox SubsuperscriptBoxOptions Subtract SubtractFrom SubtractSides SubValues Succeeds SucceedsEqual SucceedsSlantEqual SucceedsTilde Success SuchThat Sum SumConvergence SummationLayer Sunday SunPosition Sunrise Sunset SuperDagger SuperMinus SupernovaData SuperPlus Superscript SuperscriptBox SuperscriptBoxOptions Superset SupersetEqual SuperStar Surd SurdForm SurfaceArea SurfaceColor SurfaceData SurfaceGraphics SurvivalDistribution SurvivalFunction SurvivalModel SurvivalModelFit SuspendPacket SuzukiDistribution SuzukiGroupSuz SwatchLegend Switch Symbol SymbolName SymletWavelet Symmetric SymmetricGroup SymmetricKey SymmetricMatrixQ SymmetricPolynomial SymmetricReduction Symmetrize 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application_get_position application_surface_enable application_surface_is_enabled display_get_width display_get_height display_get_orientation display_get_gui_width display_get_gui_height display_reset display_mouse_get_x display_mouse_get_y display_mouse_set display_set_ui_visibility window_set_fullscreen window_get_fullscreen window_set_caption window_set_min_width window_set_max_width window_set_min_height window_set_max_height window_get_visible_rects window_get_caption window_set_cursor window_get_cursor window_set_colour window_get_colour window_set_color window_get_color window_set_position window_set_size window_set_rectangle window_center window_get_x window_get_y window_get_width window_get_height window_mouse_get_x window_mouse_get_y window_mouse_set window_view_mouse_get_x window_view_mouse_get_y window_views_mouse_get_x window_views_mouse_get_y audio_listener_position audio_listener_velocity audio_listener_orientation audio_emitter_position audio_emitter_create audio_emitter_free audio_emitter_exists audio_emitter_pitch audio_emitter_velocity audio_emitter_falloff audio_emitter_gain audio_play_sound audio_play_sound_on audio_play_sound_at audio_stop_sound audio_resume_music audio_music_is_playing audio_resume_sound audio_pause_sound audio_pause_music audio_channel_num audio_sound_length audio_get_type audio_falloff_set_model audio_play_music audio_stop_music audio_master_gain audio_music_gain audio_sound_gain audio_sound_pitch audio_stop_all audio_resume_all audio_pause_all audio_is_playing audio_is_paused audio_exists audio_sound_set_track_position audio_sound_get_track_position audio_emitter_get_gain audio_emitter_get_pitch audio_emitter_get_x audio_emitter_get_y audio_emitter_get_z audio_emitter_get_vx audio_emitter_get_vy audio_emitter_get_vz audio_listener_set_position audio_listener_set_velocity audio_listener_set_orientation audio_listener_get_data audio_set_master_gain audio_get_master_gain audio_sound_get_gain audio_sound_get_pitch audio_get_name audio_sound_set_track_position audio_sound_get_track_position audio_create_stream audio_destroy_stream audio_create_sync_group audio_destroy_sync_group audio_play_in_sync_group audio_start_sync_group audio_stop_sync_group audio_pause_sync_group audio_resume_sync_group audio_sync_group_get_track_pos audio_sync_group_debug audio_sync_group_is_playing audio_debug audio_group_load audio_group_unload audio_group_is_loaded audio_group_load_progress audio_group_name audio_group_stop_all audio_group_set_gain audio_create_buffer_sound audio_free_buffer_sound audio_create_play_queue audio_free_play_queue audio_queue_sound audio_get_recorder_count audio_get_recorder_info audio_start_recording audio_stop_recording audio_sound_get_listener_mask audio_emitter_get_listener_mask audio_get_listener_mask audio_sound_set_listener_mask audio_emitter_set_listener_mask audio_set_listener_mask audio_get_listener_count audio_get_listener_info audio_system show_message show_message_async clickable_add clickable_add_ext clickable_change clickable_change_ext clickable_delete clickable_exists clickable_set_style show_question show_question_async get_integer get_string get_integer_async get_string_async get_login_async get_open_filename get_save_filename get_open_filename_ext get_save_filename_ext show_error highscore_clear highscore_add highscore_value highscore_name draw_highscore sprite_exists sprite_get_name sprite_get_number sprite_get_width sprite_get_height sprite_get_xoffset sprite_get_yoffset sprite_get_bbox_left sprite_get_bbox_right sprite_get_bbox_top sprite_get_bbox_bottom sprite_save sprite_save_strip sprite_set_cache_size sprite_set_cache_size_ext sprite_get_tpe sprite_prefetch sprite_prefetch_multi sprite_flush sprite_flush_multi sprite_set_speed sprite_get_speed_type sprite_get_speed font_exists font_get_name font_get_fontname font_get_bold font_get_italic font_get_first font_get_last font_get_size font_set_cache_size path_exists path_get_name path_get_length path_get_time path_get_kind path_get_closed path_get_precision path_get_number path_get_point_x path_get_point_y path_get_point_speed path_get_x path_get_y path_get_speed script_exists script_get_name timeline_add timeline_delete timeline_clear timeline_exists timeline_get_name timeline_moment_clear timeline_moment_add_script timeline_size timeline_max_moment object_exists object_get_name object_get_sprite object_get_solid object_get_visible object_get_persistent object_get_mask object_get_parent object_get_physics object_is_ancestor room_exists room_get_name sprite_set_offset sprite_duplicate sprite_assign sprite_merge sprite_add sprite_replace sprite_create_from_surface sprite_add_from_surface sprite_delete sprite_set_alpha_from_sprite sprite_collision_mask font_add_enable_aa font_add_get_enable_aa font_add font_add_sprite font_add_sprite_ext font_replace font_replace_sprite font_replace_sprite_ext font_delete path_set_kind path_set_closed path_set_precision path_add path_assign path_duplicate path_append path_delete path_add_point path_insert_point path_change_point path_delete_point path_clear_points path_reverse path_mirror path_flip path_rotate path_rescale path_shift script_execute object_set_sprite object_set_solid object_set_visible object_set_persistent object_set_mask room_set_width room_set_height room_set_persistent room_set_background_colour room_set_background_color room_set_view room_set_viewport room_get_viewport room_set_view_enabled room_add room_duplicate room_assign room_instance_add room_instance_clear room_get_camera room_set_camera asset_get_index asset_get_type file_text_open_from_string file_text_open_read file_text_open_write file_text_open_append file_text_close file_text_write_string file_text_write_real file_text_writeln file_text_read_string file_text_read_real file_text_readln file_text_eof file_text_eoln file_exists file_delete file_rename file_copy directory_exists directory_create directory_destroy file_find_first file_find_next file_find_close file_attributes filename_name filename_path filename_dir filename_drive filename_ext filename_change_ext file_bin_open file_bin_rewrite file_bin_close file_bin_position file_bin_size file_bin_seek file_bin_write_byte file_bin_read_byte parameter_count parameter_string environment_get_variable ini_open_from_string ini_open ini_close ini_read_string ini_read_real ini_write_string ini_write_real ini_key_exists ini_section_exists ini_key_delete ini_section_delete ds_set_precision ds_exists ds_stack_create ds_stack_destroy ds_stack_clear ds_stack_copy ds_stack_size ds_stack_empty ds_stack_push ds_stack_pop ds_stack_top ds_stack_write ds_stack_read ds_queue_create ds_queue_destroy ds_queue_clear ds_queue_copy ds_queue_size ds_queue_empty ds_queue_enqueue ds_queue_dequeue ds_queue_head ds_queue_tail ds_queue_write ds_queue_read ds_list_create ds_list_destroy ds_list_clear ds_list_copy ds_list_size ds_list_empty ds_list_add ds_list_insert ds_list_replace ds_list_delete ds_list_find_index ds_list_find_value ds_list_mark_as_list ds_list_mark_as_map ds_list_sort ds_list_shuffle ds_list_write ds_list_read ds_list_set ds_map_create ds_map_destroy ds_map_clear ds_map_copy ds_map_size ds_map_empty ds_map_add ds_map_add_list ds_map_add_map ds_map_replace ds_map_replace_map ds_map_replace_list ds_map_delete ds_map_exists ds_map_find_value ds_map_find_previous ds_map_find_next ds_map_find_first ds_map_find_last ds_map_write ds_map_read ds_map_secure_save ds_map_secure_load ds_map_secure_load_buffer ds_map_secure_save_buffer ds_map_set ds_priority_create ds_priority_destroy ds_priority_clear ds_priority_copy ds_priority_size ds_priority_empty ds_priority_add ds_priority_change_priority ds_priority_find_priority ds_priority_delete_value ds_priority_delete_min ds_priority_find_min ds_priority_delete_max ds_priority_find_max ds_priority_write ds_priority_read ds_grid_create ds_grid_destroy ds_grid_copy ds_grid_resize ds_grid_width ds_grid_height ds_grid_clear ds_grid_set ds_grid_add ds_grid_multiply ds_grid_set_region ds_grid_add_region ds_grid_multiply_region ds_grid_set_disk ds_grid_add_disk ds_grid_multiply_disk ds_grid_set_grid_region ds_grid_add_grid_region ds_grid_multiply_grid_region ds_grid_get ds_grid_get_sum ds_grid_get_max ds_grid_get_min ds_grid_get_mean ds_grid_get_disk_sum ds_grid_get_disk_min ds_grid_get_disk_max ds_grid_get_disk_mean ds_grid_value_exists ds_grid_value_x ds_grid_value_y ds_grid_value_disk_exists ds_grid_value_disk_x ds_grid_value_disk_y ds_grid_shuffle ds_grid_write ds_grid_read ds_grid_sort ds_grid_set ds_grid_get effect_create_below effect_create_above effect_clear part_type_create part_type_destroy part_type_exists part_type_clear part_type_shape part_type_sprite part_type_size part_type_scale part_type_orientation part_type_life part_type_step part_type_death part_type_speed part_type_direction part_type_gravity part_type_colour1 part_type_colour2 part_type_colour3 part_type_colour_mix part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set 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Update-TypeData Use-Transaction Wait-Event Wait-Job Wait-Process Where-Object Write-Debug Write-Error Write-EventLog Write-Host Write-Output Write-Progress Write-Verbose Write-Warning Add-MDTPersistentDrive Disable-MDTMonitorService Enable-MDTMonitorService Get-MDTDeploymentShareStatistics Get-MDTMonitorData Get-MDTOperatingSystemCatalog Get-MDTPersistentDrive Import-MDTApplication Import-MDTDriver Import-MDTOperatingSystem Import-MDTPackage Import-MDTTaskSequence New-MDTDatabase Remove-MDTMonitorData Remove-MDTPersistentDrive Restore-MDTPersistentDrive Set-MDTMonitorData Test-MDTDeploymentShare Test-MDTMonitorData Update-MDTDatabaseSchema Update-MDTDeploymentShare Update-MDTLinkedDS Update-MDTMedia Add-VamtProductKey Export-VamtData Find-VamtManagedMachine Get-VamtConfirmationId Get-VamtProduct Get-VamtProductKey Import-VamtData Initialize-VamtData Install-VamtConfirmationId Install-VamtProductActivation Install-VamtProductKey Update-VamtProduct Add-CIDatastore Add-KeyManagementServer Add-NodeKeys Add-NsxDynamicCriteria Add-NsxDynamicMemberSet Add-NsxEdgeInterfaceAddress Add-NsxFirewallExclusionListMember Add-NsxFirewallRuleMember Add-NsxIpSetMember Add-NsxLicense Add-NsxLoadBalancerPoolMember Add-NsxLoadBalancerVip Add-NsxSecondaryManager Add-NsxSecurityGroupMember Add-NsxSecurityPolicyRule Add-NsxSecurityPolicyRuleGroup Add-NsxSecurityPolicyRuleService Add-NsxServiceGroupMember Add-NsxTransportZoneMember Add-PassthroughDevice Add-VDSwitchPhysicalNetworkAdapter Add-VDSwitchVMHost Add-VMHost Add-VMHostNtpServer Add-VirtualSwitchPhysicalNetworkAdapter Add-XmlElement Add-vRACustomForm Add-vRAPrincipalToTenantRole Add-vRAReservationNetwork Add-vRAReservationStorage Clear-NsxEdgeInterface Clear-NsxManagerTimeSettings Compress-Archive Connect-CIServer Connect-CisServer Connect-HCXServer Connect-NIServer Connect-NsxLogicalSwitch Connect-NsxServer Connect-NsxtServer Connect-SrmServer Connect-VIServer Connect-Vmc Connect-vRAServer Connect-vRNIServer ConvertFrom-Markdown ConvertTo-MOFInstance Copy-DatastoreItem Copy-HardDisk Copy-NsxEdge Copy-VDisk Copy-VMGuestFile Debug-Runspace Disable-NsxEdgeSsh Disable-RunspaceDebug Disable-vRNIDataSource Disconnect-CIServer Disconnect-CisServer Disconnect-HCXServer Disconnect-NsxLogicalSwitch Disconnect-NsxServer Disconnect-NsxtServer Disconnect-SrmServer Disconnect-VIServer Disconnect-Vmc Disconnect-vRAServer Disconnect-vRNIServer Dismount-Tools Enable-NsxEdgeSsh Enable-RunspaceDebug Enable-vRNIDataSource Expand-Archive Export-NsxObject Export-SpbmStoragePolicy Export-VApp Export-VDPortGroup Export-VDSwitch Export-VMHostProfile Export-vRAIcon Export-vRAPackage Find-Command Find-DscResource Find-Module Find-NsxWhereVMUsed Find-Package Find-PackageProvider Find-RoleCapability Find-Script Format-Hex Format-VMHostDiskPartition Format-XML Generate-VersionInfo Get-AdvancedSetting Get-AlarmAction Get-AlarmActionTrigger Get-AlarmDefinition Get-Annotation Get-CDDrive Get-CIAccessControlRule Get-CIDatastore Get-CINetworkAdapter Get-CIRole Get-CIUser Get-CIVApp Get-CIVAppNetwork Get-CIVAppStartRule Get-CIVAppTemplate Get-CIVM Get-CIVMTemplate Get-CIView Get-Catalog Get-CisCommand Get-CisService Get-CloudCommand Get-Cluster Get-CompatibleVersionAddtionaPropertiesStr Get-ComplexResourceQualifier Get-ConfigurationErrorCount Get-ContentLibraryItem Get-CustomAttribute Get-DSCResourceModules Get-Datacenter Get-Datastore Get-DatastoreCluster Get-DrsClusterGroup Get-DrsRecommendation Get-DrsRule Get-DrsVMHostRule Get-DscResource Get-EdgeGateway Get-EncryptedPassword Get-ErrorReport Get-EsxCli Get-EsxTop Get-ExternalNetwork Get-FileHash Get-FloppyDrive Get-Folder Get-HAPrimaryVMHost Get-HCXAppliance Get-HCXApplianceCompute Get-HCXApplianceDVS Get-HCXApplianceDatastore Get-HCXApplianceNetwork Get-HCXContainer Get-HCXDatastore Get-HCXGateway Get-HCXInterconnectStatus Get-HCXJob Get-HCXMigration Get-HCXNetwork Get-HCXNetworkExtension Get-HCXReplication Get-HCXReplicationSnapshot Get-HCXService Get-HCXSite Get-HCXSitePairing Get-HCXVM Get-HardDisk Get-IScsiHbaTarget Get-InnerMostErrorRecord Get-InstallPath Get-InstalledModule Get-InstalledScript Get-Inventory Get-ItemPropertyValue Get-KeyManagementServer Get-KmipClientCertificate Get-KmsCluster Get-Log Get-LogType Get-MarkdownOption Get-Media Get-MofInstanceName Get-MofInstanceText Get-NetworkAdapter Get-NetworkPool Get-NfsUser Get-NicTeamingPolicy Get-NsxApplicableMember Get-NsxApplicableSecurityAction Get-NsxBackingDVSwitch Get-NsxBackingPortGroup Get-NsxCliDfwAddrSet Get-NsxCliDfwFilter Get-NsxCliDfwRule Get-NsxClusterStatus Get-NsxController Get-NsxDynamicCriteria Get-NsxDynamicMemberSet Get-NsxEdge Get-NsxEdgeBgp Get-NsxEdgeBgpNeighbour Get-NsxEdgeCertificate Get-NsxEdgeCsr Get-NsxEdgeFirewall Get-NsxEdgeFirewallRule Get-NsxEdgeInterface Get-NsxEdgeInterfaceAddress Get-NsxEdgeNat Get-NsxEdgeNatRule Get-NsxEdgeOspf Get-NsxEdgeOspfArea Get-NsxEdgeOspfInterface Get-NsxEdgePrefix Get-NsxEdgeRedistributionRule Get-NsxEdgeRouting Get-NsxEdgeStaticRoute Get-NsxEdgeSubInterface Get-NsxFirewallExclusionListMember Get-NsxFirewallGlobalConfiguration Get-NsxFirewallPublishStatus Get-NsxFirewallRule Get-NsxFirewallRuleMember Get-NsxFirewallSavedConfiguration Get-NsxFirewallSection Get-NsxFirewallThreshold Get-NsxIpPool Get-NsxIpSet Get-NsxLicense Get-NsxLoadBalancer Get-NsxLoadBalancerApplicationProfile Get-NsxLoadBalancerApplicationRule Get-NsxLoadBalancerMonitor Get-NsxLoadBalancerPool Get-NsxLoadBalancerPoolMember Get-NsxLoadBalancerStats Get-NsxLoadBalancerVip Get-NsxLogicalRouter Get-NsxLogicalRouterBgp Get-NsxLogicalRouterBgpNeighbour Get-NsxLogicalRouterBridge Get-NsxLogicalRouterBridging Get-NsxLogicalRouterInterface Get-NsxLogicalRouterOspf Get-NsxLogicalRouterOspfArea Get-NsxLogicalRouterOspfInterface Get-NsxLogicalRouterPrefix Get-NsxLogicalRouterRedistributionRule Get-NsxLogicalRouterRouting Get-NsxLogicalRouterStaticRoute Get-NsxLogicalSwitch Get-NsxMacSet Get-NsxManagerBackup Get-NsxManagerCertificate Get-NsxManagerComponentSummary Get-NsxManagerNetwork Get-NsxManagerRole Get-NsxManagerSsoConfig Get-NsxManagerSyncStatus Get-NsxManagerSyslogServer Get-NsxManagerSystemSummary Get-NsxManagerTimeSettings Get-NsxManagerVcenterConfig Get-NsxSecondaryManager Get-NsxSecurityGroup Get-NsxSecurityGroupEffectiveIpAddress Get-NsxSecurityGroupEffectiveMacAddress Get-NsxSecurityGroupEffectiveMember Get-NsxSecurityGroupEffectiveVirtualMachine Get-NsxSecurityGroupEffectiveVnic Get-NsxSecurityGroupMemberTypes Get-NsxSecurityPolicy Get-NsxSecurityPolicyHighestUsedPrecedence Get-NsxSecurityPolicyRule Get-NsxSecurityTag Get-NsxSecurityTagAssignment Get-NsxSegmentIdRange Get-NsxService Get-NsxServiceDefinition Get-NsxServiceGroup Get-NsxServiceGroupMember Get-NsxServiceProfile Get-NsxSpoofguardNic Get-NsxSpoofguardPolicy Get-NsxSslVpn Get-NsxSslVpnAuthServer Get-NsxSslVpnClientInstallationPackage Get-NsxSslVpnIpPool Get-NsxSslVpnPrivateNetwork Get-NsxSslVpnUser Get-NsxTransportZone Get-NsxUserRole Get-NsxVdsContext Get-NsxtPolicyService Get-NsxtService Get-OSCustomizationNicMapping Get-OSCustomizationSpec Get-Org Get-OrgNetwork Get-OrgVdc Get-OrgVdcNetwork Get-OvfConfiguration Get-PSCurrentConfigurationNode Get-PSDefaultConfigurationDocument Get-PSMetaConfigDocumentInstVersionInfo Get-PSMetaConfigurationProcessed Get-PSReadLineKeyHandler Get-PSReadLineOption Get-PSRepository Get-PSTopConfigurationName Get-PSVersion Get-Package Get-PackageProvider Get-PackageSource Get-PassthroughDevice Get-PositionInfo Get-PowerCLICommunity Get-PowerCLIConfiguration Get-PowerCLIHelp Get-PowerCLIVersion Get-PowerNsxVersion Get-ProviderVdc Get-PublicKeyFromFile Get-PublicKeyFromStore Get-ResourcePool Get-Runspace Get-RunspaceDebug Get-ScsiController Get-ScsiLun Get-ScsiLunPath Get-SecurityInfo Get-SecurityPolicy Get-Snapshot Get-SpbmCapability Get-SpbmCompatibleStorage Get-SpbmEntityConfiguration Get-SpbmFaultDomain Get-SpbmPointInTimeReplica Get-SpbmReplicationGroup Get-SpbmReplicationPair Get-SpbmStoragePolicy Get-Stat Get-StatInterval Get-StatType Get-Tag Get-TagAssignment Get-TagCategory Get-Task Get-Template Get-TimeZone Get-Uptime Get-UsbDevice Get-VAIOFilter Get-VApp Get-VDBlockedPolicy Get-VDPort Get-VDPortgroup Get-VDPortgroupOverridePolicy Get-VDSecurityPolicy Get-VDSwitch Get-VDSwitchPrivateVlan Get-VDTrafficShapingPolicy Get-VDUplinkLacpPolicy Get-VDUplinkTeamingPolicy Get-VDisk Get-VIAccount Get-VICommand Get-VICredentialStoreItem Get-VIEvent Get-VIObjectByVIView Get-VIPermission Get-VIPrivilege Get-VIProperty Get-VIRole Get-VM Get-VMGuest Get-VMHost Get-VMHostAccount Get-VMHostAdvancedConfiguration Get-VMHostAuthentication Get-VMHostAvailableTimeZone Get-VMHostDiagnosticPartition Get-VMHostDisk Get-VMHostDiskPartition Get-VMHostFirewallDefaultPolicy Get-VMHostFirewallException Get-VMHostFirmware Get-VMHostHardware Get-VMHostHba Get-VMHostModule Get-VMHostNetwork Get-VMHostNetworkAdapter Get-VMHostNtpServer Get-VMHostPatch Get-VMHostPciDevice Get-VMHostProfile Get-VMHostProfileImageCacheConfiguration Get-VMHostProfileRequiredInput Get-VMHostProfileStorageDeviceConfiguration Get-VMHostProfileUserConfiguration Get-VMHostProfileVmPortGroupConfiguration Get-VMHostRoute Get-VMHostService Get-VMHostSnmp Get-VMHostStartPolicy Get-VMHostStorage Get-VMHostSysLogServer Get-VMQuestion Get-VMResourceConfiguration Get-VMStartPolicy Get-VTpm Get-VTpmCSR Get-VTpmCertificate Get-VasaProvider Get-VasaStorageArray Get-View Get-VirtualPortGroup Get-VirtualSwitch Get-VmcSddcNetworkService Get-VmcService Get-VsanClusterConfiguration Get-VsanComponent Get-VsanDisk Get-VsanDiskGroup Get-VsanEvacuationPlan Get-VsanFaultDomain Get-VsanIscsiInitiatorGroup Get-VsanIscsiInitiatorGroupTargetAssociation Get-VsanIscsiLun Get-VsanIscsiTarget Get-VsanObject Get-VsanResyncingComponent Get-VsanRuntimeInfo Get-VsanSpaceUsage Get-VsanStat Get-VsanView Get-vRAApplianceServiceStatus Get-vRAAuthorizationRole Get-vRABlueprint Get-vRABusinessGroup Get-vRACatalogItem Get-vRACatalogItemRequestTemplate Get-vRACatalogPrincipal Get-vRAComponentRegistryService Get-vRAComponentRegistryServiceEndpoint Get-vRAComponentRegistryServiceStatus Get-vRAContent Get-vRAContentData Get-vRAContentType Get-vRACustomForm Get-vRAEntitledCatalogItem Get-vRAEntitledService Get-vRAEntitlement Get-vRAExternalNetworkProfile Get-vRAGroupPrincipal Get-vRAIcon Get-vRANATNetworkProfile Get-vRANetworkProfileIPAddressList Get-vRANetworkProfileIPRangeSummary Get-vRAPackage Get-vRAPackageContent Get-vRAPropertyDefinition Get-vRAPropertyGroup Get-vRARequest Get-vRARequestDetail Get-vRAReservation Get-vRAReservationComputeResource Get-vRAReservationComputeResourceMemory Get-vRAReservationComputeResourceNetwork Get-vRAReservationComputeResourceResourcePool Get-vRAReservationComputeResourceStorage Get-vRAReservationPolicy Get-vRAReservationTemplate Get-vRAReservationType Get-vRAResource Get-vRAResourceAction Get-vRAResourceActionRequestTemplate Get-vRAResourceMetric Get-vRAResourceOperation Get-vRAResourceType Get-vRARoutedNetworkProfile Get-vRAService Get-vRAServiceBlueprint Get-vRASourceMachine Get-vRAStorageReservationPolicy Get-vRATenant Get-vRATenantDirectory Get-vRATenantDirectoryStatus Get-vRATenantRole Get-vRAUserPrincipal Get-vRAUserPrincipalGroupMembership Get-vRAVersion Get-vRNIAPIVersion Get-vRNIApplication Get-vRNIApplicationTier Get-vRNIDataSource Get-vRNIDataSourceSNMPConfig Get-vRNIDatastore Get-vRNIDistributedSwitch Get-vRNIDistributedSwitchPortGroup Get-vRNIEntity Get-vRNIEntityName Get-vRNIFirewallRule Get-vRNIFlow Get-vRNIHost Get-vRNIHostVMKNic Get-vRNIIPSet Get-vRNIL2Network Get-vRNINSXManager Get-vRNINodes Get-vRNIProblem Get-vRNIRecommendedRules Get-vRNIRecommendedRulesNsxBundle Get-vRNISecurityGroup Get-vRNISecurityTag Get-vRNIService Get-vRNIServiceGroup Get-vRNIVM Get-vRNIVMvNIC Get-vRNIvCenter Get-vRNIvCenterCluster Get-vRNIvCenterDatacenter Get-vRNIvCenterFolder Grant-NsxSpoofguardNicApproval Import-CIVApp Import-CIVAppTemplate Import-NsxObject Import-PackageProvider Import-PowerShellDataFile Import-SpbmStoragePolicy Import-VApp Import-VMHostProfile Import-vRAContentData Import-vRAIcon Import-vRAPackage Initialize-ConfigurationRuntimeState Install-Module Install-NsxCluster Install-Package Install-PackageProvider Install-Script Install-VMHostPatch Invoke-DrsRecommendation Invoke-NsxCli Invoke-NsxClusterResolveAll Invoke-NsxManagerSync Invoke-NsxRestMethod Invoke-NsxWebRequest Invoke-VMHostProfile Invoke-VMScript Invoke-XpathQuery Invoke-vRADataCollection Invoke-vRARestMethod Invoke-vRATenantDirectorySync Invoke-vRNIRestMethod Join-String Mount-Tools Move-Cluster Move-Datacenter Move-Datastore Move-Folder Move-HardDisk Move-Inventory Move-NsxSecurityPolicyRule Move-ResourcePool Move-Template Move-VApp Move-VDisk Move-VM Move-VMHost New-AdvancedSetting New-AlarmAction New-AlarmActionTrigger New-CDDrive New-CIAccessControlRule New-CIVApp New-CIVAppNetwork New-CIVAppTemplate New-CIVM New-Cluster New-CustomAttribute New-Datacenter New-Datastore New-DatastoreCluster New-DatastoreDrive New-DrsClusterGroup New-DrsRule New-DrsVMHostRule New-DscChecksum New-FloppyDrive New-Folder New-Guid New-HCXAppliance New-HCXMigration New-HCXNetworkExtension New-HCXNetworkMapping New-HCXReplication New-HCXSitePairing New-HCXStaticRoute New-HardDisk New-IScsiHbaTarget New-KmipClientCertificate New-NetworkAdapter New-NfsUser New-NsxAddressSpec New-NsxClusterVxlanConfig New-NsxController New-NsxDynamicCriteriaSpec New-NsxEdge New-NsxEdgeBgpNeighbour New-NsxEdgeCsr New-NsxEdgeFirewallRule New-NsxEdgeInterfaceSpec New-NsxEdgeNatRule New-NsxEdgeOspfArea New-NsxEdgeOspfInterface New-NsxEdgePrefix New-NsxEdgeRedistributionRule New-NsxEdgeSelfSignedCertificate New-NsxEdgeStaticRoute New-NsxEdgeSubInterface New-NsxEdgeSubInterfaceSpec New-NsxFirewallRule New-NsxFirewallSavedConfiguration New-NsxFirewallSection New-NsxIpPool New-NsxIpSet New-NsxLoadBalancerApplicationProfile New-NsxLoadBalancerApplicationRule New-NsxLoadBalancerMemberSpec New-NsxLoadBalancerMonitor New-NsxLoadBalancerPool New-NsxLogicalRouter New-NsxLogicalRouterBgpNeighbour New-NsxLogicalRouterBridge New-NsxLogicalRouterInterface New-NsxLogicalRouterInterfaceSpec New-NsxLogicalRouterOspfArea New-NsxLogicalRouterOspfInterface New-NsxLogicalRouterPrefix New-NsxLogicalRouterRedistributionRule New-NsxLogicalRouterStaticRoute New-NsxLogicalSwitch New-NsxMacSet New-NsxManager New-NsxSecurityGroup New-NsxSecurityPolicy New-NsxSecurityPolicyAssignment New-NsxSecurityPolicyFirewallRuleSpec New-NsxSecurityPolicyGuestIntrospectionSpec New-NsxSecurityPolicyNetworkIntrospectionSpec New-NsxSecurityTag New-NsxSecurityTagAssignment New-NsxSegmentIdRange New-NsxService New-NsxServiceGroup New-NsxSpoofguardPolicy New-NsxSslVpnAuthServer New-NsxSslVpnClientInstallationPackage New-NsxSslVpnIpPool New-NsxSslVpnPrivateNetwork New-NsxSslVpnUser New-NsxTransportZone New-NsxVdsContext New-OSCustomizationNicMapping New-OSCustomizationSpec New-Org New-OrgNetwork New-OrgVdc New-OrgVdcNetwork New-ResourcePool New-ScriptFileInfo New-ScsiController New-Snapshot New-SpbmRule New-SpbmRuleSet New-SpbmStoragePolicy New-StatInterval New-Tag New-TagAssignment New-TagCategory New-Template New-TemporaryFile New-VAIOFilter New-VApp New-VDPortgroup New-VDSwitch New-VDSwitchPrivateVlan New-VDisk New-VICredentialStoreItem New-VIInventoryDrive New-VIPermission New-VIProperty New-VIRole New-VISamlSecurityContext New-VM New-VMHostAccount New-VMHostNetworkAdapter New-VMHostProfile New-VMHostProfileVmPortGroupConfiguration New-VMHostRoute New-VTpm New-VasaProvider New-VcsOAuthSecurityContext New-VirtualPortGroup New-VirtualSwitch New-VsanDisk New-VsanDiskGroup New-VsanFaultDomain New-VsanIscsiInitiatorGroup New-VsanIscsiInitiatorGroupTargetAssociation New-VsanIscsiLun New-VsanIscsiTarget New-vRABusinessGroup New-vRAEntitlement New-vRAExternalNetworkProfile New-vRAGroupPrincipal New-vRANATNetworkProfile New-vRANetworkProfileIPRangeDefinition New-vRAPackage New-vRAPropertyDefinition New-vRAPropertyGroup New-vRAReservation New-vRAReservationNetworkDefinition New-vRAReservationPolicy New-vRAReservationStorageDefinition New-vRARoutedNetworkProfile New-vRAService New-vRAStorageReservationPolicy New-vRATenant New-vRATenantDirectory New-vRAUserPrincipal New-vRNIApplication New-vRNIApplicationTier New-vRNIDataSource Open-VMConsoleWindow Publish-Module Publish-NsxSpoofguardPolicy Publish-Script Register-PSRepository Register-PackageSource Remove-AdvancedSetting Remove-AlarmAction Remove-AlarmActionTrigger Remove-Alias Remove-CDDrive Remove-CIAccessControlRule Remove-CIVApp Remove-CIVAppNetwork Remove-CIVAppTemplate Remove-Cluster Remove-CustomAttribute Remove-Datacenter Remove-Datastore Remove-DatastoreCluster Remove-DrsClusterGroup Remove-DrsRule Remove-DrsVMHostRule Remove-FloppyDrive Remove-Folder Remove-HCXAppliance Remove-HCXNetworkExtension Remove-HCXReplication Remove-HCXSitePairing Remove-HardDisk Remove-IScsiHbaTarget Remove-Inventory Remove-KeyManagementServer Remove-NetworkAdapter Remove-NfsUser Remove-NsxCluster Remove-NsxClusterVxlanConfig Remove-NsxController Remove-NsxDynamicCriteria Remove-NsxDynamicMemberSet Remove-NsxEdge Remove-NsxEdgeBgpNeighbour Remove-NsxEdgeCertificate Remove-NsxEdgeCsr Remove-NsxEdgeFirewallRule Remove-NsxEdgeInterfaceAddress Remove-NsxEdgeNatRule Remove-NsxEdgeOspfArea Remove-NsxEdgeOspfInterface Remove-NsxEdgePrefix Remove-NsxEdgeRedistributionRule Remove-NsxEdgeStaticRoute Remove-NsxEdgeSubInterface Remove-NsxFirewallExclusionListMember Remove-NsxFirewallRule Remove-NsxFirewallRuleMember Remove-NsxFirewallSavedConfiguration Remove-NsxFirewallSection Remove-NsxIpPool Remove-NsxIpSet Remove-NsxIpSetMember Remove-NsxLoadBalancerApplicationProfile Remove-NsxLoadBalancerMonitor Remove-NsxLoadBalancerPool Remove-NsxLoadBalancerPoolMember Remove-NsxLoadBalancerVip Remove-NsxLogicalRouter Remove-NsxLogicalRouterBgpNeighbour Remove-NsxLogicalRouterBridge Remove-NsxLogicalRouterInterface Remove-NsxLogicalRouterOspfArea Remove-NsxLogicalRouterOspfInterface Remove-NsxLogicalRouterPrefix Remove-NsxLogicalRouterRedistributionRule Remove-NsxLogicalRouterStaticRoute Remove-NsxLogicalSwitch Remove-NsxMacSet Remove-NsxSecondaryManager Remove-NsxSecurityGroup Remove-NsxSecurityGroupMember Remove-NsxSecurityPolicy Remove-NsxSecurityPolicyAssignment Remove-NsxSecurityPolicyRule Remove-NsxSecurityPolicyRuleGroup Remove-NsxSecurityPolicyRuleService Remove-NsxSecurityTag Remove-NsxSecurityTagAssignment Remove-NsxSegmentIdRange Remove-NsxService Remove-NsxServiceGroup Remove-NsxSpoofguardPolicy Remove-NsxSslVpnClientInstallationPackage Remove-NsxSslVpnIpPool Remove-NsxSslVpnPrivateNetwork Remove-NsxSslVpnUser Remove-NsxTransportZone Remove-NsxTransportZoneMember Remove-NsxVdsContext Remove-OSCustomizationNicMapping Remove-OSCustomizationSpec Remove-Org Remove-OrgNetwork Remove-OrgVdc Remove-OrgVdcNetwork Remove-PSReadLineKeyHandler Remove-PassthroughDevice Remove-ResourcePool Remove-Snapshot Remove-SpbmStoragePolicy Remove-StatInterval Remove-Tag Remove-TagAssignment Remove-TagCategory Remove-Template Remove-UsbDevice Remove-VAIOFilter Remove-VApp Remove-VDPortGroup Remove-VDSwitch Remove-VDSwitchPhysicalNetworkAdapter Remove-VDSwitchPrivateVlan Remove-VDSwitchVMHost Remove-VDisk Remove-VICredentialStoreItem Remove-VIPermission Remove-VIProperty Remove-VIRole Remove-VM Remove-VMHost Remove-VMHostAccount Remove-VMHostNetworkAdapter Remove-VMHostNtpServer Remove-VMHostProfile Remove-VMHostProfileVmPortGroupConfiguration Remove-VMHostRoute Remove-VTpm Remove-VasaProvider Remove-VirtualPortGroup Remove-VirtualSwitch Remove-VirtualSwitchPhysicalNetworkAdapter Remove-VsanDisk Remove-VsanDiskGroup Remove-VsanFaultDomain Remove-VsanIscsiInitiatorGroup Remove-VsanIscsiInitiatorGroupTargetAssociation Remove-VsanIscsiLun Remove-VsanIscsiTarget Remove-vRABusinessGroup Remove-vRACustomForm Remove-vRAExternalNetworkProfile Remove-vRAGroupPrincipal Remove-vRAIcon Remove-vRANATNetworkProfile Remove-vRAPackage Remove-vRAPrincipalFromTenantRole Remove-vRAPropertyDefinition Remove-vRAPropertyGroup Remove-vRAReservation Remove-vRAReservationNetwork Remove-vRAReservationPolicy Remove-vRAReservationStorage Remove-vRARoutedNetworkProfile Remove-vRAService Remove-vRAStorageReservationPolicy Remove-vRATenant Remove-vRATenantDirectory Remove-vRAUserPrincipal Remove-vRNIApplication Remove-vRNIApplicationTier Remove-vRNIDataSource Repair-NsxEdge Repair-VsanObject Request-vRACatalogItem Request-vRAResourceAction Restart-CIVApp Restart-CIVAppGuest Restart-CIVM Restart-CIVMGuest Restart-VM Restart-VMGuest Restart-VMHost Restart-VMHostService Resume-HCXReplication Revoke-NsxSpoofguardNicApproval Save-Module Save-Package Save-Script Search-Cloud Set-AdvancedSetting Set-AlarmDefinition Set-Annotation Set-CDDrive Set-CIAccessControlRule Set-CINetworkAdapter Set-CIVApp Set-CIVAppNetwork Set-CIVAppStartRule Set-CIVAppTemplate Set-Cluster Set-CustomAttribute Set-Datacenter Set-Datastore Set-DatastoreCluster Set-DrsClusterGroup Set-DrsRule Set-DrsVMHostRule Set-FloppyDrive Set-Folder Set-HCXAppliance Set-HCXMigration Set-HCXReplication Set-HardDisk Set-IScsiHbaTarget Set-KeyManagementServer Set-KmsCluster Set-MarkdownOption Set-NetworkAdapter Set-NfsUser Set-NicTeamingPolicy Set-NodeExclusiveResources Set-NodeManager Set-NodeResourceSource Set-NodeResources Set-NsxEdge Set-NsxEdgeBgp Set-NsxEdgeFirewall Set-NsxEdgeInterface Set-NsxEdgeNat Set-NsxEdgeOspf Set-NsxEdgeRouting Set-NsxFirewallGlobalConfiguration Set-NsxFirewallRule Set-NsxFirewallSavedConfiguration Set-NsxFirewallThreshold Set-NsxLoadBalancer Set-NsxLoadBalancerPoolMember Set-NsxLogicalRouter Set-NsxLogicalRouterBgp Set-NsxLogicalRouterBridging Set-NsxLogicalRouterInterface Set-NsxLogicalRouterOspf Set-NsxLogicalRouterRouting Set-NsxManager Set-NsxManagerRole Set-NsxManagerTimeSettings Set-NsxSecurityPolicy Set-NsxSecurityPolicyFirewallRule Set-NsxSslVpn Set-OSCustomizationNicMapping Set-OSCustomizationSpec Set-Org Set-OrgNetwork Set-OrgVdc Set-OrgVdcNetwork Set-PSCurrentConfigurationNode Set-PSDefaultConfigurationDocument Set-PSMetaConfigDocInsProcessedBeforeMeta Set-PSMetaConfigVersionInfoV2 Set-PSReadLineKeyHandler Set-PSReadLineOption Set-PSRepository Set-PSTopConfigurationName Set-PackageSource Set-PowerCLIConfiguration Set-ResourcePool Set-ScsiController Set-ScsiLun Set-ScsiLunPath Set-SecurityPolicy Set-Snapshot Set-SpbmEntityConfiguration Set-SpbmStoragePolicy Set-StatInterval Set-Tag Set-TagCategory Set-Template Set-VAIOFilter Set-VApp Set-VDBlockedPolicy Set-VDPort Set-VDPortgroup Set-VDPortgroupOverridePolicy Set-VDSecurityPolicy Set-VDSwitch Set-VDTrafficShapingPolicy Set-VDUplinkLacpPolicy Set-VDUplinkTeamingPolicy Set-VDVlanConfiguration Set-VDisk Set-VIPermission Set-VIRole Set-VM Set-VMHost Set-VMHostAccount Set-VMHostAdvancedConfiguration Set-VMHostAuthentication Set-VMHostDiagnosticPartition Set-VMHostFirewallDefaultPolicy Set-VMHostFirewallException Set-VMHostFirmware Set-VMHostHba Set-VMHostModule Set-VMHostNetwork Set-VMHostNetworkAdapter Set-VMHostProfile Set-VMHostProfileImageCacheConfiguration Set-VMHostProfileStorageDeviceConfiguration Set-VMHostProfileUserConfiguration Set-VMHostProfileVmPortGroupConfiguration Set-VMHostRoute Set-VMHostService Set-VMHostSnmp Set-VMHostStartPolicy Set-VMHostStorage Set-VMHostSysLogServer Set-VMQuestion Set-VMResourceConfiguration Set-VMStartPolicy Set-VTpm Set-VirtualPortGroup Set-VirtualSwitch Set-VsanClusterConfiguration Set-VsanFaultDomain Set-VsanIscsiInitiatorGroup Set-VsanIscsiLun Set-VsanIscsiTarget Set-vRABusinessGroup Set-vRACatalogItem Set-vRACustomForm Set-vRAEntitlement Set-vRAExternalNetworkProfile Set-vRANATNetworkProfile Set-vRAReservation Set-vRAReservationNetwork Set-vRAReservationPolicy Set-vRAReservationStorage Set-vRARoutedNetworkProfile Set-vRAService 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diag_fpsMin diag_frameNo diag_lightNewLoad diag_list diag_log diag_logSlowFrame diag_mergeConfigFile diag_recordTurretLimits diag_setLightNew diag_tickTime diag_toggle dialog diarySubjectExists didJIP didJIPOwner difficulty difficultyEnabled difficultyEnabledRTD difficultyOption direction directSay disableAI disableCollisionWith disableConversation disableDebriefingStats disableMapIndicators disableNVGEquipment disableRemoteSensors disableSerialization disableTIEquipment disableUAVConnectability disableUserInput displayAddEventHandler displayCtrl displayParent displayRemoveAllEventHandlers displayRemoveEventHandler displaySetEventHandler dissolveTeam distance distance2D distanceSqr distributionRegion do3DENAction doArtilleryFire doFire doFollow doFSM doGetOut doMove doorPhase doStop doSuppressiveFire doTarget doWatch drawArrow drawEllipse drawIcon drawIcon3D drawLine drawLine3D drawLink drawLocation drawPolygon drawRectangle drawTriangle driver drop dynamicSimulationDistance dynamicSimulationDistanceCoef dynamicSimulationEnabled dynamicSimulationSystemEnabled echo edit3DENMissionAttributes editObject editorSetEventHandler effectiveCommander emptyPositions enableAI enableAIFeature enableAimPrecision enableAttack enableAudioFeature enableAutoStartUpRTD enableAutoTrimRTD enableCamShake enableCaustics enableChannel enableCollisionWith enableCopilot enableDebriefingStats enableDiagLegend enableDynamicSimulation enableDynamicSimulationSystem enableEndDialog enableEngineArtillery enableEnvironment enableFatigue enableGunLights enableInfoPanelComponent enableIRLasers enableMimics enablePersonTurret enableRadio enableReload enableRopeAttach enableSatNormalOnDetail enableSaving enableSentences enableSimulation enableSimulationGlobal enableStamina enableTeamSwitch enableTraffic enableUAVConnectability enableUAVWaypoints enableVehicleCargo enableVehicleSensor enableWeaponDisassembly endLoadingScreen endMission engineOn enginesIsOnRTD enginesRpmRTD enginesTorqueRTD entities environmentEnabled estimatedEndServerTime estimatedTimeLeft evalObjectArgument everyBackpack everyContainer exec execEditorScript execFSM execVM exp expectedDestination exportJIPMessages eyeDirection eyePos face faction fadeMusic fadeRadio fadeSound fadeSpeech failMission fillWeaponsFromPool find findCover findDisplay findEditorObject findEmptyPosition findEmptyPositionReady findIf findNearestEnemy finishMissionInit finite fire fireAtTarget firstBackpack flag flagAnimationPhase flagOwner flagSide flagTexture fleeing floor flyInHeight flyInHeightASL fog fogForecast fogParams forceAddUniform forcedMap forceEnd forceFlagTexture forceFollowRoad forceMap forceRespawn forceSpeed forceWalk forceWeaponFire forceWeatherChange forEachMember forEachMemberAgent forEachMemberTeam forgetTarget format formation formationDirection formationLeader formationMembers formationPosition formationTask formatText formLeader freeLook fromEditor fuel fullCrew gearIDCAmmoCount gearSlotAmmoCount gearSlotData get3DENActionState get3DENAttribute get3DENCamera get3DENConnections get3DENEntity get3DENEntityID get3DENGrid get3DENIconsVisible get3DENLayerEntities get3DENLinesVisible get3DENMissionAttribute get3DENMouseOver get3DENSelected getAimingCoef getAllEnvSoundControllers getAllHitPointsDamage getAllOwnedMines getAllSoundControllers getAmmoCargo getAnimAimPrecision getAnimSpeedCoef getArray getArtilleryAmmo getArtilleryComputerSettings getArtilleryETA getAssignedCuratorLogic getAssignedCuratorUnit getBackpackCargo getBleedingRemaining getBurningValue getCameraViewDirection getCargoIndex getCenterOfMass getClientState getClientStateNumber getCompatiblePylonMagazines getConnectedUAV getContainerMaxLoad getCursorObjectParams getCustomAimCoef getDammage getDescription getDir getDirVisual getDLCAssetsUsage getDLCAssetsUsageByName getDLCs getEditorCamera getEditorMode getEditorObjectScope getElevationOffset getEnvSoundController getFatigue getForcedFlagTexture getFriend getFSMVariable getFuelCargo getGroupIcon getGroupIconParams getGroupIcons getHideFrom getHit getHitIndex getHitPointDamage getItemCargo getMagazineCargo getMarkerColor getMarkerPos getMarkerSize getMarkerType getMass getMissionConfig getMissionConfigValue getMissionDLCs getMissionLayerEntities getModelInfo getMousePosition getMusicPlayedTime getNumber getObjectArgument getObjectChildren getObjectDLC getObjectMaterials getObjectProxy getObjectTextures getObjectType getObjectViewDistance getOxygenRemaining getPersonUsedDLCs getPilotCameraDirection getPilotCameraPosition getPilotCameraRotation getPilotCameraTarget getPlateNumber getPlayerChannel getPlayerScores getPlayerUID getPos getPosASL getPosASLVisual getPosASLW getPosATL getPosATLVisual getPosVisual getPosWorld getPylonMagazines getRelDir getRelPos getRemoteSensorsDisabled getRepairCargo getResolution getShadowDistance getShotParents getSlingLoad getSoundController getSoundControllerResult getSpeed getStamina getStatValue getSuppression getTerrainGrid getTerrainHeightASL getText getTotalDLCUsageTime getUnitLoadout getUnitTrait getUserMFDText getUserMFDvalue getVariable getVehicleCargo getWeaponCargo getWeaponSway getWingsOrientationRTD getWingsPositionRTD getWPPos glanceAt globalChat globalRadio goggles goto group groupChat groupFromNetId groupIconSelectable groupIconsVisible groupId groupOwner groupRadio groupSelectedUnits groupSelectUnit gunner gusts halt handgunItems handgunMagazine handgunWeapon handsHit hasInterface hasPilotCamera hasWeapon hcAllGroups hcGroupParams hcLeader hcRemoveAllGroups hcRemoveGroup hcSelected hcSelectGroup hcSetGroup hcShowBar hcShownBar headgear hideBody hideObject hideObjectGlobal hideSelection hint hintC hintCadet hintSilent hmd hostMission htmlLoad HUDMovementLevels humidity image importAllGroups importance in inArea inAreaArray incapacitatedState inflame inflamed infoPanel infoPanelComponentEnabled infoPanelComponents infoPanels inGameUISetEventHandler inheritsFrom initAmbientLife inPolygon inputAction inRangeOfArtillery insertEditorObject intersect is3DEN is3DENMultiplayer isAbleToBreathe isAgent isArray isAutoHoverOn isAutonomous isAutotest isBleeding isBurning isClass isCollisionLightOn isCopilotEnabled isDamageAllowed isDedicated isDLCAvailable isEngineOn isEqualTo isEqualType isEqualTypeAll isEqualTypeAny isEqualTypeArray isEqualTypeParams isFilePatchingEnabled isFlashlightOn isFlatEmpty isForcedWalk isFormationLeader isGroupDeletedWhenEmpty isHidden isInRemainsCollector isInstructorFigureEnabled isIRLaserOn isKeyActive isKindOf isLaserOn isLightOn isLocalized isManualFire isMarkedForCollection isMultiplayer isMultiplayerSolo isNil isNull isNumber isObjectHidden isObjectRTD isOnRoad isPipEnabled isPlayer isRealTime isRemoteExecuted isRemoteExecutedJIP isServer isShowing3DIcons isSimpleObject isSprintAllowed isStaminaEnabled isSteamMission isStreamFriendlyUIEnabled isText isTouchingGround isTurnedOut isTutHintsEnabled isUAVConnectable isUAVConnected isUIContext isUniformAllowed isVehicleCargo isVehicleRadarOn isVehicleSensorEnabled isWalking isWeaponDeployed isWeaponRested itemCargo items itemsWithMagazines join joinAs joinAsSilent joinSilent joinString kbAddDatabase kbAddDatabaseTargets kbAddTopic kbHasTopic kbReact kbRemoveTopic kbTell kbWasSaid keyImage keyName knowsAbout land landAt landResult language laserTarget lbAdd lbClear lbColor lbColorRight lbCurSel lbData lbDelete lbIsSelected lbPicture lbPictureRight lbSelection lbSetColor lbSetColorRight lbSetCurSel lbSetData lbSetPicture lbSetPictureColor lbSetPictureColorDisabled lbSetPictureColorSelected lbSetPictureRight lbSetPictureRightColor lbSetPictureRightColorDisabled lbSetPictureRightColorSelected lbSetSelectColor lbSetSelectColorRight lbSetSelected lbSetText lbSetTextRight lbSetTooltip lbSetValue lbSize lbSort lbSortByValue lbText lbTextRight lbValue leader leaderboardDeInit leaderboardGetRows leaderboardInit leaderboardRequestRowsFriends leaderboardsRequestUploadScore leaderboardsRequestUploadScoreKeepBest leaderboardState leaveVehicle libraryCredits libraryDisclaimers lifeState lightAttachObject lightDetachObject lightIsOn lightnings limitSpeed linearConversion lineIntersects lineIntersectsObjs lineIntersectsSurfaces lineIntersectsWith linkItem list listObjects listRemoteTargets listVehicleSensors ln lnbAddArray lnbAddColumn lnbAddRow lnbClear lnbColor lnbCurSelRow lnbData lnbDeleteColumn lnbDeleteRow lnbGetColumnsPosition lnbPicture lnbSetColor lnbSetColumnsPos lnbSetCurSelRow lnbSetData lnbSetPicture lnbSetText lnbSetValue lnbSize lnbSort lnbSortByValue lnbText lnbValue load loadAbs loadBackpack loadFile loadGame loadIdentity loadMagazine loadOverlay loadStatus loadUniform loadVest local localize locationPosition lock lockCameraTo lockCargo lockDriver locked lockedCargo lockedDriver lockedTurret lockIdentity lockTurret lockWP log logEntities logNetwork logNetworkTerminate lookAt lookAtPos magazineCargo magazines magazinesAllTurrets magazinesAmmo magazinesAmmoCargo magazinesAmmoFull magazinesDetail magazinesDetailBackpack magazinesDetailUniform magazinesDetailVest magazinesTurret magazineTurretAmmo mapAnimAdd mapAnimClear mapAnimCommit mapAnimDone mapCenterOnCamera mapGridPosition markAsFinishedOnSteam markerAlpha markerBrush markerColor markerDir markerPos markerShape markerSize markerText markerType max members menuAction menuAdd menuChecked menuClear menuCollapse menuData menuDelete menuEnable menuEnabled menuExpand menuHover menuPicture menuSetAction menuSetCheck menuSetData menuSetPicture menuSetValue menuShortcut menuShortcutText menuSize menuSort menuText menuURL menuValue min mineActive mineDetectedBy missionConfigFile missionDifficulty missionName missionNamespace missionStart missionVersion mod modelToWorld modelToWorldVisual modelToWorldVisualWorld modelToWorldWorld modParams moonIntensity moonPhase morale move move3DENCamera moveInAny moveInCargo moveInCommander moveInDriver moveInGunner moveInTurret moveObjectToEnd moveOut moveTime moveTo moveToCompleted moveToFailed musicVolume name nameSound nearEntities nearestBuilding nearestLocation nearestLocations nearestLocationWithDubbing nearestObject nearestObjects nearestTerrainObjects nearObjects nearObjectsReady nearRoads nearSupplies nearTargets needReload netId netObjNull newOverlay nextMenuItemIndex nextWeatherChange nMenuItems not numberOfEnginesRTD numberToDate objectCurators objectFromNetId objectParent objStatus onBriefingGroup onBriefingNotes onBriefingPlan onBriefingTeamSwitch onCommandModeChanged onDoubleClick onEachFrame onGroupIconClick onGroupIconOverEnter onGroupIconOverLeave onHCGroupSelectionChanged onMapSingleClick onPlayerConnected onPlayerDisconnected onPreloadFinished onPreloadStarted onShowNewObject onTeamSwitch openCuratorInterface openDLCPage openMap openSteamApp openYoutubeVideo or orderGetIn overcast overcastForecast owner param params parseNumber parseSimpleArray parseText parsingNamespace particlesQuality pickWeaponPool pitch pixelGrid pixelGridBase pixelGridNoUIScale pixelH pixelW playableSlotsNumber playableUnits playAction playActionNow player playerRespawnTime playerSide playersNumber playGesture playMission playMove playMoveNow playMusic playScriptedMission playSound playSound3D position positionCameraToWorld posScreenToWorld posWorldToScreen ppEffectAdjust ppEffectCommit ppEffectCommitted ppEffectCreate ppEffectDestroy ppEffectEnable ppEffectEnabled ppEffectForceInNVG precision preloadCamera preloadObject preloadSound preloadTitleObj preloadTitleRsc preprocessFile preprocessFileLineNumbers primaryWeapon primaryWeaponItems primaryWeaponMagazine priority processDiaryLink productVersion profileName profileNamespace profileNameSteam progressLoadingScreen progressPosition progressSetPosition publicVariable publicVariableClient publicVariableServer pushBack pushBackUnique putWeaponPool queryItemsPool queryMagazinePool queryWeaponPool rad radioChannelAdd radioChannelCreate radioChannelRemove radioChannelSetCallSign radioChannelSetLabel radioVolume rain rainbow random rank rankId rating rectangular registeredTasks registerTask reload reloadEnabled remoteControl remoteExec remoteExecCall remoteExecutedOwner remove3DENConnection remove3DENEventHandler remove3DENLayer removeAction removeAll3DENEventHandlers removeAllActions removeAllAssignedItems removeAllContainers removeAllCuratorAddons removeAllCuratorCameraAreas removeAllCuratorEditingAreas removeAllEventHandlers removeAllHandgunItems removeAllItems removeAllItemsWithMagazines removeAllMissionEventHandlers removeAllMPEventHandlers removeAllMusicEventHandlers removeAllOwnedMines removeAllPrimaryWeaponItems removeAllWeapons removeBackpack removeBackpackGlobal removeCuratorAddons removeCuratorCameraArea removeCuratorEditableObjects removeCuratorEditingArea removeDrawIcon removeDrawLinks removeEventHandler removeFromRemainsCollector removeGoggles removeGroupIcon removeHandgunItem removeHeadgear removeItem removeItemFromBackpack removeItemFromUniform removeItemFromVest removeItems removeMagazine removeMagazineGlobal removeMagazines removeMagazinesTurret removeMagazineTurret removeMenuItem removeMissionEventHandler removeMPEventHandler removeMusicEventHandler removeOwnedMine removePrimaryWeaponItem removeSecondaryWeaponItem removeSimpleTask removeSwitchableUnit removeTeamMember removeUniform removeVest removeWeapon removeWeaponAttachmentCargo removeWeaponCargo removeWeaponGlobal removeWeaponTurret reportRemoteTarget requiredVersion resetCamShake resetSubgroupDirection resize resources respawnVehicle restartEditorCamera reveal revealMine reverse reversedMouseY roadAt roadsConnectedTo roleDescription ropeAttachedObjects ropeAttachedTo ropeAttachEnabled ropeAttachTo ropeCreate ropeCut ropeDestroy ropeDetach ropeEndPosition ropeLength ropes ropeUnwind ropeUnwound rotorsForcesRTD rotorsRpmRTD round runInitScript safeZoneH safeZoneW safeZoneWAbs safeZoneX safeZoneXAbs safeZoneY save3DENInventory saveGame saveIdentity saveJoysticks saveOverlay saveProfileNamespace saveStatus saveVar savingEnabled say say2D say3D scopeName score scoreSide screenshot screenToWorld scriptDone scriptName scudState secondaryWeapon secondaryWeaponItems secondaryWeaponMagazine select selectBestPlaces selectDiarySubject selectedEditorObjects selectEditorObject selectionNames selectionPosition selectLeader selectMax selectMin selectNoPlayer selectPlayer selectRandom selectRandomWeighted selectWeapon selectWeaponTurret sendAUMessage sendSimpleCommand sendTask sendTaskResult sendUDPMessage serverCommand serverCommandAvailable serverCommandExecutable serverName serverTime set set3DENAttribute set3DENAttributes set3DENGrid set3DENIconsVisible set3DENLayer set3DENLinesVisible set3DENLogicType set3DENMissionAttribute set3DENMissionAttributes set3DENModelsVisible set3DENObjectType set3DENSelected setAccTime setActualCollectiveRTD setAirplaneThrottle setAirportSide setAmmo setAmmoCargo setAmmoOnPylon setAnimSpeedCoef setAperture setApertureNew setArmoryPoints setAttributes setAutonomous setBehaviour setBleedingRemaining setBrakesRTD setCameraInterest setCamShakeDefParams setCamShakeParams setCamUseTI setCaptive setCenterOfMass setCollisionLight setCombatMode setCompassOscillation setConvoySeparation setCuratorCameraAreaCeiling setCuratorCoef setCuratorEditingAreaType setCuratorWaypointCost setCurrentChannel setCurrentTask setCurrentWaypoint setCustomAimCoef setCustomWeightRTD setDamage setDammage setDate setDebriefingText setDefaultCamera setDestination setDetailMapBlendPars setDir setDirection setDrawIcon setDriveOnPath setDropInterval setDynamicSimulationDistance setDynamicSimulationDistanceCoef setEditorMode setEditorObjectScope setEffectCondition setEngineRPMRTD setFace setFaceAnimation setFatigue setFeatureType setFlagAnimationPhase setFlagOwner setFlagSide setFlagTexture setFog setFormation setFormationTask setFormDir setFriend setFromEditor setFSMVariable setFuel setFuelCargo setGroupIcon setGroupIconParams setGroupIconsSelectable setGroupIconsVisible setGroupId setGroupIdGlobal setGroupOwner setGusts setHideBehind setHit setHitIndex setHitPointDamage setHorizonParallaxCoef setHUDMovementLevels setIdentity setImportance setInfoPanel setLeader setLightAmbient setLightAttenuation setLightBrightness setLightColor setLightDayLight setLightFlareMaxDistance setLightFlareSize setLightIntensity setLightnings setLightUseFlare setLocalWindParams setMagazineTurretAmmo setMarkerAlpha setMarkerAlphaLocal setMarkerBrush setMarkerBrushLocal setMarkerColor setMarkerColorLocal setMarkerDir setMarkerDirLocal setMarkerPos setMarkerPosLocal setMarkerShape setMarkerShapeLocal setMarkerSize setMarkerSizeLocal setMarkerText setMarkerTextLocal setMarkerType setMarkerTypeLocal setMass setMimic setMousePosition setMusicEffect setMusicEventHandler setName setNameSound setObjectArguments setObjectMaterial setObjectMaterialGlobal setObjectProxy setObjectTexture setObjectTextureGlobal setObjectViewDistance setOvercast setOwner setOxygenRemaining setParticleCircle setParticleClass setParticleFire setParticleParams setParticleRandom setPilotCameraDirection setPilotCameraRotation setPilotCameraTarget setPilotLight setPiPEffect setPitch setPlateNumber setPlayable setPlayerRespawnTime setPos setPosASL setPosASL2 setPosASLW setPosATL setPosition setPosWorld setPylonLoadOut setPylonsPriority setRadioMsg setRain setRainbow setRandomLip setRank setRectangular setRepairCargo setRotorBrakeRTD setShadowDistance setShotParents setSide setSimpleTaskAlwaysVisible setSimpleTaskCustomData setSimpleTaskDescription setSimpleTaskDestination setSimpleTaskTarget setSimpleTaskType setSimulWeatherLayers setSize setSkill setSlingLoad setSoundEffect setSpeaker setSpeech setSpeedMode setStamina setStaminaScheme setStatValue setSuppression setSystemOfUnits setTargetAge setTaskMarkerOffset setTaskResult setTaskState setTerrainGrid setText setTimeMultiplier setTitleEffect setTrafficDensity setTrafficDistance setTrafficGap setTrafficSpeed setTriggerActivation setTriggerArea setTriggerStatements setTriggerText setTriggerTimeout setTriggerType setType setUnconscious setUnitAbility setUnitLoadout setUnitPos setUnitPosWeak setUnitRank setUnitRecoilCoefficient setUnitTrait setUnloadInCombat setUserActionText setUserMFDText setUserMFDvalue setVariable setVectorDir setVectorDirAndUp setVectorUp setVehicleAmmo setVehicleAmmoDef setVehicleArmor setVehicleCargo setVehicleId setVehicleLock setVehiclePosition setVehicleRadar setVehicleReceiveRemoteTargets setVehicleReportOwnPosition setVehicleReportRemoteTargets setVehicleTIPars setVehicleVarName setVelocity setVelocityModelSpace setVelocityTransformation setViewDistance setVisibleIfTreeCollapsed setWantedRPMRTD setWaves setWaypointBehaviour setWaypointCombatMode setWaypointCompletionRadius setWaypointDescription setWaypointForceBehaviour setWaypointFormation setWaypointHousePosition setWaypointLoiterRadius setWaypointLoiterType setWaypointName setWaypointPosition setWaypointScript setWaypointSpeed setWaypointStatements setWaypointTimeout setWaypointType setWaypointVisible setWeaponReloadingTime setWind setWindDir setWindForce setWindStr setWingForceScaleRTD setWPPos show3DIcons showChat showCinemaBorder showCommandingMenu showCompass showCuratorCompass showGPS showHUD showLegend showMap shownArtilleryComputer shownChat shownCompass shownCuratorCompass showNewEditorObject shownGPS shownHUD shownMap shownPad shownRadio shownScoretable shownUAVFeed shownWarrant shownWatch showPad showRadio showScoretable showSubtitles showUAVFeed showWarrant showWatch showWaypoint showWaypoints side sideChat sideEnemy sideFriendly sideRadio simpleTasks simulationEnabled simulCloudDensity simulCloudOcclusion simulInClouds simulWeatherSync sin size sizeOf skill skillFinal skipTime sleep sliderPosition sliderRange sliderSetPosition sliderSetRange sliderSetSpeed sliderSpeed slingLoadAssistantShown soldierMagazines someAmmo sort soundVolume spawn speaker speed speedMode splitString sqrt squadParams stance startLoadingScreen step stop stopEngineRTD stopped str sunOrMoon supportInfo suppressFor surfaceIsWater surfaceNormal surfaceType swimInDepth switchableUnits switchAction switchCamera switchGesture switchLight switchMove synchronizedObjects synchronizedTriggers synchronizedWaypoints synchronizeObjectsAdd synchronizeObjectsRemove synchronizeTrigger synchronizeWaypoint systemChat systemOfUnits tan targetKnowledge targets targetsAggregate targetsQuery taskAlwaysVisible taskChildren taskCompleted taskCustomData taskDescription taskDestination taskHint taskMarkerOffset taskParent taskResult taskState taskType teamMember teamName teams teamSwitch teamSwitchEnabled teamType terminate terrainIntersect terrainIntersectASL terrainIntersectAtASL text textLog textLogFormat tg time timeMultiplier titleCut titleFadeOut titleObj titleRsc titleText toArray toFixed toLower toString toUpper triggerActivated triggerActivation triggerArea triggerAttachedVehicle triggerAttachObject triggerAttachVehicle triggerDynamicSimulation triggerStatements triggerText triggerTimeout triggerTimeoutCurrent triggerType turretLocal turretOwner turretUnit tvAdd tvClear tvCollapse tvCollapseAll tvCount tvCurSel tvData tvDelete tvExpand tvExpandAll tvPicture tvSetColor tvSetCurSel tvSetData tvSetPicture tvSetPictureColor tvSetPictureColorDisabled tvSetPictureColorSelected tvSetPictureRight tvSetPictureRightColor tvSetPictureRightColorDisabled tvSetPictureRightColorSelected tvSetText tvSetTooltip tvSetValue tvSort tvSortByValue tvText tvTooltip tvValue type typeName typeOf UAVControl uiNamespace uiSleep unassignCurator unassignItem unassignTeam unassignVehicle underwater uniform uniformContainer uniformItems uniformMagazines unitAddons unitAimPosition unitAimPositionVisual unitBackpack unitIsUAV unitPos unitReady unitRecoilCoefficient units unitsBelowHeight unlinkItem 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копироватьфайл краткоепредставлениеошибки лев макс местноевремя месяц мин минута монопольныйрежим найти найтинедопустимыесимволыxml найтиокнопонавигационнойссылке найтипомеченныенаудаление найтипоссылкам найтифайлы началогода началодня началоквартала началомесяца началоминуты началонедели началочаса начатьзапросразрешенияпользователя начатьзапускприложения начатькопированиефайла начатьперемещениефайла начатьподключениевнешнейкомпоненты начатьподключениерасширенияработыскриптографией начатьподключениерасширенияработысфайлами начатьпоискфайлов начатьполучениекаталогавременныхфайлов начатьполучениекаталогадокументов начатьполучениерабочегокаталогаданныхпользователя начатьполучениефайлов начатьпомещениефайла начатьпомещениефайлов начатьсозданиедвоичныхданныхизфайла начатьсозданиекаталога начатьтранзакцию начатьудалениефайлов начатьустановкувнешнейкомпоненты начатьустановкурасширенияработыскриптографией начатьустановкурасширенияработысфайлами неделягода необходимостьзавершениясоединения номерсеансаинформационнойбазы номерсоединенияинформационнойбазы нрег нстр обновитьинтерфейс обновитьнумерациюобъектов обновитьповторноиспользуемыезначения обработкапрерыванияпользователя объединитьфайлы окр описаниеошибки оповестить оповеститьобизменении отключитьобработчикзапросанастроекклиенталицензирования отключитьобработчикожидания отключитьобработчикоповещения открытьзначение открытьиндекссправки открытьсодержаниесправки открытьсправку открытьформу открытьформумодально отменитьтранзакцию очиститьжурналрегистрации очиститьнастройкипользователя очиститьсообщения параметрыдоступа перейтипонавигационнойссылке переместитьфайл подключитьвнешнююкомпоненту подключитьобработчикзапросанастроекклиенталицензирования подключитьобработчикожидания подключитьобработчикоповещения подключитьрасширениеработыскриптографией подключитьрасширениеработысфайлами подробноепредставлениеошибки показатьвводдаты показатьвводзначения показатьвводстроки показатьвводчисла показатьвопрос показатьзначение показатьинформациюобошибке показатьнакарте показатьоповещениепользователя показатьпредупреждение полноеимяпользователя получитьcomобъект получитьxmlтип получитьадреспоместоположению получитьблокировкусеансов получитьвремязавершенияспящегосеанса получитьвремязасыпанияпассивногосеанса получитьвремяожиданияблокировкиданных получитьданныевыбора получитьдополнительныйпараметрклиенталицензирования получитьдопустимыекодылокализации получитьдопустимыечасовыепояса получитьзаголовокклиентскогоприложения получитьзаголовоксистемы получитьзначенияотборажурналарегистрации получитьидентификаторконфигурации получитьизвременногохранилища получитьимявременногофайла получитьимяклиенталицензирования получитьинформациюэкрановклиента получитьиспользованиежурналарегистрации получитьиспользованиесобытияжурналарегистрации получитькраткийзаголовокприложения получитьмакетоформления получитьмаскувсефайлы получитьмаскувсефайлыклиента получитьмаскувсефайлысервера получитьместоположениепоадресу получитьминимальнуюдлинупаролейпользователей получитьнавигационнуюссылку получитьнавигационнуюссылкуинформационнойбазы получитьобновлениеконфигурациибазыданных получитьобновлениепредопределенныхданныхинформационнойбазы получитьобщиймакет получитьобщуюформу получитьокна получитьоперативнуюотметкувремени получитьотключениебезопасногорежима получитьпараметрыфункциональныхопцийинтерфейса получитьполноеимяпредопределенногозначения получитьпредставлениянавигационныхссылок получитьпроверкусложностипаролейпользователей получитьразделительпути получитьразделительпутиклиента получитьразделительпутисервера получитьсеансыинформационнойбазы получитьскоростьклиентскогосоединения получитьсоединенияинформационнойбазы получитьсообщенияпользователю получитьсоответствиеобъектаиформы получитьсоставстандартногоинтерфейсаodata получитьструктурухранениябазыданных получитьтекущийсеансинформационнойбазы получитьфайл получитьфайлы получитьформу получитьфункциональнуюопцию получитьфункциональнуюопциюинтерфейса 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стрразделить стрсоединить стрсравнить стрчисловхождений стрчислострок стршаблон текущаядата текущаядатасеанса текущаяуниверсальнаядата текущаяуниверсальнаядатавмиллисекундах текущийвариантинтерфейсаклиентскогоприложения текущийвариантосновногошрифтаклиентскогоприложения текущийкодлокализации текущийрежимзапуска текущийязык текущийязыксистемы тип типзнч транзакцияактивна трег удалитьданныеинформационнойбазы удалитьизвременногохранилища удалитьобъекты удалитьфайлы универсальноевремя установитьбезопасныйрежим установитьбезопасныйрежимразделенияданных установитьблокировкусеансов установитьвнешнююкомпоненту установитьвремязавершенияспящегосеанса установитьвремязасыпанияпассивногосеанса установитьвремяожиданияблокировкиданных установитьзаголовокклиентскогоприложения установитьзаголовоксистемы установитьиспользованиежурналарегистрации установитьиспользованиесобытияжурналарегистрации установитькраткийзаголовокприложения установитьминимальнуюдлинупаролейпользователей установитьмонопольныйрежим установитьнастройкиклиенталицензирования установитьобновлениепредопределенныхданныхинформационнойбазы установитьотключениебезопасногорежима установитьпараметрыфункциональныхопцийинтерфейса установитьпривилегированныйрежим установитьпроверкусложностипаролейпользователей установитьрасширениеработыскриптографией установитьрасширениеработысфайлами установитьсоединениесвнешнимисточникомданных установитьсоответствиеобъектаиформы установитьсоставстандартногоинтерфейсаodata установитьчасовойпоясинформационнойбазы установитьчасовойпояссеанса формат цел час часовойпояс часовойпояссеанса число числопрописью этоадресвременногохранилища wsссылки библиотекакартинок библиотекамакетовоформлениякомпоновкиданных библиотекастилей бизнеспроцессы внешниеисточникиданных внешниеобработки внешниеотчеты встроенныепокупки главныйинтерфейс главныйстиль документы доставляемыеуведомления журналыдокументов задачи информацияобинтернетсоединении использованиерабочейдаты историяработыпользователя константы критерииотбора метаданные обработки отображениерекламы отправкадоставляемыхуведомлений отчеты панельзадачос параметрзапуска параметрысеанса перечисления планывидоврасчета планывидовхарактеристик планыобмена планысчетов полнотекстовыйпоиск пользователиинформационнойбазы последовательности проверкавстроенныхпокупок рабочаядата расширенияконфигурации регистрыбухгалтерии регистрынакопления регистрырасчета регистрысведений регламентныезадания сериализаторxdto справочники средствагеопозиционирования средствакриптографии средствамультимедиа средстваотображениярекламы средствапочты средствателефонии фабрикаxdto файловыепотоки фоновыезадания хранилищанастроек хранилищевариантовотчетов хранилищенастроекданныхформ хранилищеобщихнастроек хранилищепользовательскихнастроекдинамическихсписков хранилищепользовательскихнастроекотчетов хранилищесистемныхнастроек ",class:"webцвета windowsцвета windowsшрифты библиотекакартинок рамкистиля символы цветастиля шрифтыстиля 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DeviceStreams DeviceWrite DeviceWriteBuffer DGaussianWavelet DiacriticalPositioning Diagonal DiagonalizableMatrixQ DiagonalMatrix DiagonalMatrixQ Dialog DialogIndent DialogInput DialogLevel DialogNotebook DialogProlog DialogReturn DialogSymbols Diamond DiamondMatrix DiceDissimilarity DictionaryLookup DictionaryWordQ DifferenceDelta DifferenceOrder DifferenceQuotient DifferenceRoot DifferenceRootReduce Differences DifferentialD DifferentialRoot DifferentialRootReduce DifferentiatorFilter DigitalSignature DigitBlock DigitBlockMinimum DigitCharacter DigitCount DigitQ DihedralAngle DihedralGroup Dilation DimensionalCombinations DimensionalMeshComponents DimensionReduce DimensionReducerFunction DimensionReduction Dimensions DiracComb DiracDelta DirectedEdge DirectedEdges DirectedGraph DirectedGraphQ DirectedInfinity Direction Directive Directory DirectoryName DirectoryQ DirectoryStack DirichletBeta DirichletCharacter DirichletCondition DirichletConvolve DirichletDistribution DirichletEta DirichletL DirichletLambda DirichletTransform DirichletWindow DisableConsolePrintPacket DisableFormatting DiscreteChirpZTransform DiscreteConvolve DiscreteDelta DiscreteHadamardTransform DiscreteIndicator DiscreteLimit DiscreteLQEstimatorGains DiscreteLQRegulatorGains DiscreteLyapunovSolve DiscreteMarkovProcess DiscreteMaxLimit DiscreteMinLimit DiscretePlot DiscretePlot3D DiscreteRatio DiscreteRiccatiSolve DiscreteShift DiscreteTimeModelQ DiscreteUniformDistribution DiscreteVariables DiscreteWaveletData DiscreteWaveletPacketTransform DiscreteWaveletTransform DiscretizeGraphics DiscretizeRegion Discriminant DisjointQ Disjunction Disk DiskBox DiskMatrix DiskSegment Dispatch DispatchQ DispersionEstimatorFunction Display DisplayAllSteps DisplayEndPacket DisplayFlushImagePacket DisplayForm DisplayFunction DisplayPacket DisplayRules DisplaySetSizePacket DisplayString DisplayTemporary DisplayWith DisplayWithRef DisplayWithVariable DistanceFunction DistanceMatrix DistanceTransform Distribute Distributed DistributedContexts DistributeDefinitions DistributionChart DistributionDomain DistributionFitTest DistributionParameterAssumptions DistributionParameterQ Dithering Div Divergence Divide DivideBy Dividers DivideSides Divisible Divisors DivisorSigma DivisorSum DMSList DMSString Do DockedCells DocumentGenerator DocumentGeneratorInformation DocumentGeneratorInformationData DocumentGenerators DocumentNotebook DocumentWeightingRules Dodecahedron DomainRegistrationInformation DominantColors DOSTextFormat Dot DotDashed DotEqual DotLayer DotPlusLayer Dotted DoubleBracketingBar DoubleContourIntegral DoubleDownArrow DoubleLeftArrow DoubleLeftRightArrow DoubleLeftTee DoubleLongLeftArrow DoubleLongLeftRightArrow DoubleLongRightArrow DoubleRightArrow DoubleRightTee DoubleUpArrow DoubleUpDownArrow DoubleVerticalBar DoublyInfinite Down DownArrow DownArrowBar DownArrowUpArrow DownLeftRightVector DownLeftTeeVector DownLeftVector DownLeftVectorBar DownRightTeeVector DownRightVector DownRightVectorBar Downsample DownTee DownTeeArrow DownValues DragAndDrop DrawEdges DrawFrontFaces DrawHighlighted Drop DropoutLayer DSolve DSolveValue Dt DualLinearProgramming DualPolyhedron DualSystemsModel DumpGet DumpSave DuplicateFreeQ Duration Dynamic DynamicBox DynamicBoxOptions DynamicEvaluationTimeout DynamicGeoGraphics DynamicImage DynamicLocation DynamicModule DynamicModuleBox DynamicModuleBoxOptions DynamicModuleParent DynamicModuleValues DynamicName DynamicNamespace DynamicReference DynamicSetting DynamicUpdating DynamicWrapper DynamicWrapperBox DynamicWrapperBoxOptionsE EarthImpactData EarthquakeData EccentricityCentrality Echo EchoFunction EclipseType EdgeAdd EdgeBetweennessCentrality EdgeCapacity EdgeCapForm EdgeColor EdgeConnectivity EdgeContract EdgeCost EdgeCount EdgeCoverQ EdgeCycleMatrix EdgeDashing EdgeDelete EdgeDetect EdgeForm EdgeIndex EdgeJoinForm EdgeLabeling EdgeLabels EdgeLabelStyle EdgeList EdgeOpacity EdgeQ EdgeRenderingFunction EdgeRules EdgeShapeFunction EdgeStyle EdgeThickness EdgeWeight EdgeWeightedGraphQ Editable EditButtonSettings EditCellTagsSettings EditDistance EffectiveInterest Eigensystem Eigenvalues EigenvectorCentrality Eigenvectors Element ElementData ElementwiseLayer ElidedForms Eliminate EliminationOrder Ellipsoid EllipticE EllipticExp EllipticExpPrime EllipticF EllipticFilterModel EllipticK EllipticLog EllipticNomeQ EllipticPi EllipticReducedHalfPeriods EllipticTheta EllipticThetaPrime EmbedCode EmbeddedHTML EmbeddedService EmbeddingLayer EmbeddingObject EmitSound EmphasizeSyntaxErrors EmpiricalDistribution Empty EmptyGraphQ EmptyRegion EnableConsolePrintPacket Enabled Encode Encrypt EncryptedObject EncryptFile End EndAdd EndDialogPacket EndFrontEndInteractionPacket EndOfBuffer EndOfFile EndOfLine EndOfString EndPackage EngineEnvironment EngineeringForm Enter EnterExpressionPacket EnterTextPacket Entity EntityClass EntityClassList EntityCopies EntityFunction EntityGroup EntityInstance EntityList EntityPrefetch EntityProperties EntityProperty EntityPropertyClass EntityRegister EntityStore EntityStores EntityTypeName EntityUnregister EntityValue Entropy EntropyFilter Environment Epilog EpilogFunction Equal EqualColumns EqualRows EqualTilde EqualTo EquatedTo Equilibrium EquirippleFilterKernel Equivalent Erf Erfc Erfi ErlangB ErlangC ErlangDistribution Erosion ErrorBox ErrorBoxOptions ErrorNorm ErrorPacket ErrorsDialogSettings EscapeRadius EstimatedBackground EstimatedDistribution EstimatedProcess EstimatorGains EstimatorRegulator EuclideanDistance EulerAngles EulerCharacteristic EulerE EulerGamma EulerianGraphQ EulerMatrix EulerPhi Evaluatable Evaluate Evaluated EvaluatePacket EvaluateScheduledTask EvaluationBox EvaluationCell EvaluationCompletionAction EvaluationData EvaluationElements EvaluationEnvironment EvaluationMode EvaluationMonitor EvaluationNotebook EvaluationObject EvaluationOrder Evaluator EvaluatorNames EvenQ EventData EventEvaluator EventHandler EventHandlerTag EventLabels EventSeries ExactBlackmanWindow ExactNumberQ ExactRootIsolation ExampleData Except ExcludedForms ExcludedLines ExcludedPhysicalQuantities ExcludePods Exclusions ExclusionsStyle Exists Exit ExitDialog ExoplanetData Exp Expand ExpandAll ExpandDenominator ExpandFileName ExpandNumerator Expectation ExpectationE ExpectedValue ExpGammaDistribution ExpIntegralE ExpIntegralEi ExpirationDate Exponent ExponentFunction ExponentialDistribution ExponentialFamily ExponentialGeneratingFunction ExponentialMovingAverage ExponentialPowerDistribution ExponentPosition ExponentStep Export ExportAutoReplacements ExportByteArray ExportForm ExportPacket ExportString Expression ExpressionCell ExpressionPacket ExpressionUUID ExpToTrig ExtendedEntityClass ExtendedGCD Extension ExtentElementFunction ExtentMarkers ExtentSize ExternalBundle ExternalCall ExternalDataCharacterEncoding ExternalEvaluate ExternalFunction ExternalFunctionName ExternalObject ExternalOptions ExternalSessionObject ExternalSessions ExternalTypeSignature ExternalValue Extract ExtractArchive ExtractLayer ExtremeValueDistributionFaceForm FaceGrids FaceGridsStyle FacialFeatures Factor FactorComplete Factorial Factorial2 FactorialMoment FactorialMomentGeneratingFunction FactorialPower FactorInteger FactorList FactorSquareFree FactorSquareFreeList FactorTerms FactorTermsList Fail Failure FailureAction FailureDistribution FailureQ False FareySequence FARIMAProcess FeatureDistance FeatureExtract FeatureExtraction FeatureExtractor FeatureExtractorFunction FeatureNames FeatureNearest FeatureSpacePlot FeatureSpacePlot3D FeatureTypes FEDisableConsolePrintPacket FeedbackLinearize FeedbackSector FeedbackSectorStyle FeedbackType FEEnableConsolePrintPacket FetalGrowthData Fibonacci Fibonorial FieldCompletionFunction FieldHint FieldHintStyle FieldMasked FieldSize File FileBaseName FileByteCount FileConvert FileDate FileExistsQ FileExtension FileFormat FileHandler FileHash FileInformation FileName FileNameDepth FileNameDialogSettings FileNameDrop FileNameForms FileNameJoin FileNames FileNameSetter FileNameSplit FileNameTake FilePrint FileSize FileSystemMap FileSystemScan FileTemplate FileTemplateApply FileType FilledCurve FilledCurveBox FilledCurveBoxOptions Filling FillingStyle FillingTransform FilteredEntityClass FilterRules FinancialBond FinancialData FinancialDerivative FinancialIndicator Find FindAnomalies FindArgMax FindArgMin FindChannels FindClique FindClusters FindCookies FindCurvePath FindCycle FindDevices FindDistribution FindDistributionParameters FindDivisions FindEdgeCover FindEdgeCut FindEdgeIndependentPaths FindEquationalProof FindEulerianCycle FindExternalEvaluators FindFaces FindFile FindFit FindFormula FindFundamentalCycles FindGeneratingFunction FindGeoLocation FindGeometricConjectures FindGeometricTransform FindGraphCommunities FindGraphIsomorphism FindGraphPartition FindHamiltonianCycle FindHamiltonianPath FindHiddenMarkovStates FindIndependentEdgeSet FindIndependentVertexSet FindInstance FindIntegerNullVector FindKClan FindKClique FindKClub FindKPlex FindLibrary FindLinearRecurrence FindList FindMatchingColor FindMaximum FindMaximumFlow FindMaxValue FindMeshDefects FindMinimum FindMinimumCostFlow FindMinimumCut FindMinValue FindMoleculeSubstructure FindPath FindPeaks FindPermutation FindPostmanTour FindProcessParameters FindRepeat FindRoot FindSequenceFunction FindSettings FindShortestPath FindShortestTour FindSpanningTree FindSystemModelEquilibrium FindTextualAnswer FindThreshold FindTransientRepeat FindVertexCover FindVertexCut FindVertexIndependentPaths Fine FinishDynamic FiniteAbelianGroupCount FiniteGroupCount FiniteGroupData First FirstCase FirstPassageTimeDistribution FirstPosition FischerGroupFi22 FischerGroupFi23 FischerGroupFi24Prime FisherHypergeometricDistribution FisherRatioTest FisherZDistribution Fit FitAll FitRegularization FittedModel FixedOrder FixedPoint FixedPointList FlashSelection Flat Flatten FlattenAt FlattenLayer FlatTopWindow FlipView Floor FlowPolynomial FlushPrintOutputPacket Fold FoldList FoldPair FoldPairList FollowRedirects Font FontColor FontFamily FontForm FontName FontOpacity FontPostScriptName FontProperties FontReencoding FontSize FontSlant FontSubstitutions FontTracking FontVariations FontWeight For ForAll Format FormatRules FormatType FormatTypeAutoConvert FormatValues FormBox FormBoxOptions FormControl FormFunction FormLayoutFunction FormObject FormPage FormTheme FormulaData FormulaLookup FortranForm Forward ForwardBackward Fourier FourierCoefficient FourierCosCoefficient FourierCosSeries FourierCosTransform FourierDCT FourierDCTFilter FourierDCTMatrix FourierDST FourierDSTMatrix FourierMatrix FourierParameters FourierSequenceTransform FourierSeries FourierSinCoefficient FourierSinSeries FourierSinTransform FourierTransform FourierTrigSeries FractionalBrownianMotionProcess FractionalGaussianNoiseProcess FractionalPart FractionBox FractionBoxOptions FractionLine Frame FrameBox FrameBoxOptions Framed FrameInset FrameLabel Frameless FrameMargins FrameRate FrameStyle FrameTicks FrameTicksStyle FRatioDistribution FrechetDistribution FreeQ FrenetSerretSystem FrequencySamplingFilterKernel FresnelC FresnelF FresnelG FresnelS Friday FrobeniusNumber FrobeniusSolve FromAbsoluteTime FromCharacterCode FromCoefficientRules FromContinuedFraction FromDate FromDigits FromDMS FromEntity FromJulianDate FromLetterNumber FromPolarCoordinates FromRomanNumeral FromSphericalCoordinates FromUnixTime Front FrontEndDynamicExpression FrontEndEventActions FrontEndExecute FrontEndObject FrontEndResource FrontEndResourceString FrontEndStackSize FrontEndToken FrontEndTokenExecute FrontEndValueCache FrontEndVersion FrontFaceColor FrontFaceOpacity Full FullAxes FullDefinition FullForm FullGraphics FullInformationOutputRegulator FullOptions FullRegion FullSimplify Function FunctionCompile FunctionCompileExport FunctionCompileExportByteArray FunctionCompileExportLibrary FunctionCompileExportString FunctionDomain FunctionExpand FunctionInterpolation FunctionPeriod FunctionRange FunctionSpace FussellVeselyImportanceGaborFilter GaborMatrix GaborWavelet GainMargins GainPhaseMargins GalaxyData GalleryView Gamma GammaDistribution GammaRegularized GapPenalty GARCHProcess GatedRecurrentLayer Gather GatherBy GaugeFaceElementFunction GaugeFaceStyle GaugeFrameElementFunction GaugeFrameSize GaugeFrameStyle GaugeLabels GaugeMarkers GaugeStyle GaussianFilter GaussianIntegers GaussianMatrix GaussianOrthogonalMatrixDistribution GaussianSymplecticMatrixDistribution GaussianUnitaryMatrixDistribution GaussianWindow GCD GegenbauerC General GeneralizedLinearModelFit GenerateAsymmetricKeyPair GenerateConditions GeneratedCell GeneratedDocumentBinding GenerateDerivedKey GenerateDigitalSignature GenerateDocument GeneratedParameters GeneratedQuantityMagnitudes GenerateHTTPResponse GenerateSecuredAuthenticationKey GenerateSymmetricKey GeneratingFunction GeneratorDescription GeneratorHistoryLength GeneratorOutputType Generic GenericCylindricalDecomposition GenomeData GenomeLookup GeoAntipode GeoArea GeoArraySize GeoBackground GeoBoundingBox GeoBounds GeoBoundsRegion GeoBubbleChart GeoCenter GeoCircle GeodesicClosing GeodesicDilation GeodesicErosion GeodesicOpening GeoDestination GeodesyData GeoDirection GeoDisk GeoDisplacement GeoDistance GeoDistanceList GeoElevationData GeoEntities GeoGraphics GeogravityModelData GeoGridDirectionDifference GeoGridLines GeoGridLinesStyle GeoGridPosition GeoGridRange GeoGridRangePadding GeoGridUnitArea GeoGridUnitDistance GeoGridVector GeoGroup GeoHemisphere GeoHemisphereBoundary GeoHistogram GeoIdentify GeoImage GeoLabels GeoLength GeoListPlot GeoLocation GeologicalPeriodData GeomagneticModelData GeoMarker GeometricAssertion GeometricBrownianMotionProcess GeometricDistribution GeometricMean GeometricMeanFilter GeometricScene GeometricTransformation GeometricTransformation3DBox GeometricTransformation3DBoxOptions GeometricTransformationBox GeometricTransformationBoxOptions GeoModel GeoNearest GeoPath GeoPosition GeoPositionENU GeoPositionXYZ GeoProjection GeoProjectionData GeoRange GeoRangePadding GeoRegionValuePlot GeoResolution GeoScaleBar GeoServer GeoSmoothHistogram GeoStreamPlot GeoStyling GeoStylingImageFunction GeoVariant GeoVector GeoVectorENU GeoVectorPlot GeoVectorXYZ GeoVisibleRegion GeoVisibleRegionBoundary GeoWithinQ GeoZoomLevel GestureHandler GestureHandlerTag Get GetBoundingBoxSizePacket GetContext GetEnvironment GetFileName GetFrontEndOptionsDataPacket GetLinebreakInformationPacket GetMenusPacket GetPageBreakInformationPacket Glaisher GlobalClusteringCoefficient GlobalPreferences GlobalSession Glow GoldenAngle GoldenRatio GompertzMakehamDistribution GoodmanKruskalGamma GoodmanKruskalGammaTest Goto Grad Gradient GradientFilter GradientOrientationFilter GrammarApply GrammarRules GrammarToken Graph Graph3D GraphAssortativity GraphAutomorphismGroup GraphCenter GraphComplement GraphData GraphDensity GraphDiameter GraphDifference GraphDisjointUnion GraphDistance GraphDistanceMatrix GraphElementData GraphEmbedding GraphHighlight GraphHighlightStyle GraphHub Graphics Graphics3D Graphics3DBox Graphics3DBoxOptions GraphicsArray GraphicsBaseline GraphicsBox GraphicsBoxOptions GraphicsColor GraphicsColumn GraphicsComplex GraphicsComplex3DBox GraphicsComplex3DBoxOptions GraphicsComplexBox GraphicsComplexBoxOptions GraphicsContents GraphicsData GraphicsGrid GraphicsGridBox GraphicsGroup GraphicsGroup3DBox GraphicsGroup3DBoxOptions GraphicsGroupBox GraphicsGroupBoxOptions GraphicsGrouping GraphicsHighlightColor GraphicsRow GraphicsSpacing GraphicsStyle GraphIntersection GraphLayout GraphLinkEfficiency GraphPeriphery GraphPlot GraphPlot3D GraphPower GraphPropertyDistribution GraphQ GraphRadius GraphReciprocity GraphRoot GraphStyle GraphUnion Gray GrayLevel Greater GreaterEqual GreaterEqualLess GreaterEqualThan GreaterFullEqual GreaterGreater GreaterLess GreaterSlantEqual GreaterThan GreaterTilde Green GreenFunction Grid GridBaseline GridBox GridBoxAlignment GridBoxBackground GridBoxDividers GridBoxFrame GridBoxItemSize GridBoxItemStyle GridBoxOptions GridBoxSpacings GridCreationSettings GridDefaultElement GridElementStyleOptions GridFrame GridFrameMargins GridGraph GridLines GridLinesStyle GroebnerBasis GroupActionBase GroupBy GroupCentralizer GroupElementFromWord GroupElementPosition GroupElementQ GroupElements GroupElementToWord GroupGenerators Groupings GroupMultiplicationTable GroupOrbits GroupOrder GroupPageBreakWithin GroupSetwiseStabilizer GroupStabilizer GroupStabilizerChain GroupTogetherGrouping GroupTogetherNestedGrouping GrowCutComponents Gudermannian GuidedFilter GumbelDistributionHaarWavelet HadamardMatrix HalfLine HalfNormalDistribution HalfPlane HalfSpace HamiltonianGraphQ HammingDistance HammingWindow HandlerFunctions HandlerFunctionsKeys HankelH1 HankelH2 HankelMatrix HankelTransform HannPoissonWindow HannWindow HaradaNortonGroupHN HararyGraph HarmonicMean HarmonicMeanFilter HarmonicNumber Hash Haversine HazardFunction Head HeadCompose HeaderLines Heads HeavisideLambda HeavisidePi HeavisideTheta HeldGroupHe HeldPart HelpBrowserLookup HelpBrowserNotebook HelpBrowserSettings Here HermiteDecomposition HermiteH HermitianMatrixQ HessenbergDecomposition Hessian HexadecimalCharacter Hexahedron HexahedronBox HexahedronBoxOptions HiddenMarkovProcess HiddenSurface Highlighted HighlightGraph HighlightImage HighlightMesh HighpassFilter HigmanSimsGroupHS HilbertCurve HilbertFilter HilbertMatrix Histogram Histogram3D HistogramDistribution HistogramList HistogramTransform HistogramTransformInterpolation HistoricalPeriodData HitMissTransform HITSCentrality HjorthDistribution HodgeDual HoeffdingD HoeffdingDTest Hold HoldAll HoldAllComplete HoldComplete HoldFirst HoldForm HoldPattern HoldRest HolidayCalendar HomeDirectory HomePage Horizontal HorizontalForm HorizontalGauge HorizontalScrollPosition HornerForm HostLookup HotellingTSquareDistribution HoytDistribution HTMLSave HTTPErrorResponse HTTPRedirect HTTPRequest HTTPRequestData HTTPResponse Hue HumanGrowthData HumpDownHump HumpEqual HurwitzLerchPhi HurwitzZeta HyperbolicDistribution HypercubeGraph HyperexponentialDistribution Hyperfactorial Hypergeometric0F1 Hypergeometric0F1Regularized Hypergeometric1F1 Hypergeometric1F1Regularized Hypergeometric2F1 Hypergeometric2F1Regularized HypergeometricDistribution HypergeometricPFQ HypergeometricPFQRegularized HypergeometricU Hyperlink HyperlinkCreationSettings Hyperplane Hyphenation HyphenationOptions HypoexponentialDistribution HypothesisTestDataI IconData Iconize IconizedObject IconRules Icosahedron Identity IdentityMatrix If IgnoreCase IgnoreDiacritics IgnorePunctuation IgnoreSpellCheck IgnoringInactive Im Image Image3D Image3DProjection Image3DSlices ImageAccumulate ImageAdd ImageAdjust ImageAlign ImageApply ImageApplyIndexed ImageAspectRatio ImageAssemble ImageAugmentationLayer ImageBoundingBoxes ImageCache ImageCacheValid ImageCapture ImageCaptureFunction ImageCases ImageChannels ImageClip ImageCollage ImageColorSpace ImageCompose ImageContainsQ ImageContents ImageConvolve ImageCooccurrence ImageCorners ImageCorrelate ImageCorrespondingPoints ImageCrop ImageData ImageDeconvolve ImageDemosaic ImageDifference ImageDimensions ImageDisplacements ImageDistance ImageEffect ImageExposureCombine ImageFeatureTrack ImageFileApply ImageFileFilter ImageFileScan ImageFilter ImageFocusCombine ImageForestingComponents ImageFormattingWidth ImageForwardTransformation ImageGraphics ImageHistogram ImageIdentify ImageInstanceQ ImageKeypoints ImageLevels ImageLines ImageMargins ImageMarker ImageMarkers ImageMeasurements ImageMesh ImageMultiply ImageOffset ImagePad ImagePadding ImagePartition ImagePeriodogram ImagePerspectiveTransformation ImagePosition ImagePreviewFunction ImagePyramid ImagePyramidApply ImageQ ImageRangeCache ImageRecolor ImageReflect ImageRegion ImageResize ImageResolution ImageRestyle ImageRotate ImageRotated ImageSaliencyFilter ImageScaled ImageScan ImageSize ImageSizeAction ImageSizeCache ImageSizeMultipliers ImageSizeRaw ImageSubtract ImageTake ImageTransformation ImageTrim ImageType ImageValue ImageValuePositions ImagingDevice ImplicitRegion Implies Import ImportAutoReplacements ImportByteArray ImportOptions ImportString ImprovementImportance In Inactivate Inactive IncidenceGraph IncidenceList IncidenceMatrix IncludeAromaticBonds IncludeConstantBasis IncludeDefinitions IncludeDirectories IncludeFileExtension IncludeGeneratorTasks IncludeHydrogens IncludeInflections IncludeMetaInformation IncludePods IncludeQuantities IncludeRelatedTables IncludeSingularTerm IncludeWindowTimes Increment IndefiniteMatrixQ Indent IndentingNewlineSpacings IndentMaxFraction IndependenceTest IndependentEdgeSetQ IndependentPhysicalQuantity IndependentUnit IndependentUnitDimension IndependentVertexSetQ Indeterminate IndeterminateThreshold IndexCreationOptions Indexed IndexGraph IndexTag Inequality InexactNumberQ InexactNumbers InfiniteLine InfinitePlane Infinity Infix InflationAdjust InflationMethod Information InformationData InformationDataGrid Inherited InheritScope InhomogeneousPoissonProcess InitialEvaluationHistory Initialization InitializationCell InitializationCellEvaluation InitializationCellWarning InitializationObjects InitializationValue Initialize InitialSeeding InlineCounterAssignments InlineCounterIncrements InlineRules Inner InnerPolygon InnerPolyhedron Inpaint Input InputAliases InputAssumptions InputAutoReplacements InputField InputFieldBox InputFieldBoxOptions InputForm InputGrouping InputNamePacket InputNotebook InputPacket InputSettings InputStream InputString InputStringPacket InputToBoxFormPacket Insert InsertionFunction InsertionPointObject InsertLinebreaks InsertResults Inset Inset3DBox Inset3DBoxOptions InsetBox InsetBoxOptions Insphere Install InstallService InstanceNormalizationLayer InString Integer IntegerDigits IntegerExponent IntegerLength IntegerName IntegerPart IntegerPartitions IntegerQ IntegerReverse Integers IntegerString Integral Integrate Interactive InteractiveTradingChart Interlaced Interleaving InternallyBalancedDecomposition InterpolatingFunction InterpolatingPolynomial Interpolation InterpolationOrder InterpolationPoints InterpolationPrecision Interpretation InterpretationBox InterpretationBoxOptions InterpretationFunction Interpreter InterpretTemplate InterquartileRange Interrupt InterruptSettings IntersectingQ Intersection Interval IntervalIntersection IntervalMarkers IntervalMarkersStyle IntervalMemberQ IntervalSlider IntervalUnion Into Inverse InverseBetaRegularized InverseCDF InverseChiSquareDistribution InverseContinuousWaveletTransform InverseDistanceTransform InverseEllipticNomeQ InverseErf InverseErfc InverseFourier InverseFourierCosTransform InverseFourierSequenceTransform InverseFourierSinTransform InverseFourierTransform InverseFunction InverseFunctions InverseGammaDistribution InverseGammaRegularized InverseGaussianDistribution InverseGudermannian InverseHankelTransform InverseHaversine InverseImagePyramid InverseJacobiCD InverseJacobiCN InverseJacobiCS InverseJacobiDC InverseJacobiDN InverseJacobiDS InverseJacobiNC InverseJacobiND InverseJacobiNS InverseJacobiSC InverseJacobiSD InverseJacobiSN InverseLaplaceTransform InverseMellinTransform InversePermutation InverseRadon InverseRadonTransform InverseSeries InverseShortTimeFourier InverseSpectrogram InverseSurvivalFunction InverseTransformedRegion InverseWaveletTransform InverseWeierstrassP InverseWishartMatrixDistribution InverseZTransform Invisible InvisibleApplication InvisibleTimes IPAddress IrreduciblePolynomialQ IslandData IsolatingInterval IsomorphicGraphQ IsotopeData Italic Item ItemAspectRatio ItemBox ItemBoxOptions ItemSize ItemStyle ItoProcessJaccardDissimilarity JacobiAmplitude Jacobian JacobiCD JacobiCN JacobiCS JacobiDC JacobiDN JacobiDS JacobiNC JacobiND JacobiNS JacobiP JacobiSC JacobiSD JacobiSN JacobiSymbol JacobiZeta JankoGroupJ1 JankoGroupJ2 JankoGroupJ3 JankoGroupJ4 JarqueBeraALMTest JohnsonDistribution Join JoinAcross Joined JoinedCurve JoinedCurveBox JoinedCurveBoxOptions JoinForm JordanDecomposition JordanModelDecomposition JulianDate JuliaSetBoettcher JuliaSetIterationCount JuliaSetPlot JuliaSetPointsK KagiChart KaiserBesselWindow KaiserWindow KalmanEstimator KalmanFilter KarhunenLoeveDecomposition KaryTree KatzCentrality KCoreComponents KDistribution KEdgeConnectedComponents KEdgeConnectedGraphQ KelvinBei KelvinBer KelvinKei KelvinKer KendallTau KendallTauTest KernelExecute KernelFunction KernelMixtureDistribution Kernels Ket Key KeyCollisionFunction KeyComplement KeyDrop KeyDropFrom KeyExistsQ KeyFreeQ KeyIntersection KeyMap KeyMemberQ KeypointStrength Keys KeySelect KeySort KeySortBy KeyTake KeyUnion KeyValueMap KeyValuePattern Khinchin KillProcess KirchhoffGraph KirchhoffMatrix KleinInvariantJ KnapsackSolve KnightTourGraph KnotData KnownUnitQ KochCurve KolmogorovSmirnovTest KroneckerDelta KroneckerModelDecomposition KroneckerProduct KroneckerSymbol KuiperTest KumaraswamyDistribution Kurtosis KuwaharaFilter KVertexConnectedComponents KVertexConnectedGraphQLABColor Label Labeled LabeledSlider LabelingFunction LabelingSize LabelStyle LabelVisibility LaguerreL LakeData LambdaComponents LambertW LaminaData LanczosWindow LandauDistribution Language LanguageCategory LanguageData LanguageIdentify LanguageOptions LaplaceDistribution LaplaceTransform Laplacian LaplacianFilter LaplacianGaussianFilter Large Larger Last Latitude LatitudeLongitude LatticeData LatticeReduce Launch LaunchKernels LayeredGraphPlot LayerSizeFunction LayoutInformation LCHColor LCM LeaderSize LeafCount LeapYearQ LearnDistribution LearnedDistribution LearningRate LearningRateMultipliers LeastSquares LeastSquaresFilterKernel Left LeftArrow LeftArrowBar LeftArrowRightArrow LeftDownTeeVector LeftDownVector LeftDownVectorBar LeftRightArrow LeftRightVector LeftTee LeftTeeArrow LeftTeeVector LeftTriangle LeftTriangleBar LeftTriangleEqual LeftUpDownVector LeftUpTeeVector LeftUpVector LeftUpVectorBar LeftVector LeftVectorBar LegendAppearance Legended LegendFunction LegendLabel LegendLayout LegendMargins LegendMarkers LegendMarkerSize LegendreP LegendreQ LegendreType Length LengthWhile LerchPhi Less LessEqual LessEqualGreater LessEqualThan LessFullEqual LessGreater LessLess LessSlantEqual LessThan LessTilde LetterCharacter LetterCounts LetterNumber LetterQ Level LeveneTest LeviCivitaTensor LevyDistribution Lexicographic LibraryDataType LibraryFunction LibraryFunctionError LibraryFunctionInformation LibraryFunctionLoad LibraryFunctionUnload LibraryLoad LibraryUnload LicenseID LiftingFilterData LiftingWaveletTransform LightBlue LightBrown LightCyan Lighter LightGray LightGreen Lighting LightingAngle LightMagenta LightOrange LightPink LightPurple LightRed LightSources LightYellow Likelihood Limit LimitsPositioning LimitsPositioningTokens LindleyDistribution Line Line3DBox Line3DBoxOptions LinearFilter LinearFractionalOptimization LinearFractionalTransform LinearGradientImage LinearizingTransformationData LinearLayer LinearModelFit LinearOffsetFunction LinearOptimization LinearProgramming LinearRecurrence LinearSolve LinearSolveFunction LineBox LineBoxOptions LineBreak LinebreakAdjustments LineBreakChart LinebreakSemicolonWeighting LineBreakWithin LineColor LineGraph LineIndent LineIndentMaxFraction LineIntegralConvolutionPlot LineIntegralConvolutionScale LineLegend LineOpacity LineSpacing LineWrapParts LinkActivate LinkClose LinkConnect LinkConnectedQ LinkCreate LinkError LinkFlush LinkFunction LinkHost LinkInterrupt LinkLaunch LinkMode LinkObject LinkOpen LinkOptions LinkPatterns LinkProtocol LinkRankCentrality LinkRead LinkReadHeld LinkReadyQ Links LinkService LinkWrite LinkWriteHeld LiouvilleLambda List Listable ListAnimate ListContourPlot ListContourPlot3D ListConvolve ListCorrelate ListCurvePathPlot ListDeconvolve ListDensityPlot ListDensityPlot3D Listen ListFormat ListFourierSequenceTransform ListInterpolation ListLineIntegralConvolutionPlot ListLinePlot ListLogLinearPlot ListLogLogPlot ListLogPlot ListPicker ListPickerBox ListPickerBoxBackground ListPickerBoxOptions ListPlay ListPlot ListPlot3D ListPointPlot3D ListPolarPlot ListQ ListSliceContourPlot3D ListSliceDensityPlot3D ListSliceVectorPlot3D ListStepPlot ListStreamDensityPlot ListStreamPlot ListSurfacePlot3D ListVectorDensityPlot ListVectorPlot ListVectorPlot3D ListZTransform Literal LiteralSearch LocalAdaptiveBinarize LocalCache LocalClusteringCoefficient LocalizeDefinitions LocalizeVariables LocalObject LocalObjects LocalResponseNormalizationLayer LocalSubmit LocalSymbol LocalTime LocalTimeZone LocationEquivalenceTest LocationTest Locator LocatorAutoCreate LocatorBox LocatorBoxOptions LocatorCentering LocatorPane LocatorPaneBox LocatorPaneBoxOptions LocatorRegion Locked Log Log10 Log2 LogBarnesG LogGamma LogGammaDistribution LogicalExpand LogIntegral LogisticDistribution LogisticSigmoid LogitModelFit LogLikelihood LogLinearPlot LogLogisticDistribution LogLogPlot LogMultinormalDistribution LogNormalDistribution LogPlot LogRankTest LogSeriesDistribution LongEqual Longest LongestCommonSequence LongestCommonSequencePositions LongestCommonSubsequence LongestCommonSubsequencePositions LongestMatch LongestOrderedSequence LongForm Longitude LongLeftArrow LongLeftRightArrow LongRightArrow LongShortTermMemoryLayer Lookup Loopback LoopFreeGraphQ LossFunction LowerCaseQ LowerLeftArrow LowerRightArrow LowerTriangularize LowerTriangularMatrixQ LowpassFilter LQEstimatorGains LQGRegulator LQOutputRegulatorGains LQRegulatorGains LUBackSubstitution LucasL LuccioSamiComponents LUDecomposition LunarEclipse LUVColor LyapunovSolve LyonsGroupLyMachineID MachineName MachineNumberQ MachinePrecision MacintoshSystemPageSetup Magenta Magnification Magnify MailAddressValidation MailExecute MailFolder MailItem MailReceiverFunction MailResponseFunction MailSearch MailServerConnect MailServerConnection MailSettings MainSolve MaintainDynamicCaches Majority MakeBoxes MakeExpression MakeRules ManagedLibraryExpressionID ManagedLibraryExpressionQ MandelbrotSetBoettcher MandelbrotSetDistance MandelbrotSetIterationCount MandelbrotSetMemberQ MandelbrotSetPlot MangoldtLambda ManhattanDistance Manipulate Manipulator MannedSpaceMissionData MannWhitneyTest MantissaExponent Manual Map MapAll MapAt MapIndexed MAProcess MapThread MarchenkoPasturDistribution MarcumQ MardiaCombinedTest MardiaKurtosisTest MardiaSkewnessTest MarginalDistribution MarkovProcessProperties Masking MatchingDissimilarity MatchLocalNameQ MatchLocalNames MatchQ Material MathematicalFunctionData MathematicaNotation MathieuC MathieuCharacteristicA MathieuCharacteristicB MathieuCharacteristicExponent MathieuCPrime MathieuGroupM11 MathieuGroupM12 MathieuGroupM22 MathieuGroupM23 MathieuGroupM24 MathieuS MathieuSPrime MathMLForm MathMLText Matrices MatrixExp MatrixForm MatrixFunction MatrixLog MatrixNormalDistribution MatrixPlot MatrixPower MatrixPropertyDistribution MatrixQ MatrixRank MatrixTDistribution Max MaxBend MaxCellMeasure MaxColorDistance MaxDetect MaxDuration MaxExtraBandwidths MaxExtraConditions MaxFeatureDisplacement MaxFeatures MaxFilter MaximalBy Maximize MaxItems MaxIterations MaxLimit MaxMemoryUsed MaxMixtureKernels MaxOverlapFraction MaxPlotPoints MaxPoints MaxRecursion MaxStableDistribution MaxStepFraction MaxSteps MaxStepSize MaxTrainingRounds MaxValue MaxwellDistribution MaxWordGap McLaughlinGroupMcL Mean MeanAbsoluteLossLayer MeanAround MeanClusteringCoefficient MeanDegreeConnectivity MeanDeviation MeanFilter MeanGraphDistance MeanNeighborDegree MeanShift MeanShiftFilter MeanSquaredLossLayer Median MedianDeviation MedianFilter MedicalTestData Medium MeijerG MeijerGReduce MeixnerDistribution MellinConvolve MellinTransform MemberQ MemoryAvailable MemoryConstrained MemoryConstraint MemoryInUse MengerMesh Menu MenuAppearance MenuCommandKey MenuEvaluator MenuItem MenuList MenuPacket MenuSortingValue MenuStyle MenuView Merge MergeDifferences MergingFunction MersennePrimeExponent MersennePrimeExponentQ Mesh MeshCellCentroid MeshCellCount MeshCellHighlight MeshCellIndex MeshCellLabel MeshCellMarker MeshCellMeasure MeshCellQuality MeshCells MeshCellShapeFunction MeshCellStyle MeshCoordinates MeshFunctions MeshPrimitives MeshQualityGoal MeshRange MeshRefinementFunction MeshRegion MeshRegionQ MeshShading MeshStyle Message MessageDialog MessageList MessageName MessageObject MessageOptions MessagePacket Messages MessagesNotebook MetaCharacters MetaInformation MeteorShowerData Method MethodOptions MexicanHatWavelet MeyerWavelet Midpoint Min MinColorDistance MinDetect MineralData MinFilter MinimalBy MinimalPolynomial MinimalStateSpaceModel Minimize MinimumTimeIncrement MinIntervalSize MinkowskiQuestionMark MinLimit MinMax MinorPlanetData Minors MinRecursion MinSize MinStableDistribution Minus MinusPlus MinValue Missing MissingBehavior MissingDataMethod MissingDataRules MissingQ MissingString MissingStyle MissingValuePattern MittagLefflerE MixedFractionParts MixedGraphQ MixedMagnitude MixedRadix MixedRadixQuantity MixedUnit MixtureDistribution Mod Modal Mode Modular ModularInverse ModularLambda Module Modulus MoebiusMu Molecule MoleculeContainsQ MoleculeEquivalentQ MoleculeGraph MoleculeModify MoleculePattern MoleculePlot MoleculePlot3D MoleculeProperty MoleculeQ MoleculeValue Moment Momentary MomentConvert MomentEvaluate MomentGeneratingFunction MomentOfInertia Monday Monitor MonomialList MonomialOrder MonsterGroupM MoonPhase MoonPosition MorletWavelet MorphologicalBinarize MorphologicalBranchPoints MorphologicalComponents MorphologicalEulerNumber MorphologicalGraph MorphologicalPerimeter MorphologicalTransform MortalityData Most MountainData MouseAnnotation MouseAppearance MouseAppearanceTag MouseButtons Mouseover MousePointerNote MousePosition MovieData MovingAverage MovingMap MovingMedian MoyalDistribution Multicolumn MultiedgeStyle MultigraphQ MultilaunchWarning MultiLetterItalics MultiLetterStyle MultilineFunction Multinomial MultinomialDistribution MultinormalDistribution MultiplicativeOrder Multiplicity MultiplySides Multiselection MultivariateHypergeometricDistribution MultivariatePoissonDistribution MultivariateTDistributionN NakagamiDistribution NameQ Names NamespaceBox NamespaceBoxOptions Nand NArgMax NArgMin NBernoulliB NBodySimulation NBodySimulationData NCache NDEigensystem NDEigenvalues NDSolve NDSolveValue Nearest NearestFunction NearestNeighborGraph NearestTo NebulaData NeedCurrentFrontEndPackagePacket NeedCurrentFrontEndSymbolsPacket NeedlemanWunschSimilarity Needs Negative NegativeBinomialDistribution NegativeDefiniteMatrixQ NegativeIntegers NegativeMultinomialDistribution NegativeRationals NegativeReals NegativeSemidefiniteMatrixQ NeighborhoodData NeighborhoodGraph Nest NestedGreaterGreater NestedLessLess NestedScriptRules NestGraph NestList NestWhile NestWhileList NetAppend NetBidirectionalOperator NetChain NetDecoder NetDelete NetDrop NetEncoder NetEvaluationMode NetExtract NetFlatten NetFoldOperator NetGraph NetInformation NetInitialize NetInsert NetInsertSharedArrays NetJoin NetMapOperator NetMapThreadOperator NetMeasurements NetModel NetNestOperator NetPairEmbeddingOperator NetPort NetPortGradient NetPrepend NetRename NetReplace NetReplacePart NetSharedArray NetStateObject NetTake NetTrain NetTrainResultsObject NetworkPacketCapture NetworkPacketRecording NetworkPacketRecordingDuring NetworkPacketTrace NeumannValue NevilleThetaC NevilleThetaD NevilleThetaN NevilleThetaS NewPrimitiveStyle NExpectation Next NextCell NextDate NextPrime NextScheduledTaskTime NHoldAll NHoldFirst NHoldRest NicholsGridLines NicholsPlot NightHemisphere NIntegrate NMaximize NMaxValue NMinimize NMinValue NominalVariables NonAssociative NoncentralBetaDistribution NoncentralChiSquareDistribution NoncentralFRatioDistribution NoncentralStudentTDistribution NonCommutativeMultiply NonConstants NondimensionalizationTransform None NoneTrue NonlinearModelFit NonlinearStateSpaceModel NonlocalMeansFilter NonNegative NonNegativeIntegers NonNegativeRationals NonNegativeReals NonPositive NonPositiveIntegers NonPositiveRationals NonPositiveReals Nor NorlundB Norm Normal NormalDistribution NormalGrouping NormalizationLayer Normalize Normalized NormalizedSquaredEuclideanDistance NormalMatrixQ NormalsFunction NormFunction Not NotCongruent NotCupCap NotDoubleVerticalBar Notebook NotebookApply NotebookAutoSave NotebookClose NotebookConvertSettings NotebookCreate NotebookCreateReturnObject NotebookDefault NotebookDelete NotebookDirectory NotebookDynamicExpression NotebookEvaluate NotebookEventActions NotebookFileName NotebookFind NotebookFindReturnObject NotebookGet NotebookGetLayoutInformationPacket NotebookGetMisspellingsPacket NotebookImport NotebookInformation NotebookInterfaceObject NotebookLocate NotebookObject NotebookOpen NotebookOpenReturnObject NotebookPath NotebookPrint NotebookPut NotebookPutReturnObject NotebookRead NotebookResetGeneratedCells Notebooks NotebookSave NotebookSaveAs NotebookSelection NotebookSetupLayoutInformationPacket NotebooksMenu NotebookTemplate NotebookWrite NotElement NotEqualTilde NotExists NotGreater NotGreaterEqual NotGreaterFullEqual NotGreaterGreater NotGreaterLess NotGreaterSlantEqual NotGreaterTilde Nothing NotHumpDownHump NotHumpEqual NotificationFunction NotLeftTriangle NotLeftTriangleBar NotLeftTriangleEqual NotLess NotLessEqual NotLessFullEqual NotLessGreater NotLessLess NotLessSlantEqual NotLessTilde NotNestedGreaterGreater NotNestedLessLess NotPrecedes NotPrecedesEqual NotPrecedesSlantEqual NotPrecedesTilde NotReverseElement NotRightTriangle NotRightTriangleBar NotRightTriangleEqual NotSquareSubset NotSquareSubsetEqual NotSquareSuperset NotSquareSupersetEqual NotSubset NotSubsetEqual NotSucceeds NotSucceedsEqual NotSucceedsSlantEqual NotSucceedsTilde NotSuperset NotSupersetEqual NotTilde NotTildeEqual NotTildeFullEqual NotTildeTilde NotVerticalBar Now NoWhitespace NProbability NProduct NProductFactors NRoots NSolve NSum NSumTerms NuclearExplosionData NuclearReactorData Null NullRecords NullSpace NullWords Number NumberCompose NumberDecompose NumberExpand NumberFieldClassNumber NumberFieldDiscriminant NumberFieldFundamentalUnits NumberFieldIntegralBasis NumberFieldNormRepresentatives NumberFieldRegulator NumberFieldRootsOfUnity NumberFieldSignature NumberForm NumberFormat NumberLinePlot NumberMarks NumberMultiplier NumberPadding NumberPoint NumberQ NumberSeparator NumberSigns NumberString Numerator NumeratorDenominator NumericalOrder NumericalSort NumericArray NumericArrayQ NumericArrayType NumericFunction NumericQ NuttallWindow NValues NyquistGridLines NyquistPlotO ObservabilityGramian ObservabilityMatrix ObservableDecomposition ObservableModelQ OceanData Octahedron OddQ Off Offset OLEData On ONanGroupON Once OneIdentity Opacity OpacityFunction OpacityFunctionScaling Open OpenAppend Opener OpenerBox OpenerBoxOptions OpenerView OpenFunctionInspectorPacket Opening OpenRead OpenSpecialOptions OpenTemporary OpenWrite Operate OperatingSystem OptimumFlowData Optional OptionalElement OptionInspectorSettings OptionQ Options OptionsPacket OptionsPattern OptionValue OptionValueBox OptionValueBoxOptions Or Orange Order OrderDistribution OrderedQ Ordering OrderingBy OrderingLayer Orderless OrderlessPatternSequence OrnsteinUhlenbeckProcess Orthogonalize OrthogonalMatrixQ Out Outer OuterPolygon OuterPolyhedron OutputAutoOverwrite OutputControllabilityMatrix OutputControllableModelQ OutputForm OutputFormData OutputGrouping OutputMathEditExpression OutputNamePacket OutputResponse OutputSizeLimit OutputStream Over OverBar OverDot Overflow OverHat Overlaps Overlay OverlayBox OverlayBoxOptions Overscript OverscriptBox OverscriptBoxOptions OverTilde OverVector OverwriteTarget OwenT OwnValuesPackage PackingMethod PaddedForm Padding PaddingLayer PaddingSize PadeApproximant PadLeft PadRight PageBreakAbove PageBreakBelow PageBreakWithin PageFooterLines PageFooters PageHeaderLines PageHeaders PageHeight PageRankCentrality PageTheme PageWidth Pagination PairedBarChart PairedHistogram PairedSmoothHistogram PairedTTest PairedZTest PaletteNotebook PalettePath PalindromeQ Pane PaneBox PaneBoxOptions Panel PanelBox PanelBoxOptions Paneled PaneSelector PaneSelectorBox PaneSelectorBoxOptions PaperWidth ParabolicCylinderD ParagraphIndent ParagraphSpacing ParallelArray ParallelCombine ParallelDo Parallelepiped ParallelEvaluate Parallelization Parallelize ParallelMap ParallelNeeds Parallelogram ParallelProduct ParallelSubmit ParallelSum ParallelTable ParallelTry Parameter ParameterEstimator ParameterMixtureDistribution ParameterVariables ParametricFunction ParametricNDSolve ParametricNDSolveValue ParametricPlot ParametricPlot3D ParametricRegion ParentBox ParentCell ParentConnect ParentDirectory ParentForm Parenthesize ParentList ParentNotebook ParetoDistribution ParetoPickandsDistribution ParkData Part PartBehavior PartialCorrelationFunction PartialD ParticleAcceleratorData ParticleData Partition PartitionGranularity PartitionsP PartitionsQ PartLayer PartOfSpeech PartProtection ParzenWindow PascalDistribution PassEventsDown PassEventsUp Paste PasteAutoQuoteCharacters PasteBoxFormInlineCells PasteButton Path PathGraph PathGraphQ Pattern PatternSequence PatternTest PauliMatrix PaulWavelet Pause PausedTime PDF PeakDetect PeanoCurve PearsonChiSquareTest PearsonCorrelationTest PearsonDistribution PercentForm PerfectNumber PerfectNumberQ PerformanceGoal Perimeter PeriodicBoundaryCondition PeriodicInterpolation Periodogram PeriodogramArray Permanent Permissions PermissionsGroup PermissionsGroupMemberQ PermissionsGroups PermissionsKey PermissionsKeys PermutationCycles PermutationCyclesQ PermutationGroup PermutationLength PermutationList PermutationListQ PermutationMax PermutationMin PermutationOrder PermutationPower PermutationProduct PermutationReplace Permutations PermutationSupport Permute PeronaMalikFilter Perpendicular PerpendicularBisector PersistenceLocation PersistenceTime PersistentObject PersistentObjects PersistentValue PersonData PERTDistribution PetersenGraph PhaseMargins PhaseRange PhysicalSystemData Pi Pick PIDData PIDDerivativeFilter PIDFeedforward PIDTune Piecewise PiecewiseExpand PieChart PieChart3D PillaiTrace PillaiTraceTest PingTime Pink PitchRecognize Pivoting PixelConstrained PixelValue PixelValuePositions Placed Placeholder PlaceholderReplace Plain PlanarAngle PlanarGraph PlanarGraphQ PlanckRadiationLaw PlaneCurveData PlanetaryMoonData PlanetData PlantData Play PlayRange Plot Plot3D Plot3Matrix PlotDivision PlotJoined PlotLabel PlotLabels PlotLayout PlotLegends PlotMarkers PlotPoints PlotRange PlotRangeClipping PlotRangeClipPlanesStyle PlotRangePadding PlotRegion PlotStyle PlotTheme Pluralize Plus PlusMinus Pochhammer PodStates PodWidth Point Point3DBox Point3DBoxOptions PointBox PointBoxOptions PointFigureChart PointLegend PointSize PoissonConsulDistribution PoissonDistribution PoissonProcess PoissonWindow PolarAxes PolarAxesOrigin PolarGridLines PolarPlot PolarTicks PoleZeroMarkers PolyaAeppliDistribution PolyGamma Polygon Polygon3DBox Polygon3DBoxOptions PolygonalNumber PolygonAngle PolygonBox PolygonBoxOptions PolygonCoordinates PolygonDecomposition PolygonHoleScale PolygonIntersections PolygonScale Polyhedron PolyhedronAngle PolyhedronCoordinates PolyhedronData PolyhedronDecomposition PolyhedronGenus PolyLog PolynomialExtendedGCD PolynomialForm PolynomialGCD PolynomialLCM PolynomialMod PolynomialQ PolynomialQuotient PolynomialQuotientRemainder PolynomialReduce PolynomialRemainder Polynomials PoolingLayer PopupMenu PopupMenuBox PopupMenuBoxOptions PopupView PopupWindow Position PositionIndex Positive PositiveDefiniteMatrixQ PositiveIntegers PositiveRationals PositiveReals PositiveSemidefiniteMatrixQ PossibleZeroQ Postfix PostScript Power PowerDistribution PowerExpand PowerMod PowerModList PowerRange PowerSpectralDensity PowersRepresentations PowerSymmetricPolynomial Precedence PrecedenceForm Precedes PrecedesEqual PrecedesSlantEqual PrecedesTilde Precision PrecisionGoal PreDecrement Predict PredictionRoot PredictorFunction PredictorInformation PredictorMeasurements PredictorMeasurementsObject PreemptProtect PreferencesPath Prefix PreIncrement Prepend PrependLayer PrependTo PreprocessingRules PreserveColor PreserveImageOptions Previous PreviousCell PreviousDate PriceGraphDistribution PrimaryPlaceholder Prime PrimeNu PrimeOmega PrimePi PrimePowerQ PrimeQ Primes PrimeZetaP PrimitivePolynomialQ PrimitiveRoot PrimitiveRootList PrincipalComponents PrincipalValue Print PrintableASCIIQ PrintAction PrintForm PrintingCopies PrintingOptions PrintingPageRange PrintingStartingPageNumber PrintingStyleEnvironment Printout3D Printout3DPreviewer PrintPrecision 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RangeSpecification RankedMax RankedMin RarerProbability Raster Raster3D Raster3DBox Raster3DBoxOptions RasterArray RasterBox RasterBoxOptions Rasterize RasterSize Rational RationalFunctions Rationalize Rationals Ratios RawArray RawBoxes RawData RawMedium RayleighDistribution Re Read ReadByteArray ReadLine ReadList ReadProtected ReadString Real RealAbs RealBlockDiagonalForm RealDigits RealExponent Reals RealSign Reap RecognitionPrior RecognitionThreshold Record RecordLists RecordSeparators Rectangle RectangleBox RectangleBoxOptions RectangleChart RectangleChart3D RectangularRepeatingElement RecurrenceFilter RecurrenceTable RecurringDigitsForm Red Reduce RefBox ReferenceLineStyle ReferenceMarkers ReferenceMarkerStyle Refine ReflectionMatrix ReflectionTransform Refresh RefreshRate Region RegionBinarize RegionBoundary RegionBounds RegionCentroid RegionDifference RegionDimension RegionDisjoint RegionDistance RegionDistanceFunction RegionEmbeddingDimension RegionEqual RegionFunction RegionImage RegionIntersection RegionMeasure RegionMember RegionMemberFunction RegionMoment RegionNearest RegionNearestFunction RegionPlot RegionPlot3D RegionProduct RegionQ RegionResize RegionSize RegionSymmetricDifference RegionUnion RegionWithin RegisterExternalEvaluator RegularExpression Regularization RegularlySampledQ RegularPolygon ReIm ReImLabels ReImPlot ReImStyle Reinstall RelationalDatabase RelationGraph Release ReleaseHold ReliabilityDistribution ReliefImage ReliefPlot RemoteAuthorizationCaching RemoteConnect RemoteConnectionObject RemoteFile RemoteRun RemoteRunProcess Remove RemoveAlphaChannel RemoveAsynchronousTask RemoveAudioStream RemoveBackground RemoveChannelListener RemoveChannelSubscribers Removed RemoveDiacritics RemoveInputStreamMethod RemoveOutputStreamMethod RemoveProperty RemoveScheduledTask RemoveUsers RenameDirectory RenameFile RenderAll RenderingOptions RenewalProcess RenkoChart RepairMesh Repeated RepeatedNull RepeatedString RepeatedTiming RepeatingElement Replace ReplaceAll ReplaceHeldPart ReplaceImageValue ReplaceList ReplacePart ReplacePixelValue ReplaceRepeated ReplicateLayer RequiredPhysicalQuantities Resampling ResamplingAlgorithmData ResamplingMethod Rescale RescalingTransform ResetDirectory ResetMenusPacket ResetScheduledTask ReshapeLayer Residue ResizeLayer Resolve ResourceAcquire ResourceData ResourceFunction ResourceObject ResourceRegister ResourceRemove ResourceSearch ResourceSubmissionObject ResourceSubmit ResourceSystemBase ResourceUpdate ResponseForm Rest RestartInterval Restricted Resultant ResumePacket Return ReturnEntersInput ReturnExpressionPacket ReturnInputFormPacket ReturnPacket ReturnReceiptFunction ReturnTextPacket Reverse ReverseBiorthogonalSplineWavelet ReverseElement ReverseEquilibrium ReverseGraph ReverseSort ReverseSortBy ReverseUpEquilibrium RevolutionAxis RevolutionPlot3D RGBColor RiccatiSolve RiceDistribution RidgeFilter RiemannR RiemannSiegelTheta RiemannSiegelZ RiemannXi Riffle Right RightArrow RightArrowBar RightArrowLeftArrow RightComposition RightCosetRepresentative RightDownTeeVector RightDownVector RightDownVectorBar RightTee RightTeeArrow RightTeeVector RightTriangle RightTriangleBar RightTriangleEqual RightUpDownVector RightUpTeeVector RightUpVector RightUpVectorBar RightVector RightVectorBar RiskAchievementImportance RiskReductionImportance RogersTanimotoDissimilarity RollPitchYawAngles RollPitchYawMatrix RomanNumeral Root RootApproximant RootIntervals RootLocusPlot RootMeanSquare RootOfUnityQ RootReduce Roots RootSum Rotate RotateLabel RotateLeft RotateRight RotationAction RotationBox RotationBoxOptions RotationMatrix RotationTransform Round RoundImplies RoundingRadius Row RowAlignments RowBackgrounds RowBox RowHeights RowLines RowMinHeight RowReduce RowsEqual RowSpacings RSolve RSolveValue RudinShapiro RudvalisGroupRu Rule RuleCondition RuleDelayed RuleForm RulePlot RulerUnits Run RunProcess RunScheduledTask RunThrough RuntimeAttributes RuntimeOptions RussellRaoDissimilaritySameQ SameTest SampledEntityClass SampleDepth SampledSoundFunction SampledSoundList SampleRate SamplingPeriod SARIMAProcess SARMAProcess SASTriangle SatelliteData SatisfiabilityCount SatisfiabilityInstances SatisfiableQ Saturday Save Saveable SaveAutoDelete SaveConnection SaveDefinitions SavitzkyGolayMatrix SawtoothWave Scale Scaled ScaleDivisions ScaledMousePosition ScaleOrigin ScalePadding ScaleRanges ScaleRangeStyle ScalingFunctions ScalingMatrix ScalingTransform Scan ScheduledTask ScheduledTaskActiveQ ScheduledTaskInformation ScheduledTaskInformationData ScheduledTaskObject ScheduledTasks SchurDecomposition ScientificForm ScientificNotationThreshold ScorerGi ScorerGiPrime ScorerHi ScorerHiPrime ScreenRectangle ScreenStyleEnvironment ScriptBaselineShifts ScriptForm ScriptLevel ScriptMinSize ScriptRules ScriptSizeMultipliers Scrollbars ScrollingOptions ScrollPosition SearchAdjustment SearchIndexObject SearchIndices SearchQueryString SearchResultObject Sec Sech 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SequenceSplit Series SeriesCoefficient SeriesData ServiceConnect ServiceDisconnect ServiceExecute ServiceObject ServiceRequest ServiceResponse ServiceSubmit SessionSubmit SessionTime Set SetAccuracy SetAlphaChannel SetAttributes Setbacks SetBoxFormNamesPacket SetCloudDirectory SetCookies SetDelayed SetDirectory SetEnvironment SetEvaluationNotebook SetFileDate SetFileLoadingContext SetNotebookStatusLine SetOptions SetOptionsPacket SetPermissions SetPrecision SetProperty SetSecuredAuthenticationKey SetSelectedNotebook SetSharedFunction SetSharedVariable SetSpeechParametersPacket SetStreamPosition SetSystemModel SetSystemOptions Setter SetterBar SetterBox SetterBoxOptions Setting SetUsers SetValue Shading Shallow ShannonWavelet ShapiroWilkTest Share SharingList Sharpen ShearingMatrix ShearingTransform ShellRegion ShenCastanMatrix ShiftedGompertzDistribution ShiftRegisterSequence Short ShortDownArrow Shortest ShortestMatch ShortestPathFunction ShortLeftArrow ShortRightArrow 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SkinStyle Skip SliceContourPlot3D SliceDensityPlot3D SliceDistribution SliceVectorPlot3D Slider Slider2D Slider2DBox Slider2DBoxOptions SliderBox SliderBoxOptions SlideView Slot SlotSequence Small SmallCircle Smaller SmithDecomposition SmithDelayCompensator SmithWatermanSimilarity SmoothDensityHistogram SmoothHistogram SmoothHistogram3D SmoothKernelDistribution SnDispersion Snippet SnubPolyhedron SocialMediaData Socket SocketConnect SocketListen SocketListener SocketObject SocketOpen SocketReadMessage SocketReadyQ Sockets SocketWaitAll SocketWaitNext SoftmaxLayer SokalSneathDissimilarity SolarEclipse SolarSystemFeatureData SolidAngle SolidData SolidRegionQ Solve SolveAlways SolveDelayed Sort SortBy SortedBy SortedEntityClass Sound SoundAndGraphics SoundNote SoundVolume SourceLink Sow Space SpaceCurveData SpaceForm Spacer Spacings Span SpanAdjustments SpanCharacterRounding SpanFromAbove SpanFromBoth SpanFromLeft SpanLineThickness SpanMaxSize SpanMinSize SpanningCharacters SpanSymmetric SparseArray SpatialGraphDistribution SpatialMedian SpatialTransformationLayer Speak SpeakTextPacket SpearmanRankTest SpearmanRho SpeciesData SpecificityGoal SpectralLineData Spectrogram SpectrogramArray Specularity SpeechRecognize SpeechSynthesize SpellingCorrection SpellingCorrectionList SpellingDictionaries SpellingDictionariesPath SpellingOptions SpellingSuggestionsPacket Sphere SphereBox SpherePoints SphericalBesselJ SphericalBesselY SphericalHankelH1 SphericalHankelH2 SphericalHarmonicY SphericalPlot3D SphericalRegion SphericalShell SpheroidalEigenvalue SpheroidalJoiningFactor SpheroidalPS SpheroidalPSPrime SpheroidalQS SpheroidalQSPrime SpheroidalRadialFactor SpheroidalS1 SpheroidalS1Prime SpheroidalS2 SpheroidalS2Prime Splice SplicedDistribution SplineClosed SplineDegree SplineKnots SplineWeights Split SplitBy SpokenString Sqrt SqrtBox SqrtBoxOptions Square SquaredEuclideanDistance SquareFreeQ SquareIntersection SquareMatrixQ SquareRepeatingElement SquaresR SquareSubset 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WronskianXMLElement XMLObject XMLTemplate Xnor Xor XYZColorYellow Yesterday YuleDissimilarityZernikeR ZeroSymmetric ZeroTest ZeroWidthTimes Zeta ZetaZero ZIPCodeData ZipfDistribution ZoomCenter ZoomFactor ZTest ZTransform$Aborted $ActivationGroupID $ActivationKey $ActivationUserRegistered $AddOnsDirectory $AllowExternalChannelFunctions $AssertFunction $Assumptions $AsynchronousTask $AudioInputDevices $AudioOutputDevices $BaseDirectory $BatchInput $BatchOutput $BlockchainBase $BoxForms $ByteOrdering $CacheBaseDirectory $Canceled $ChannelBase $CharacterEncoding $CharacterEncodings $CloudBase $CloudConnected $CloudCreditsAvailable $CloudEvaluation $CloudExpressionBase $CloudObjectNameFormat $CloudObjectURLType $CloudRootDirectory $CloudSymbolBase $CloudUserID $CloudUserUUID $CloudVersion $CloudVersionNumber $CloudWolframEngineVersionNumber $CommandLine $CompilationTarget $ConditionHold $ConfiguredKernels $Context $ContextPath $ControlActiveSetting $Cookies $CookieStore $CreationDate $CurrentLink $CurrentTask $CurrentWebSession $DateStringFormat $DefaultAudioInputDevice $DefaultAudioOutputDevice $DefaultFont $DefaultFrontEnd $DefaultImagingDevice $DefaultLocalBase $DefaultMailbox $DefaultNetworkInterface $DefaultPath $Display $DisplayFunction $DistributedContexts $DynamicEvaluation $Echo $EmbedCodeEnvironments $EmbeddableServices $EntityStores $Epilog $EvaluationCloudBase $EvaluationCloudObject $EvaluationEnvironment $ExportFormats $Failed $FinancialDataSource $FontFamilies $FormatType $FrontEnd $FrontEndSession $GeoEntityTypes $GeoLocation $GeoLocationCity $GeoLocationCountry $GeoLocationPrecision $GeoLocationSource $HistoryLength $HomeDirectory $HTMLExportRules $HTTPCookies $HTTPRequest $IgnoreEOF $ImageFormattingWidth $ImagingDevice $ImagingDevices $ImportFormats $IncomingMailSettings $InitialDirectory $Initialization $InitializationContexts $Input $InputFileName $InputStreamMethods $Inspector $InstallationDate $InstallationDirectory $InterfaceEnvironment 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part_type_colour_rgb part_type_colour_hsv part_type_color1 part_type_color2 part_type_color3 part_type_color_mix part_type_color_rgb part_type_color_hsv part_type_alpha1 part_type_alpha2 part_type_alpha3 part_type_blend part_system_create part_system_create_layer part_system_destroy part_system_exists part_system_clear part_system_draw_order part_system_depth part_system_position part_system_automatic_update part_system_automatic_draw part_system_update part_system_drawit part_system_get_layer part_system_layer part_particles_create part_particles_create_colour part_particles_create_color part_particles_clear part_particles_count part_emitter_create part_emitter_destroy part_emitter_destroy_all part_emitter_exists part_emitter_clear part_emitter_region part_emitter_burst part_emitter_stream external_call external_define external_free window_handle window_device matrix_get matrix_set matrix_build_identity matrix_build matrix_build_lookat matrix_build_projection_ortho matrix_build_projection_perspective matrix_build_projection_perspective_fov matrix_multiply matrix_transform_vertex matrix_stack_push matrix_stack_pop matrix_stack_multiply matrix_stack_set matrix_stack_clear matrix_stack_top matrix_stack_is_empty browser_input_capture os_get_config os_get_info os_get_language os_get_region os_lock_orientation display_get_dpi_x display_get_dpi_y display_set_gui_size display_set_gui_maximise display_set_gui_maximize device_mouse_dbclick_enable display_set_timing_method display_get_timing_method display_set_sleep_margin display_get_sleep_margin virtual_key_add virtual_key_hide virtual_key_delete virtual_key_show draw_enable_drawevent draw_enable_swf_aa draw_set_swf_aa_level draw_get_swf_aa_level draw_texture_flush draw_flush gpu_set_blendenable gpu_set_ztestenable gpu_set_zfunc gpu_set_zwriteenable gpu_set_lightingenable gpu_set_fog gpu_set_cullmode gpu_set_blendmode gpu_set_blendmode_ext gpu_set_blendmode_ext_sepalpha gpu_set_colorwriteenable gpu_set_colourwriteenable gpu_set_alphatestenable gpu_set_alphatestref gpu_set_alphatestfunc gpu_set_texfilter gpu_set_texfilter_ext gpu_set_texrepeat gpu_set_texrepeat_ext gpu_set_tex_filter gpu_set_tex_filter_ext gpu_set_tex_repeat gpu_set_tex_repeat_ext gpu_set_tex_mip_filter gpu_set_tex_mip_filter_ext gpu_set_tex_mip_bias gpu_set_tex_mip_bias_ext gpu_set_tex_min_mip gpu_set_tex_min_mip_ext gpu_set_tex_max_mip gpu_set_tex_max_mip_ext gpu_set_tex_max_aniso gpu_set_tex_max_aniso_ext gpu_set_tex_mip_enable gpu_set_tex_mip_enable_ext gpu_get_blendenable gpu_get_ztestenable gpu_get_zfunc gpu_get_zwriteenable gpu_get_lightingenable gpu_get_fog gpu_get_cullmode gpu_get_blendmode gpu_get_blendmode_ext gpu_get_blendmode_ext_sepalpha gpu_get_blendmode_src gpu_get_blendmode_dest gpu_get_blendmode_srcalpha gpu_get_blendmode_destalpha gpu_get_colorwriteenable gpu_get_colourwriteenable gpu_get_alphatestenable gpu_get_alphatestref gpu_get_alphatestfunc gpu_get_texfilter gpu_get_texfilter_ext gpu_get_texrepeat gpu_get_texrepeat_ext gpu_get_tex_filter gpu_get_tex_filter_ext gpu_get_tex_repeat gpu_get_tex_repeat_ext gpu_get_tex_mip_filter gpu_get_tex_mip_filter_ext gpu_get_tex_mip_bias gpu_get_tex_mip_bias_ext gpu_get_tex_min_mip gpu_get_tex_min_mip_ext gpu_get_tex_max_mip gpu_get_tex_max_mip_ext gpu_get_tex_max_aniso gpu_get_tex_max_aniso_ext gpu_get_tex_mip_enable gpu_get_tex_mip_enable_ext gpu_push_state gpu_pop_state gpu_get_state gpu_set_state draw_light_define_ambient draw_light_define_direction draw_light_define_point draw_light_enable draw_set_lighting draw_light_get_ambient draw_light_get draw_get_lighting shop_leave_rating url_get_domain url_open url_open_ext url_open_full get_timer achievement_login achievement_logout achievement_post achievement_increment achievement_post_score achievement_available achievement_show_achievements achievement_show_leaderboards achievement_load_friends achievement_load_leaderboard achievement_send_challenge achievement_load_progress achievement_reset achievement_login_status achievement_get_pic achievement_show_challenge_notifications achievement_get_challenges achievement_event achievement_show achievement_get_info cloud_file_save cloud_string_save cloud_synchronise ads_enable ads_disable ads_setup ads_engagement_launch ads_engagement_available ads_engagement_active ads_event ads_event_preload ads_set_reward_callback ads_get_display_height ads_get_display_width ads_move ads_interstitial_available ads_interstitial_display device_get_tilt_x device_get_tilt_y device_get_tilt_z device_is_keypad_open device_mouse_check_button device_mouse_check_button_pressed device_mouse_check_button_released device_mouse_x device_mouse_y device_mouse_raw_x device_mouse_raw_y device_mouse_x_to_gui device_mouse_y_to_gui iap_activate iap_status iap_enumerate_products iap_restore_all iap_acquire iap_consume iap_product_details iap_purchase_details facebook_init facebook_login facebook_status facebook_graph_request facebook_dialog facebook_logout facebook_launch_offerwall facebook_post_message facebook_send_invite facebook_user_id facebook_accesstoken facebook_check_permission facebook_request_read_permissions facebook_request_publish_permissions gamepad_is_supported gamepad_get_device_count gamepad_is_connected gamepad_get_description gamepad_get_button_threshold gamepad_set_button_threshold gamepad_get_axis_deadzone gamepad_set_axis_deadzone gamepad_button_count gamepad_button_check gamepad_button_check_pressed gamepad_button_check_released gamepad_button_value gamepad_axis_count gamepad_axis_value gamepad_set_vibration gamepad_set_colour gamepad_set_color os_is_paused window_has_focus code_is_compiled http_get http_get_file http_post_string http_request json_encode json_decode zip_unzip load_csv base64_encode base64_decode md5_string_unicode md5_string_utf8 md5_file os_is_network_connected sha1_string_unicode sha1_string_utf8 sha1_file os_powersave_enable analytics_event analytics_event_ext win8_livetile_tile_notification win8_livetile_tile_clear win8_livetile_badge_notification win8_livetile_badge_clear win8_livetile_queue_enable win8_secondarytile_pin win8_secondarytile_badge_notification win8_secondarytile_delete win8_livetile_notification_begin win8_livetile_notification_secondary_begin win8_livetile_notification_expiry win8_livetile_notification_tag win8_livetile_notification_text_add win8_livetile_notification_image_add win8_livetile_notification_end win8_appbar_enable win8_appbar_add_element win8_appbar_remove_element win8_settingscharm_add_entry win8_settingscharm_add_html_entry win8_settingscharm_add_xaml_entry win8_settingscharm_set_xaml_property win8_settingscharm_get_xaml_property win8_settingscharm_remove_entry win8_share_image win8_share_screenshot win8_share_file win8_share_url win8_share_text win8_search_enable win8_search_disable win8_search_add_suggestions win8_device_touchscreen_available win8_license_initialize_sandbox win8_license_trial_version winphone_license_trial_version winphone_tile_title winphone_tile_count winphone_tile_back_title winphone_tile_back_content winphone_tile_back_content_wide winphone_tile_front_image winphone_tile_front_image_small winphone_tile_front_image_wide winphone_tile_back_image winphone_tile_back_image_wide winphone_tile_background_colour winphone_tile_background_color winphone_tile_icon_image winphone_tile_small_icon_image winphone_tile_wide_content winphone_tile_cycle_images winphone_tile_small_background_image physics_world_create physics_world_gravity physics_world_update_speed physics_world_update_iterations physics_world_draw_debug physics_pause_enable physics_fixture_create physics_fixture_set_kinematic physics_fixture_set_density physics_fixture_set_awake physics_fixture_set_restitution physics_fixture_set_friction physics_fixture_set_collision_group physics_fixture_set_sensor physics_fixture_set_linear_damping physics_fixture_set_angular_damping physics_fixture_set_circle_shape physics_fixture_set_box_shape physics_fixture_set_edge_shape physics_fixture_set_polygon_shape physics_fixture_set_chain_shape physics_fixture_add_point physics_fixture_bind physics_fixture_bind_ext physics_fixture_delete physics_apply_force physics_apply_impulse physics_apply_angular_impulse physics_apply_local_force physics_apply_local_impulse physics_apply_torque physics_mass_properties physics_draw_debug physics_test_overlap physics_remove_fixture physics_set_friction physics_set_density physics_set_restitution physics_get_friction physics_get_density physics_get_restitution physics_joint_distance_create physics_joint_rope_create physics_joint_revolute_create physics_joint_prismatic_create physics_joint_pulley_create physics_joint_wheel_create physics_joint_weld_create physics_joint_friction_create physics_joint_gear_create physics_joint_enable_motor physics_joint_get_value physics_joint_set_value physics_joint_delete physics_particle_create physics_particle_delete physics_particle_delete_region_circle physics_particle_delete_region_box physics_particle_delete_region_poly physics_particle_set_flags physics_particle_set_category_flags physics_particle_draw physics_particle_draw_ext physics_particle_count physics_particle_get_data physics_particle_get_data_particle physics_particle_group_begin physics_particle_group_circle physics_particle_group_box physics_particle_group_polygon physics_particle_group_add_point physics_particle_group_end physics_particle_group_join physics_particle_group_delete physics_particle_group_count physics_particle_group_get_data physics_particle_group_get_mass physics_particle_group_get_inertia physics_particle_group_get_centre_x physics_particle_group_get_centre_y physics_particle_group_get_vel_x physics_particle_group_get_vel_y physics_particle_group_get_ang_vel physics_particle_group_get_x physics_particle_group_get_y physics_particle_group_get_angle physics_particle_set_group_flags physics_particle_get_group_flags physics_particle_get_max_count physics_particle_get_radius physics_particle_get_density physics_particle_get_damping physics_particle_get_gravity_scale physics_particle_set_max_count physics_particle_set_radius physics_particle_set_density physics_particle_set_damping physics_particle_set_gravity_scale network_create_socket network_create_socket_ext network_create_server network_create_server_raw network_connect network_connect_raw network_send_packet network_send_raw network_send_broadcast network_send_udp network_send_udp_raw network_set_timeout network_set_config network_resolve network_destroy buffer_create buffer_write buffer_read buffer_seek buffer_get_surface buffer_set_surface buffer_delete buffer_exists buffer_get_type buffer_get_alignment buffer_poke buffer_peek buffer_save buffer_save_ext buffer_load buffer_load_ext buffer_load_partial buffer_copy buffer_fill buffer_get_size buffer_tell buffer_resize buffer_md5 buffer_sha1 buffer_base64_encode buffer_base64_decode buffer_base64_decode_ext buffer_sizeof buffer_get_address buffer_create_from_vertex_buffer buffer_create_from_vertex_buffer_ext buffer_copy_from_vertex_buffer buffer_async_group_begin buffer_async_group_option buffer_async_group_end buffer_load_async buffer_save_async gml_release_mode gml_pragma steam_activate_overlay steam_is_overlay_enabled steam_is_overlay_activated steam_get_persona_name steam_initialised steam_is_cloud_enabled_for_app steam_is_cloud_enabled_for_account steam_file_persisted steam_get_quota_total steam_get_quota_free steam_file_write steam_file_write_file steam_file_read steam_file_delete steam_file_exists steam_file_size steam_file_share steam_is_screenshot_requested steam_send_screenshot steam_is_user_logged_on steam_get_user_steam_id steam_user_owns_dlc steam_user_installed_dlc steam_set_achievement steam_get_achievement steam_clear_achievement steam_set_stat_int steam_set_stat_float steam_set_stat_avg_rate steam_get_stat_int steam_get_stat_float steam_get_stat_avg_rate steam_reset_all_stats steam_reset_all_stats_achievements steam_stats_ready steam_create_leaderboard steam_upload_score steam_upload_score_ext steam_download_scores_around_user steam_download_scores steam_download_friends_scores steam_upload_score_buffer steam_upload_score_buffer_ext steam_current_game_language steam_available_languages steam_activate_overlay_browser steam_activate_overlay_user steam_activate_overlay_store steam_get_user_persona_name steam_get_app_id steam_get_user_account_id steam_ugc_download steam_ugc_create_item steam_ugc_start_item_update steam_ugc_set_item_title steam_ugc_set_item_description steam_ugc_set_item_visibility steam_ugc_set_item_tags steam_ugc_set_item_content steam_ugc_set_item_preview steam_ugc_submit_item_update steam_ugc_get_item_update_progress steam_ugc_subscribe_item steam_ugc_unsubscribe_item steam_ugc_num_subscribed_items steam_ugc_get_subscribed_items steam_ugc_get_item_install_info steam_ugc_get_item_update_info steam_ugc_request_item_details steam_ugc_create_query_user steam_ugc_create_query_user_ex steam_ugc_create_query_all steam_ugc_create_query_all_ex steam_ugc_query_set_cloud_filename_filter steam_ugc_query_set_match_any_tag steam_ugc_query_set_search_text steam_ugc_query_set_ranked_by_trend_days steam_ugc_query_add_required_tag steam_ugc_query_add_excluded_tag steam_ugc_query_set_return_long_description steam_ugc_query_set_return_total_only steam_ugc_query_set_allow_cached_response steam_ugc_send_query shader_set shader_get_name shader_reset shader_current shader_is_compiled shader_get_sampler_index shader_get_uniform shader_set_uniform_i shader_set_uniform_i_array shader_set_uniform_f shader_set_uniform_f_array shader_set_uniform_matrix shader_set_uniform_matrix_array shader_enable_corner_id texture_set_stage texture_get_texel_width texture_get_texel_height shaders_are_supported vertex_format_begin vertex_format_end vertex_format_delete vertex_format_add_position vertex_format_add_position_3d vertex_format_add_colour vertex_format_add_color vertex_format_add_normal vertex_format_add_texcoord vertex_format_add_textcoord vertex_format_add_custom vertex_create_buffer vertex_create_buffer_ext vertex_delete_buffer vertex_begin vertex_end vertex_position vertex_position_3d vertex_colour vertex_color vertex_argb vertex_texcoord vertex_normal vertex_float1 vertex_float2 vertex_float3 vertex_float4 vertex_ubyte4 vertex_submit vertex_freeze vertex_get_number vertex_get_buffer_size vertex_create_buffer_from_buffer vertex_create_buffer_from_buffer_ext push_local_notification push_get_first_local_notification push_get_next_local_notification push_cancel_local_notification skeleton_animation_set skeleton_animation_get skeleton_animation_mix skeleton_animation_set_ext skeleton_animation_get_ext skeleton_animation_get_duration skeleton_animation_get_frames skeleton_animation_clear skeleton_skin_set skeleton_skin_get skeleton_attachment_set skeleton_attachment_get skeleton_attachment_create skeleton_collision_draw_set skeleton_bone_data_get skeleton_bone_data_set skeleton_bone_state_get skeleton_bone_state_set skeleton_get_minmax skeleton_get_num_bounds skeleton_get_bounds skeleton_animation_get_frame skeleton_animation_set_frame draw_skeleton draw_skeleton_time draw_skeleton_instance draw_skeleton_collision skeleton_animation_list skeleton_skin_list skeleton_slot_data layer_get_id layer_get_id_at_depth layer_get_depth layer_create layer_destroy layer_destroy_instances layer_add_instance layer_has_instance layer_set_visible layer_get_visible layer_exists layer_x layer_y layer_get_x layer_get_y layer_hspeed layer_vspeed layer_get_hspeed layer_get_vspeed layer_script_begin layer_script_end layer_shader layer_get_script_begin layer_get_script_end layer_get_shader layer_set_target_room layer_get_target_room layer_reset_target_room layer_get_all layer_get_all_elements layer_get_name layer_depth layer_get_element_layer layer_get_element_type layer_element_move layer_force_draw_depth layer_is_draw_depth_forced layer_get_forced_depth layer_background_get_id layer_background_exists layer_background_create layer_background_destroy layer_background_visible layer_background_change layer_background_sprite layer_background_htiled layer_background_vtiled layer_background_stretch layer_background_yscale layer_background_xscale layer_background_blend layer_background_alpha layer_background_index layer_background_speed layer_background_get_visible layer_background_get_sprite layer_background_get_htiled layer_background_get_vtiled layer_background_get_stretch layer_background_get_yscale layer_background_get_xscale layer_background_get_blend layer_background_get_alpha layer_background_get_index layer_background_get_speed layer_sprite_get_id layer_sprite_exists layer_sprite_create layer_sprite_destroy layer_sprite_change layer_sprite_index layer_sprite_speed layer_sprite_xscale layer_sprite_yscale layer_sprite_angle layer_sprite_blend layer_sprite_alpha layer_sprite_x layer_sprite_y layer_sprite_get_sprite layer_sprite_get_index layer_sprite_get_speed layer_sprite_get_xscale layer_sprite_get_yscale layer_sprite_get_angle layer_sprite_get_blend layer_sprite_get_alpha layer_sprite_get_x layer_sprite_get_y layer_tilemap_get_id layer_tilemap_exists layer_tilemap_create layer_tilemap_destroy tilemap_tileset tilemap_x tilemap_y tilemap_set tilemap_set_at_pixel tilemap_get_tileset tilemap_get_tile_width tilemap_get_tile_height tilemap_get_width tilemap_get_height tilemap_get_x tilemap_get_y tilemap_get tilemap_get_at_pixel tilemap_get_cell_x_at_pixel tilemap_get_cell_y_at_pixel tilemap_clear draw_tilemap draw_tile tilemap_set_global_mask tilemap_get_global_mask tilemap_set_mask tilemap_get_mask tilemap_get_frame tile_set_empty tile_set_index tile_set_flip tile_set_mirror tile_set_rotate tile_get_empty tile_get_index tile_get_flip tile_get_mirror tile_get_rotate layer_tile_exists layer_tile_create layer_tile_destroy layer_tile_change layer_tile_xscale layer_tile_yscale layer_tile_blend layer_tile_alpha layer_tile_x layer_tile_y layer_tile_region layer_tile_visible layer_tile_get_sprite layer_tile_get_xscale layer_tile_get_yscale layer_tile_get_blend layer_tile_get_alpha layer_tile_get_x layer_tile_get_y layer_tile_get_region layer_tile_get_visible layer_instance_get_instance instance_activate_layer instance_deactivate_layer camera_create camera_create_view camera_destroy camera_apply camera_get_active camera_get_default camera_set_default camera_set_view_mat camera_set_proj_mat camera_set_update_script camera_set_begin_script camera_set_end_script camera_set_view_pos camera_set_view_size camera_set_view_speed camera_set_view_border camera_set_view_angle camera_set_view_target camera_get_view_mat camera_get_proj_mat camera_get_update_script camera_get_begin_script camera_get_end_script camera_get_view_x camera_get_view_y camera_get_view_width camera_get_view_height camera_get_view_speed_x camera_get_view_speed_y camera_get_view_border_x camera_get_view_border_y camera_get_view_angle camera_get_view_target view_get_camera view_get_visible view_get_xport view_get_yport view_get_wport view_get_hport view_get_surface_id view_set_camera view_set_visible view_set_xport view_set_yport view_set_wport view_set_hport view_set_surface_id gesture_drag_time gesture_drag_distance gesture_flick_speed gesture_double_tap_time gesture_double_tap_distance gesture_pinch_distance gesture_pinch_angle_towards gesture_pinch_angle_away gesture_rotate_time gesture_rotate_angle gesture_tap_count gesture_get_drag_time gesture_get_drag_distance gesture_get_flick_speed gesture_get_double_tap_time gesture_get_double_tap_distance gesture_get_pinch_distance gesture_get_pinch_angle_towards gesture_get_pinch_angle_away gesture_get_rotate_time gesture_get_rotate_angle gesture_get_tap_count keyboard_virtual_show keyboard_virtual_hide keyboard_virtual_status keyboard_virtual_height",literal:"self other all noone global local undefined pointer_invalid pointer_null path_action_stop path_action_restart path_action_continue path_action_reverse true false pi GM_build_date GM_version GM_runtime_version timezone_local timezone_utc gamespeed_fps gamespeed_microseconds ev_create ev_destroy ev_step ev_alarm ev_keyboard ev_mouse ev_collision ev_other ev_draw ev_draw_begin ev_draw_end ev_draw_pre ev_draw_post ev_keypress ev_keyrelease ev_trigger ev_left_button ev_right_button ev_middle_button ev_no_button ev_left_press ev_right_press ev_middle_press ev_left_release ev_right_release ev_middle_release ev_mouse_enter ev_mouse_leave ev_mouse_wheel_up ev_mouse_wheel_down ev_global_left_button ev_global_right_button ev_global_middle_button ev_global_left_press ev_global_right_press ev_global_middle_press ev_global_left_release ev_global_right_release ev_global_middle_release ev_joystick1_left ev_joystick1_right ev_joystick1_up ev_joystick1_down 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Basi di dati

\n \n \n

\n Uno scritto con tre domande:\n

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\n Prossimo appello:\n

\n \n \n \n

\n In gruppo, progettare un database secondo queste specifiche.\n

\n

\n Termine ultimo per la consegna:\n

\n \n

\n Consegnando il progetto prima della fine di Luglio si otterrà un bonus!\n

\n \n

\n Esempi di progetti degli anni passati:\n

\n \n

\n Presentando il progetto si otterrà un bonus!\n

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\n

Basi di dati

\n \n \n

\n Uno scritto con tre domande:\n

\n
    \n
  • Progettazione concettuale e logica
    • \n
  • Formulazione interrogazione
    • \n
  • Una domanda tra:\n
      \n
    • Studio dato derivato
      • \n
    • Progettazione fisica
      • \n
    • Tecnologia database
      • \n
    \n
    • \n
\n

\n Prossimo appello:\n

\n \n \n \n

\n In gruppo, progettare un database secondo queste specifiche.\n

\n

\n Termine ultimo per la consegna:\n

\n \n

\n Consegnando il progetto prima della fine di Luglio si otterrà un bonus!\n

\n \n

\n Esempi di progetti degli anni passati:\n

\n \n

\n Presentando il progetto si otterrà un bonus!\n

\n \n \n
\n )\n }\n}\n","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n render() {\n return (\n
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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__2PzAa\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1UVRh\"};","import {Component} from 'preact'\nimport Split from \"../components/old/split\";\nimport Latex from \"../components/Latex\";\nimport Panel from \"../components/old/panel\";\nimport Example from \"../components/example\";\nimport Todo from \"../components/old/todo\";\nimport Timer from \"../components/old/timer\";\n\nconst r = String.raw;\n\nexport default class CalcoloNumerico extends Component {\n render() {\n return (\n
\n

Calcolo Numerico

\n \n \n

\n silvia.bonettini@unimore.it\n

\n \n \n

\n Su appuntamento.\n

\n \n \n \n \n

\n E' composto da:\n

\n
    \n
  • 2 domande sugli argomenti teorici
    • \n
  • 1 domanda di implementazione algoritmo in MATLAB (facoltativa per i punteggi migliori del TBL)
    • \n
\n

\n Prossimo appello:\n \n

\n \n \n \n \n

\n Algoritmi che hanno:\n

\n
    \n
  • numeri reali in input e output
    • \n
  • successioni delle quattro operazioni aritmetiche fondamentali come passi
    • \n
\n \n \n \n \n

\n Con i numeri floating point può capitare che un certo numero {r`\\alpha`} non sia rappresentato correttamente.\n

\n

\n In tal caso, il numero si indica con {r`\\alpha^*`}.\n

\n \n \n

\n È la differenza tra il numero desiderato e il numero rappresentato:\n

\n

\n {r`E_a = \\left | \\alpha - \\alpha^* \\right |`}\n

\n \n Vale sempre 0, tranne in caso di underflow o overflow.\n \n \n \n

\n Indica quanto il numero rappresentato differisce dal numero desiderato:\n

\n

\n {r`\\forall \\alpha \\neq 0, E_r = \\frac{E_a}{\\left | \\alpha \\right |}`}\n

\n \n \n \n \n

\n L'errore relativo di un numero reale rappresentato in virgola mobile è minore o uguale alla precisione di macchina:\n

\n

\n {r`E_r \\leq k \\cdot \\beta^{1-t}`}\n

\n
    \n
  • \n \\beta è uguale alla base utilizzata (solitamente 2).\n
    • \n
  • \n t è uguale al numero di cifre della mantissa.\n
    • \n
  • \n k è uguale a 1 se il numero viene rappresentato per troncamento oppure a {r`\\frac{1}{2}`} se viene rappresentato per arrotondamento.\n
    • \n
\n \n \n \n \n

\n L'insieme F è il sottoinsieme dei numeri reali rappresentabili in floating point dalla macchina che stiamo usando.\n

\n

\n Operazioni tra elementi di F producono risultati in {r`\\mathbb{R}`}, che però decaderanno nuovamente a elementi di F, perdendo informazioni.\n

\n

\n Il teorema della precisione di macchina si applica quindi anche ai risultati delle operazioni.\n

\n \n \n
    \n
  • Hanno più di un elemento neutro.
    • \n
  • Un numero ha più opposti.
    • \n
  • Non sono associative.
    • \n
  • Non sono distributive.
    • \n
  • Non vale la legge di annullamento del prodotto.
    • \n
\n \n \n

\n Indica che un valore è soggetto alla precisione di macchina:\n

\n

\n {r`fl(x) = (x)(1 + \\epsilon_x)`}\n

\n \n \n \n \n

\n Errore dipendente solo dai dati.\n

\n

\n TODO: qual è la formula?\n

\n

\n È l'errore che si presenterebbe se {r`\\epsilon_1 = \\epsilon_2 = \\dots = 0`}.\n

\n \n \n

\n Errore dipendente solo dalle operazioni effettuate.\n

\n

\n TODO: qual è la formula?\n

\n

\n È l'errore che si presenterebbe se {r`\\epsilon_x = \\epsilon_y = \\dots = 0`}.\n

\n \n \n \n \n

\n Un problema poco sensibile all'errore inerente.\n

\n \n {r`y = \\frac{1}{x}`} è mal condizionato intorno allo 0 e ben condizionato lontano dallo 0.\n \n \n \n

\n Un algoritmo poco sensibile all'errore algoritmico.\n

\n \n

\n Cerchiamo un algoritmo che risolva {r`2x = 4`}.\n

\n

\n Calcolare prima {r`t = fl \\left( \\frac{1}{4} \\right)`} e poi {r`x^* = fl ( 2 \\cdot t )`} porta a una perdita di precisione.\n

\n

\n Calcolare direttamente {r`x^* = fl \\left( \\frac{2}{4} \\right)`} non ha alcuna perdita di precisione e rende l'algoritmo più stabile del precedente.\n

\n \n \n \n \n \n

\n È il coefficiente di proporzionalità tra i dati e l'errore inerente.\n

\n

\n Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n

\n

\n Minore è l'indice di condizionamento, meglio condizionato è un problema.\n

\n \n \n

\n È il coefficiente di proporzionalità tra i dati e l'errore algoritmico.\n

\n

\n Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n

\n \n \n \n \n

\n Matrice con determinante 0.\n

\n

\n Le matrici singolari non sono invertibili.\n

\n \n \n \n \n

\n Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero.\n

\n \n Esempi su Wikipedia\n \n \n \n

\n Massimo dei valori assoluti di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_\\infty = max_{i = 1..n} | x_i |`}\n

\n \n \n

\n Somma dei valori assoluti di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_1 = \\sum_{i = 1}^n | x_i |`}\n

\n \n \n

\n Radice quadrata della somma dei quadrati di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_2 = \\sqrt{\\sum_{i = 1}^n x_i^2}`}\n

\n \n \n \n \n

\n Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero.\n

\n

\n Si ricavano dalle norme vettoriali:\n

\n

\n {r`\\Vert A \\Vert = sup_{x \\in \\mathbb{R}, x \\neq 0} \\frac{\\Vert A \\cdot x \\Vert}{\\Vert x \\Vert}`}\n

\n \n sup è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?\n \n \n \n

\n Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice.\n

\n

\n {r`\\Vert A \\Vert_\\infty = max_{i = 1..n} \\sum_{j = 1}^n | a_{ij} |`}\n

\n \n \n

\n Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice.\n

\n

\n {r`\\Vert A \\Vert_1 = max_{j = 1..n} \\sum_{i = 1}^n | a_{ij} |`}\n

\n \n \n

\n Radice quadrata del rango del prodotto tra una matrice e la sua trasposta.\n

\n

\n {r`\\Vert A \\Vert_2 = \\sqrt{\\rho ( A^T \\times A ) }`}\n

\n \n \n \n \n

\n Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:\n

\n

\n {r`\\frac{\\Vert x - y \\Vert}{\\Vert x \\Vert}`}\n

\n \n \n \n \n

\n La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice.\n

\n

\n Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere velocità e indici algoritmici diversi.\n

\n

\n Il sistema lineare da risolvere viene diviso in due parti: la matrice dei coefficienti e il vettore termine noto.\n

\n \n \n

\n\n

\n \n \n
\n )\n }\n}\n","import {Component} from 'preact'\nimport style from \"./timer.less\"\n\n\nexport default class Timer extends Component {\n constructor() {\n super();\n this.state = {\n \"now\": Date.now()\n };\n this.timer = null;\n }\n\n componentDidMount() {\n this.timer = setInterval(() => {\n this.setState({\"now\": Date.now()})\n }, 1000)\n }\n\n componentWillUnmount() {\n if(this.timer !== null) {\n clearInterval(this.timer)\n }\n }\n\n render() {\n let dateTo = \"Unknown date\";\n let className = style.timer;\n\n let parts = {\n milliseconds: \"?\",\n seconds: \"?\",\n minutes: \"?\",\n hours: \"?\",\n days: \"?\",\n };\n\n if(this.props.to) {\n dateTo = new Date(this.props.to);\n let timeLeft = dateTo - this.state.now;\n\n if(timeLeft > 0) {\n parts = {\n milliseconds: timeLeft % 1000,\n seconds: Math.floor(timeLeft / 1000) % 60,\n minutes: Math.floor(timeLeft / 60000) % 60,\n hours: Math.floor(timeLeft / 3600000) % 24,\n days: Math.floor(timeLeft / 86400000),\n };\n }\n\n else {\n parts = {\n milliseconds: 0,\n seconds: 0,\n minutes: 0,\n hours: 0,\n days: 0,\n };\n\n className += \" \" + style.expired;\n }\n }\n else {\n className += \" \" + style.unknown;\n }\n\n return (\n
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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__P0_NL\"};","import {Component} from 'preact'\nimport Split from \"../components/split\";\nimport Latex from \"../components/latex\";\nimport Panel from \"../components/panel\";\nimport Example from \"../components/example\";\nimport Todo from \"../components/todo\";\nimport Timer from \"../components/timer\";\n\nconst r = String.raw;\n\nexport default class CalcoloNumerico extends Component {\n render() {\n return (\n
\n

Calcolo Numerico

\n \n \n

\n silvia.bonettini@unimore.it\n

\n \n \n

\n Su appuntamento.\n

\n \n \n \n \n

\n E' composto da:\n

\n
    \n
  • 2 domande sugli argomenti teorici
    • \n
  • 1 domanda di implementazione algoritmo in MATLAB (facoltativa per i punteggi migliori del TBL)
    • \n
\n

\n Prossimo appello:\n \n

\n \n \n \n \n

\n Algoritmi che hanno:\n

\n
    \n
  • numeri reali in input e output
    • \n
  • successioni delle quattro operazioni aritmetiche fondamentali come passi
    • \n
\n \n \n \n \n

\n Con i numeri floating point può capitare che un certo numero {r`\\alpha`} non sia rappresentato correttamente.\n

\n

\n In tal caso, il numero si indica con {r`\\alpha^*`}.\n

\n \n \n

\n È la differenza tra il numero desiderato e il numero rappresentato:\n

\n

\n {r`E_a = \\left | \\alpha - \\alpha^* \\right |`}\n

\n \n Vale sempre 0, tranne in caso di underflow o overflow.\n \n \n \n

\n Indica quanto il numero rappresentato differisce dal numero desiderato:\n

\n

\n {r`\\forall \\alpha \\neq 0, E_r = \\frac{E_a}{\\left | \\alpha \\right |}`}\n

\n \n \n \n \n

\n L'errore relativo di un numero reale rappresentato in virgola mobile è minore o uguale alla precisione di macchina:\n

\n

\n {r`E_r \\leq k \\cdot \\beta^{1-t}`}\n

\n
    \n
  • \n \\beta è uguale alla base utilizzata (solitamente 2).\n
    • \n
  • \n t è uguale al numero di cifre della mantissa.\n
    • \n
  • \n k è uguale a 1 se il numero viene rappresentato per troncamento oppure a {r`\\frac{1}{2}`} se viene rappresentato per arrotondamento.\n
    • \n
\n \n \n \n \n

\n L'insieme F è il sottoinsieme dei numeri reali rappresentabili in floating point dalla macchina che stiamo usando.\n

\n

\n Operazioni tra elementi di F producono risultati in {r`\\mathbb{R}`}, che però decaderanno nuovamente a elementi di F, perdendo informazioni.\n

\n

\n Il teorema della precisione di macchina si applica quindi anche ai risultati delle operazioni.\n

\n \n \n
    \n
  • Hanno più di un elemento neutro.
    • \n
  • Un numero ha più opposti.
    • \n
  • Non sono associative.
    • \n
  • Non sono distributive.
    • \n
  • Non vale la legge di annullamento del prodotto.
    • \n
\n \n \n

\n Indica che un valore è soggetto alla precisione di macchina:\n

\n

\n {r`fl(x) = (x)(1 + \\epsilon_x)`}\n

\n \n \n \n \n

\n Errore dipendente solo dai dati.\n

\n

\n TODO: qual è la formula?\n

\n

\n È l'errore che si presenterebbe se {r`\\epsilon_1 = \\epsilon_2 = \\dots = 0`}.\n

\n \n \n

\n Errore dipendente solo dalle operazioni effettuate.\n

\n

\n TODO: qual è la formula?\n

\n

\n È l'errore che si presenterebbe se {r`\\epsilon_x = \\epsilon_y = \\dots = 0`}.\n

\n \n \n \n \n

\n Un problema poco sensibile all'errore inerente.\n

\n \n {r`y = \\frac{1}{x}`} è mal condizionato intorno allo 0 e ben condizionato lontano dallo 0.\n \n \n \n

\n Un algoritmo poco sensibile all'errore algoritmico.\n

\n \n

\n Cerchiamo un algoritmo che risolva {r`2x = 4`}.\n

\n

\n Calcolare prima {r`t = fl \\left( \\frac{1}{4} \\right)`} e poi {r`x^* = fl ( 2 \\cdot t )`} porta a una perdita di precisione.\n

\n

\n Calcolare direttamente {r`x^* = fl \\left( \\frac{2}{4} \\right)`} non ha alcuna perdita di precisione e rende l'algoritmo più stabile del precedente.\n

\n \n \n \n \n \n

\n È il coefficiente di proporzionalità tra i dati e l'errore inerente.\n

\n

\n Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n

\n

\n Minore è l'indice di condizionamento, meglio condizionato è un problema.\n

\n \n \n

\n È il coefficiente di proporzionalità tra i dati e l'errore algoritmico.\n

\n

\n Essendo sempre maggiore di uno, si può dire che sia un coefficiente di amplificazione.\n

\n \n \n \n \n

\n Matrice con determinante 0.\n

\n

\n Le matrici singolari non sono invertibili.\n

\n \n \n \n \n

\n Funzione che associa un valore positivo a ogni vettore diverso da 0, e 0 al vettore zero.\n

\n \n Esempi su Wikipedia\n \n \n \n

\n Massimo dei valori assoluti di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_\\infty = max_{i = 1..n} | x_i |`}\n

\n \n \n

\n Somma dei valori assoluti di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_1 = \\sum_{i = 1}^n | x_i |`}\n

\n \n \n

\n Radice quadrata della somma dei quadrati di tutti gli elementi del vettore.\n

\n

\n {r`\\Vert x \\Vert_2 = \\sqrt{\\sum_{i = 1}^n x_i^2}`}\n

\n \n \n \n \n

\n Funzione che associa un valore positivo a ogni matrice diversa da 0, e 0 alla matrice zero.\n

\n

\n Si ricavano dalle norme vettoriali:\n

\n

\n {r`\\Vert A \\Vert = sup_{x \\in \\mathbb{R}, x \\neq 0} \\frac{\\Vert A \\cdot x \\Vert}{\\Vert x \\Vert}`}\n

\n \n sup è l'estremo superiore di un insieme. E' molto simile al massimo: ricordi le prime lezioni di Analisi?\n \n \n \n

\n Massimo delle somme dei valori assoluti di tutti gli elementi di ogni riga di una matrice.\n

\n

\n {r`\\Vert A \\Vert_\\infty = max_{i = 1..n} \\sum_{j = 1}^n | a_{ij} |`}\n

\n \n \n

\n Massimo delle somme dei valori assoluti di tutti gli elementi di ogni colonna di una matrice.\n

\n

\n {r`\\Vert A \\Vert_1 = max_{j = 1..n} \\sum_{i = 1}^n | a_{ij} |`}\n

\n \n \n

\n Radice quadrata del rango del prodotto tra una matrice e la sua trasposta.\n

\n

\n {r`\\Vert A \\Vert_2 = \\sqrt{\\rho ( A^T \\times A ) }`}\n

\n \n \n \n \n

\n Le norme sono usate per calcolare l'errore relativo tra due vettori o matrici:\n

\n

\n {r`\\frac{\\Vert x - y \\Vert}{\\Vert x \\Vert}`}\n

\n \n \n \n \n

\n La fattorizzazione è il processo che permette di risolvere sistemi di equazioni lineari rappresentati in forma di matrice.\n

\n

\n Esistono molteplici algoritmi in grado di realizzarla: mentre tutti portano alla stessa soluzione, possono avere velocità e indici algoritmici diversi.\n

\n

\n Il sistema lineare da risolvere viene diviso in due parti: la matrice dei coefficienti e il vettore termine noto.\n

\n \n \n

\n\n

\n \n \n
\n )\n }\n}\n","import style from \"./todo.css\";\nimport { Component } from 'preact';\n\nexport default class Todo extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import {Component} from 'preact'\nimport style from \"./timer.less\"\n\n\nexport default class Timer extends Component {\n constructor() {\n super();\n this.state = {\n \"now\": Date.now()\n };\n this.timer = null;\n }\n\n componentDidMount() {\n this.timer = setInterval(() => {\n this.setState({\"now\": Date.now()})\n }, 1000)\n }\n\n componentWillUnmount() {\n if(this.timer !== null) {\n clearInterval(this.timer)\n }\n }\n\n render() {\n let dateTo = \"Unknown date\";\n let className = style.timer;\n\n let parts = {\n milliseconds: \"?\",\n seconds: \"?\",\n minutes: \"?\",\n hours: \"?\",\n days: \"?\",\n };\n\n if(this.props.to) {\n dateTo = new Date(this.props.to);\n let timeLeft = dateTo - this.state.now;\n\n if(timeLeft > 0) {\n parts = {\n milliseconds: timeLeft % 1000,\n seconds: Math.floor(timeLeft / 1000) % 60,\n minutes: Math.floor(timeLeft / 60000) % 60,\n hours: Math.floor(timeLeft / 3600000) % 24,\n days: Math.floor(timeLeft / 86400000),\n };\n }\n\n else {\n parts = {\n milliseconds: 0,\n seconds: 0,\n minutes: 0,\n hours: 0,\n days: 0,\n };\n\n className += \" \" + style.expired;\n }\n }\n else {\n className += \" \" + style.unknown;\n }\n\n return (\n
\n
\n {parts.days}\n
\n
\n giorni\n
\n
\n {parts.hours}\n
\n
\n ore\n
\n
\n {parts.minutes}\n
\n
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\n
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e},e}function ln(){var e=Sn(["\vec{v} = lim_{Delta t \to 0} \frac{Delta \vec{s}}{Delta t} = \frac{d \vec{s}}{dt}"],["\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}"]);return ln=function(){return e},e}function rn(){var e=Sn(["\vec{v} = \frac{Delta \vec{s}}{Delta t}"],["\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}"]);return rn=function(){return e},e}function on(){var e=Sn(["Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)"],["\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)"]);return on=function(){return e},e}function un(){var e=Sn(["F = -k x"]);return un=function(){return e},e}function cn(){var e=Sn(["left | \vec{F} \right | leq mu_{d} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |"]);return cn=function(){return e},e}function pn(){var e=Sn(["left | \vec{F} \right | leq mu_{s} left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |"]);return pn=function(){return e},e}function sn(){var e=Sn(["g_{marte} = 3.71 \frac{m}{s^2}"],["g_{marte} = 3.71 \\frac{m}{s^2}"]);return sn=function(){return e},e}function dn(){var e=Sn(["g_{luna} = 1.62 \frac{m}{s^2}"],["g_{luna} = 1.62 \\frac{m}{s^2}"]);return dn=function(){return e},e}function fn(){var e=Sn(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return fn=function(){return e},e}function vn(){var e=Sn(["g = 9.81 \frac{m}{s^2}"],["g = 9.81 \\frac{m}{s^2}"]);return vn=function(){return e},e}function mn(){var e=Sn(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return mn=function(){return e},e}function gn(){var e=Sn(["G = 6.67 cdot 10^{-11} \frac{N m^2}{{kg}^2}"],["G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}"]);return gn=function(){return e},e}function hn(){var e=Sn(["left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}"],["\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}"]);return hn=function(){return e},e}function _n(){var e=Sn(["\vec{F}_{21} = -\vec{F}_{12}"],["\\vec{F}_{21} = -\\vec{F}_{12}"]);return _n=function(){return e},e}function zn(){var e=Sn(["Sigma \vec{F} = m \vec{a}"],["\\Sigma \\vec{F} = m \\vec{a}"]);return zn=function(){return e},e}function bn(){var e=Sn(["Sigma \vec{F} = 0 Longleftrightarrow Delta v = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0"]);return bn=function(){return e},e}function Dn(){var e=Sn(["left | \vec{c} \right | = left | \vec{a} \right | cdot left | \vec{b} \right | cdot sin(alpha)"],["\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)"]);return Dn=function(){return e},e}function Ln(){var e=Sn(["\vec{c} = \vec{a} \times \vec{b}"],["\\vec{c} = \\vec{a} \\times \\vec{b}"]);return Ln=function(){return e},e}function qn(){var e=Sn(["\vec{b}"],["\\vec{b}"]);return qn=function(){return e},e}function Fn(){var e=Sn(["\vec{a}"],["\\vec{a}"]);return Fn=function(){return e},e}function Cn(){var e=Sn(["\vec{v} cdot \vec{w} = left | \vec{v} \right | left | \vec{w} \right | cos alpha"],["\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha"]);return Cn=function(){return e},e}function An(){var e=Sn(["\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)"],["\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]);return An=function(){return e},e}function En(){var e=Sn(["\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)"],["\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)"]);return En=function(){return e},e}function Pn(){var e=Sn(["left | \vec{v}_y \right | = left | \vec{v} \right | cos alpha"],["\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha"]);return Pn=function(){return e},e}function yn(){var e=Sn(["left | \vec{v}_x \right | = left | \vec{v} \right | sin alpha"],["\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha"]);return yn=function(){return e},e}function In(){var e=Sn(["\vec{v} = \vec{v}_x + \vec{v}_y"],["\\vec{v} = \\vec{v}_x + \\vec{v}_y"]);return In=function(){return e},e}function Sn(e,n){return n||(n=e.slice(0)),e.raw=n,e}t.d(n,"default",(function(){return Mn}));var Bn=t("hosL"),kn=t("ZsnK"),wn=t("9yVG"),xn=t("ddBW"),Vn=t("bQQT"),Tn=t("GC6P"),Nn=t("7bXG"),Rn=String.raw,Mn=function(n){function t(){return n.apply(this,arguments)||this}var Sn,Bn;return Bn=n,(Sn=t).prototype=Object.create(Bn.prototype),Sn.prototype.constructor=Sn,Sn.__proto__=Bn,t.prototype.render=function(){return e("div",null,e("h1",null,"Fisica"),e(xn.a,{title:"Vettori"},e(wn.a,{title:"Componenti cartesiane"},e("p",null,"Usa le regole base della trigonometria:"),e("p",null,e(kn.a,null,Rn(In()))),e("p",null,e(kn.a,null,Rn(yn()))),e("p",null,e(kn.a,null,Rn(Pn())))),e(wn.a,{title:"Somma"},e("p",null,"Scomponi in componenti, poi sommali:"),e("p",null,e(kn.a,null,Rn(En()))),e("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),e(wn.a,{title:"Differenza"},e("p",null,"Alla fine è sempre una somma:"),e("p",null,e(kn.a,null,Rn(An()))),e("p",null,"Produce il vettore che parte da ",e(kn.a,null,"w")," e arriva a ",e(kn.a,null,"v"),".")),e(wn.a,{title:"Prodotto scalare"},e("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),e("p",null,e(kn.a,null,Rn(Cn()))),e("p",null,"Produce il modulo della proiezione di ",e(kn.a,null,Rn(Fn()))," su ",e(kn.a,null,Rn(qn())),".")),e(wn.a,{title:"Prodotto vettoriale"},e("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),e("ul",null,e("li",null,e(kn.a,null,Rn(Ln()))),e("li",null,e(kn.a,null,Rn(Dn()))),e("li",null,e("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),e("p",null,"Non è commutativo!"))),e(xn.a,{title:"Leggi di Newton"},e(wn.a,{title:"1ᵃ: Inerzia"},e("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),e("p",null,e(kn.a,null,Rn(bn())))),e(wn.a,{title:"2ᵃ: Proporzionalità"},e("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",e("i",null,"massa"),"."),e("p",null,e(kn.a,null,Rn(zn())))),e(wn.a,{title:"3ᵃ: Azione e reazione"},e("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),e("p",null,e(kn.a,null,Rn(_n()))))),e(xn.a,{title:"Forza di gravità"},e(wn.a,{title:"Tra due corpi"},e("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),e("p",null,e(kn.a,null,Rn(hn()))),e("p",null,e(kn.a,null,"G")," è la ",e("i",null,"costante di gravitazione universale")," e vale:"),e("p",null,e(kn.a,null,Rn(gn())))),e(wn.a,{title:"Verso la Terra"},e("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",e("i",null,"peso")," uguale a:"),e("p",null,e(kn.a,null,Rn(mn()))),e("p",null,e(kn.a,null,"g")," è la ",e("i",null,"costante di gravità")," della Terra, e vale:"),e("p",null,e(kn.a,null,Rn(vn())))),e(wn.a,{title:"Su pianeti diversi"},e("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),e("p",null,e(kn.a,null,Rn(fn()))),e("p",null,"L'unica differenza è che cambia la ",e("i",null,"costante di gravità"),":"),e("p",null,e(kn.a,null,Rn(dn()))),e("p",null,e(kn.a,null,Rn(sn()))))),e(xn.a,{title:"Forze di contatto"},e(wn.a,{title:"Normale"},e("p",null,"Si oppone alle forze applicate alla superficie di contatto."),e("p",null,"Un libro appoggiato su un tavolo ha la ",e("b",null,"forza di gravità")," che lo attira verso il terreno e la ",e("b",null,"forza normale")," che lo trattiene dal cadere.")),e(wn.a,{title:"Attrito statico"},e("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),e("p",null,e(kn.a,null,Rn(pn())))),e(wn.a,{title:"Attrito dinamico"},e("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),e("p",null,e(kn.a,null,Rn(cn())))),e(wn.a,{title:"Tensione"},e("p",null,"E' forza trasmessa tra due estremi di una fune."),e("p",null,"Può essere redirezionata per mezzo di carrucole.")),e(wn.a,{title:"Elastica"},e("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),e("p",null,e(kn.a,null,Rn(un()))),e("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),e(xn.a,{title:"Cinematica"},e(wn.a,{title:"Spostamento"},e("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),e("p",null,e(kn.a,null,Rn(on())))),e(wn.a,{title:"Velocità"},e("p",null,"È un vettore che misura la variazione di posizione nel tempo."),e("p",null,e(kn.a,null,Rn(rn()))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"velocità istantanea"),":"),e("p",null,e(kn.a,null,Rn(ln())))),e(wn.a,{title:"Accelerazione"},e("p",null,"È un vettore che misura la variazione di velocità nel tempo."),e("p",null,e(kn.a,null,Rn(an()))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"accelerazione istantanea"),":"),e("p",null,e(kn.a,null,Rn(tn())))),e(wn.a,{title:e("span",null,"Quantità di moto ",e("small",null,"(momento lineare)"))},e("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),e("p",null,e(kn.a,null,Rn(nn()))),e("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),e("p",null,e(kn.a,null,Rn(en()))))),e(xn.a,{title:"Moto rettilineo uniforme"},e(wn.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(kn.a,null,Rn($e())))),e(wn.a,{title:"Velocità"},e("p",null,"È costante:"),e("p",null,e(kn.a,null,Rn(Ze())))),e(wn.a,{title:"Accelerazione"},e("p",null,"La velocità non varia:"),e("p",null,e(kn.a,null,Rn(Ye())))),e(wn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(kn.a,null,"f(t) = 0")))),e(xn.a,{title:"Moto rettilineo uniformemente accelerato"},e(wn.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(kn.a,null,Rn(Xe())))),e(wn.a,{title:"Velocità"},e("p",null,"È una retta:"),e("p",null,e(kn.a,null,Rn(Ke())))),e(wn.a,{title:"Accelerazione"},e("p",null,"È costante:"),e("p",null,e(kn.a,null,Rn(He())))),e(wn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(kn.a,null,"f(t) = m a")))),e(xn.a,{title:"Moto armonico semplice"},e(wn.a,{title:"Ampiezza"},e("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),e("p",null,"(L'ampiezza di una sinusoide.)")),e(wn.a,{title:"Velocità angolare"},e("p",null,"Indica quanto in fretta cambia la posizione del corpo."),e("p",null,"Dipende dal periodo:"),e("p",null,e(kn.a,null,Rn(Je())))),e(wn.a,{title:"Spostamento"},e("p",null,"E' una sinusoide:"),e("p",null,e(kn.a,null,Rn(je())))),e(wn.a,{title:"Velocità"},e("p",null,"E' la sinusoide dello spostamento, sfasata di ",e(kn.a,null,Rn(We())),":"),e("p",null,e(kn.a,null,Rn(Ge())))),e(wn.a,{title:"Accelerazione"},e("p",null,"E' la sinusoide della velocità, sfasata di ",e(kn.a,null,Rn(Qe())),":"),e("p",null,e(kn.a,null,Rn(Oe())))),e(wn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(kn.a,null,"f(t) = m a")))),e(xn.a,{title:"Moti composti"},e(wn.a,{title:"Moto parabolico"},e("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),e(wn.a,{title:"Moto circolare uniforme"},e("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",e(kn.a,null,Rn(Ue())),", sull'asse Y."))),e(xn.a,{title:"Moto circolare uniforme"},e(wn.a,null,e("h3",null,"Velocità angolare"),e("p",null,"Quanto cambia la fase nel tempo."),e("p",null,e(kn.a,null,Rn(Me())))),e(wn.a,{title:"Fase"},e("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),e("p",null,"Si indica con ",e(kn.a,null,Rn(Re())),", e generalmente si usa in radianti.")),e(wn.a,{title:"Velocità"},e("p",null,"Si applicano le formule per la circonferenza:"),e("p",null,e(kn.a,null,Rn(Ne())))),e(wn.a,{title:"Accelerazione"},e("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),e("p",null,e(kn.a,null,Rn(Te())))),e(wn.a,{title:"Forza centripeta"},e("p",null,"È verso il centro e si calcola con:"),e("p",null,e(kn.a,null,Rn(Ve()))))),e(xn.a,{title:"Lavoro ed energia"},e(wn.a,{title:"Lavoro"},e("p",null,"E' compiuto da una forza che sposta un corpo."),e("p",null,e(kn.a,null,Rn(xe()))),e("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),e(wn.a,{title:"Energia cinetica"},e("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),e("p",null,e(kn.a,null,Rn(we()))),e("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),e("p",null,e(kn.a,null,Rn(ke())))),e(wn.a,{title:"Energia potenziale gravitazionale"},e("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),e("p",null,e(kn.a,null,Rn(Be()))),e("p",null,"(Con ",e(kn.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),e(wn.a,{title:"Energia potenziale elastica"},e("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),e("p",null,e(kn.a,null,Rn(Se())))),e(wn.a,{title:"Forze conservative"},e("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),e("p",null,"Ad esempio, è conservativa la ",e("i",null,"forza di gravità"),", ma ",e("b",null,"non")," è conservativa la forza di attrito."),e("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),e("p",null,e(kn.a,null,Rn(Ie())))),e(wn.a,{title:"Potenza"},e("p",null,"È la velocità di trasferimento di energia:"),e("p",null,e(kn.a,null,Rn(ye()))))),e(xn.a,{title:"Elettrostatica"},e(wn.a,{title:"Carica elettrica"},e("p",null,"È una proprietà dei corpi che può essere ",e(Vn.a,null,"positiva")," o ",e(Tn.a,null,"negativa"),"."),e("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),e("p",null,"Esiste un'unità elementare: ",e(kn.a,null,Rn(Pe())),"."),e("p",null,"Cariche ",e(Vn.a,null,"opp"),e(Tn.a,null,"oste")," si attraggono; cariche ",e(Vn.a,null,"uguali")," si respingono.")),e(wn.a,{title:"Conduttori e isolanti"},e("p",null,"Più ",e("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),e("p",null,"I corpi in cui la carica si muove bene sono ",e("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",e("i",null,"isolanti"),"."),e("p",null,e("i",null,"Il corpo umano è un buon conduttore.")))),e(xn.a,{title:"Polarizzazione"},e(wn.a,{title:"Polarizzazione"},e("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),e(xn.a,null,e(wn.a,{title:"Messa a terra"},e("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",e("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",e(Vn.a,null,"cariche positive")," e ",e(Tn.a,null,"negative")," all'interno)."))),e(xn.a,null,e(wn.a,{title:"Polarizzazione per strofinio"},e("p",null,"Strofinando tra loro due corpi isolanti, essi si ",e("i",null,"polarizzeranno per strofinio"),".")),e(wn.a,{title:"Polarizzazione per contatto"},e("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",e("i",null,"polarizzarsi per contatto"),".")),e(wn.a,{title:"Polarizzazione per induzione"},e("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',e(Vn.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",e(Tn.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",e(Vn.a,null,"stesso segno")," più lontano possibile da esse."),e("p",null,"Mettendo a terra il conduttore, nuove cariche del ",e(Tn.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),e("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",e(Tn.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),e(xn.a,{title:"Forza elettrica"},e(wn.a,{title:"Legge di Coulomb"},e("p",null,"Due corpi carichi si attraggono tra loro con forza:"),e("p",null,e(kn.a,null,Rn(Ee()))),e("p",null,e(kn.a,null,Rn(Ae()))," è la ",e("i",null,"costante di Coulomb"),", e vale ",e(kn.a,null,Rn(Ce())),".")),e(wn.a,{title:"Permeabilità dello spazio vuoto"},e("p",null,"La costante ",e(kn.a,null,Rn(Fe()))," è in realtà dipendente da un altra costante, ",e(kn.a,null,Rn(qe())),", la ",e("i",null,"permeabilità del vuoto"),"."),e("p",null,e(kn.a,null,Rn(Le()))),e("p",null,e(kn.a,null,Rn(De())))),e(wn.a,{title:"Campo elettrico"},e("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),e("p",null,e(kn.a,null,Rn(be())))),e(wn.a,{title:"Flusso elettrico"},e("p",null,'È la differenza tra "quanto" campo elettrico ',e(Vn.a,null,"entra")," e quanto campo elettrico ",e(Tn.a,null,"esce")," da una certa area."),e("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),e("p",null,e(kn.a,null,Rn(ze()))),e("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),e("p",null,e(kn.a,null,Rn(_e()))),e("p",null,e(Nn.a,null,"Circa. E' una specie di integrale..."))),e(wn.a,{title:"Legge di Gauss per i campi elettrostatici"},e("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),e("p",null,e(kn.a,null,Rn(he()))),e("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),e(xn.a,{title:"Energia elettrica"},e(wn.a,{title:"Energia potenziale elettrica"},e("p",null,"Un corpo carico vicino ad altre cariche possiede un'",e("i",null,"energia potenziale elettrica")," ",e(kn.a,null,Rn(ge())),"."))),e(xn.a,{title:"Circuiti elettrici"},e(wn.a,{title:e("span",null,"Potenziale elettrico ",e("small",null,"(tensione)"))},e("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),e("p",null,e(kn.a,null,Rn(me()))),e("p",null,"La sua unità di misura è il Volt (",e(kn.a,null,Rn(ve())),")."),e("p",null,"In una batteria è detto ",e("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),e(wn.a,{title:e("span",null,"Corrente elettrica ",e("small",null,"(intensità)"))},e("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),e("p",null,e(kn.a,null,Rn(fe()))),e("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),e("p",null,"La sua unità di misura è l'Ampere (",e(kn.a,null,Rn(de())),").")),e(wn.a,{title:e("span",null,"Corrente continua ",e("small",null,"(",e("abbr",{title:"Direct Current"},"DC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente è costante.")),e(wn.a,{title:e("span",null,"Corrente alternata ",e("small",null,"(",e("abbr",{title:"Alternate Current"},"AC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),e(wn.a,{title:"Potenza elettrica"},e("p",null,"Possiamo calcolare la potenza di un circuito:"),e("p",null,e(kn.a,null,Rn(se()))))),e(xn.a,{title:"Elementi di un circuito"},e(wn.a,{title:"Resistore"},e("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),e("p",null,"Il potenziale utilizzato è pari a:"),e("p",null,e(kn.a,null,Rn(pe()))),e("p",null,"Dove ",e(kn.a,null,Rn(ce()))," è una costante detta ",e("i",null,"resistenza")," con unità di misura Ohm (",e(kn.a,null,Rn(ue())),")."),e("p",null,"La resistenza di un conduttore vale:"),e("p",null,e(kn.a,null,Rn(oe()))),e("p",null,e(kn.a,null,Rn(re()))," è la ",e("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),e("p",null,e(kn.a,null,Rn(ie())))),e(wn.a,{title:"Condensatore"},e("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),e("p",null,"Per farlo, cattura cariche ",e(Vn.a,null,"positive")," e ",e(Tn.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),e("p",null,"Ha una ",e("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),e("p",null,e(kn.a,null,Rn(le()))),e("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),e("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),e("p",null,e(kn.a,null,Rn(ae()))),e("p",null,"Dove ",e(kn.a,null,Rn(te()))," è la ",e("i",null,"costante dielettrica relativa")," del materiale inserito, ",e(kn.a,null,Rn(ne()))," l'area di una armatura e ",e(kn.a,null,Rn(ee()))," la distanza tra le due armature."),e("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",e("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",e("i",null,"breakdown"),"."),e("p",null,"La sua unità di misura è il Farad (",e(kn.a,null,Rn($())),")")),e(wn.a,{title:"Amperometro"},e("p",null,"Misura la corrente elettrica se messo in serie."),e("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),e(wn.a,{title:"Voltmetro"},e("p",null,"Misura la differenza di potenziale se messo in parallelo."),e("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),e(xn.a,{title:"Principi di Kirchhoff"},e(wn.a,{title:"Legge dei nodi"},e("p",null,"Per nodo si intende un qualsiasi punto del circuito."),e("p",null,"Da un nodo entra ed esce la stessa corrente.")),e(wn.a,{title:"Legge delle maglie"},e("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),e("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),e(xn.a,{title:"Serie e Parallelo"},e(wn.a,{title:"Circuito in serie"},e("p",null,"Più parti di circuito sono ",e("i",null,"in serie")," se sono consecutive e senza biforcazioni."),e("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),e(wn.a,{title:"Circuito in parallelo"},e("p",null,"Più parti di circuito sono ",e("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),e("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),e(xn.a,{title:"Resistenze equivalenti"},e(wn.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),e("p",null,e(kn.a,null,Rn(Z())))),e(wn.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),e("p",null,e(kn.a,null,Rn(Y()))))),e(xn.a,{title:"Condensatori equivalenti"},e(wn.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),e("p",null,e(kn.a,null,Rn(X())))),e(wn.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),e("p",null,e(kn.a,null,Rn(K()))))),e(xn.a,{title:"Magnetismo"},e(wn.a,{title:"Permeabilità magnetica dello spazio vuoto"},e("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),e("p",null,e(kn.a,null,Rn(H()))," (",e(kn.a,null,Rn(J())),")")),e(wn.a,{title:"Campo magnetico"},e("p",null,"Come un campo elettrico, ma per i magneti."),e("p",null,"Il suo simbolo è ",e(kn.a,null,Rn(j())),", e la sua unità di misura è il Tesla (",e(kn.a,null,"T"),").")),e(wn.a,{title:"Flusso magnetico"},e("p",null,'È "quanto" campo magnetico ',e("b",null,"attraversa")," un percorso chiuso."),e("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),e("p",null,e(kn.a,null,Rn(W()))),e("p",null,e(kn.a,null,Rn(G()))),e("p",null,"La sua unità di misura è il Weber (",e(kn.a,null,Rn(Q())),").")),e(wn.a,{title:"Legge di Gauss per i campi magnetici"},e("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),e("p",null,"Ovvero, non esistono monopoli magnetici.")),e(wn.a,{title:"Legge di Ampère"},e("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),e("p",null,e(kn.a,null,Rn(O()))))),e(xn.a,{title:"Forze magnetiche"},e(wn.a,{title:e("span",null,"Forza magnetica su carica puntiforme ",e("small",null,"(Forza di Lorentz)"))},e("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),e("p",null,e(kn.a,null,Rn(U()))),e("p",null,"Dove ",e(kn.a,null,Rn(M()))," è l'intensità del campo magnetico e ",e(kn.a,null,Rn(R()))," la velocità della carica considerata."),e("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),e("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),e(wn.a,{title:"Forza magnetica in un filo"},e("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),e("p",null,e(kn.a,null,Rn(N()))," ",e("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),e("p",null,"Dove ",e(kn.a,null,Rn(T()))," è la corrente elettrica, ",e(kn.a,null,Rn(V()))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),e(xn.a,{title:"Campi magnetici"},e(wn.a,{title:"Campo magnetico in una spira"},e("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),e(wn.a,{title:"Campo magnetico di un solenoide"},e("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),e("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),e("p",null,e(kn.a,null,Rn(x())))),e(wn.a,{title:"Legge di Oersted"},e("p",null,e("i",null,"Caso particolare della ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),e("p",null,"Il modulo del campo magnetico ",e(kn.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",e(kn.a,null,"I")," alla distanza ",e(kn.a,null,"s")," è:"),e("p",null,e(kn.a,null,Rn(w()))),e("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),e("p",null,"Due fili attraversati dalla ",e(Vn.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",e(Vn.a,null,"corr"),e(Tn.a,null,"enti")," ",e(Vn.a,null,"opp"),e(Tn.a,null,"oste")," si respingono."))),e(xn.a,{title:"Induzione elettromagnetica"},e(wn.a,{title:"Forza elettromotrice indotta"},e("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),e("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),e("p",null,"Essa vale:"),e("p",null,e(kn.a,null,Rn(k()))),e("p",null,"Dove ",e(kn.a,null,"v")," è la velocità del conduttore, ",e(kn.a,null,"B")," è l'intensità del campo magnetico ed ",e(kn.a,null,"L")," è la lunghezza del conduttore.")),e(wn.a,{title:"Flusso magnetico in una spira"},e("p",null,"In un campo magnetico ",e(kn.a,null,Rn(B()))," uniforme e perpendicolare al piano di una spira di area ",e(kn.a,null,Rn(S())),", il flusso magnetico si può determinare con la ",e("i",null,"Legge di Faraday-Neumann-Lenz"),":"),e("p",null,e(kn.a,null,Rn(I()))))),e(xn.a,null,e(wn.a,{title:"Legge di Faraday-Neumann-Lenz"},e("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),e("p",null,e(kn.a,null,Rn(y()))),e("p",null,"Il meno è dovuto alla ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),e(wn.a,{title:"Faraday in un solenoide"},e("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),e("p",null,e(kn.a,null,Rn(P()))),e("p",null,"Dove ",e(kn.a,null,Rn(E()))," è il numero delle spire del solenoide.")),e(wn.a,{title:"Legge di Ampère-Maxwell"},e("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),e(xn.a,{title:"Elettromagnetismo"},e(wn.a,{title:"Onde elettromagnetiche"},e("p",null,"Nel vuoto, il campo elettrico ",e(kn.a,null,Rn(A()))," e il campo magnetico ",e(kn.a,null,Rn(C()))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),e("p",null,"Si dice quindi che sono ",e("i",null,"onde elettromagnetiche"),"."),e("p",null,"Esse sono legate dalla relazione:"),e("p",null,e(kn.a,null,Rn(F()))),e("p",null,"Dove ",e(kn.a,null,Rn(q()))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),e("p",null,e(kn.a,null,Rn(L())))),e(wn.a,{title:"Formula delle onde"},e("p",null,e(kn.a,null,Rn(D()))),e("p",null,"Dove ",e(kn.a,null,Rn(b()))," è l'ampiezza massima che può avere l'onda, ",e(kn.a,null,Rn(z()))," è il vettore d'onda, ",e(kn.a,null,Rn(_()))," la frequenza angolare e ",e(kn.a,null,Rn(h()))," la fase."))),e(xn.a,{title:"Spettroscopia"},e(wn.a,{title:"Emissione"},e("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",e("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),e("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),e("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),e("p",null,e(kn.a,null,Rn(g()))),e("p",null,"Con ",e(kn.a,null,Rn(m())),", detta costante di Rydberg, e ",e(kn.a,null,Rn(v()))," un numero intero.")),e(wn.a,{title:"Grandezza quantizzata"},e("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),e("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),e("p",null,"Energia, momento angolare e raggio sono quantizzati."),e("p",null,"Nota costante quantica è ",e(kn.a,null,Rn(f())),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",e(kn.a,null,Rn(d())),"."))),e(xn.a,null,e(wn.a,{title:"Modello di Bohr"},e("p",null,"L'energia degli elettroni è quantizzata."),e("p",null,"Inoltre, per essi è valido che:"),e("p",null,e(kn.a,null,Rn(s()))),e("p",null,"Ancora, il raggio delle orbite è uguale a:"),e("p",null,e(kn.a,null,Rn(p()))),e("p",null,"Con ",e(kn.a,null,Rn(c())),"."),e("p",null,"Infine, in ogni stato, l'energia è pari a:"),e("p",null,e(kn.a,null,Rn(u()))),e("p",null,"Due elettroni non possono occupare lo stesso stato."),e("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),e(xn.a,null,e(wn.a,{title:"Nei solidi"},e("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),e("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),e(xn.a,{title:"Semiconduttori"},e(wn.a,{title:"Semiconduttori"},e("p",null,e(Nn.a,null,"Refactor this")),e("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",e(kn.a,null,Rn(o())),", allora il corpo è un isolante."),e("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),e("p",null,"Se il gap è invece dell'ordine di grandezza di ",e(kn.a,null,Rn(r())),", allora il corpo è un semiconduttore.")),e(wn.a,{title:"Lacune"},e("p",null,"Legami in cui ",e(Vn.a,null,"mancano elettroni"),"."),e("p",null,e(Tn.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",e(Vn.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),e(wn.a,{title:"Accettori e donori"},e("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),e("ul",null,e("li",null,"Con numero atomico maggiore, un semiconduttore di ",e(Tn.a,null,"tipo N")," con ",e(Tn.a,null,"elettroni in eccesso")," liberi di scorrere."),e("li",null,"Con numero atomico minore, un semiconduttore di ",e(Vn.a,null,"tipo P")," con ",e(Vn.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),e("p",null,"Maggiore impurezza porta a maggiore conduttività.")),e(wn.a,{title:"Temperatura"},e("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",e(Tn.a,null,"elettroni")," e ",e(Vn.a,null,"lacune"),"."))),e(xn.a,{title:e("span",null,"Ottica ",e("small",null,"(non l'abbiamo fatta)"))},e(wn.a,{title:"Assorbimento e riflessione"},e("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),e(wn.a,{title:"Corpo nero"},e("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),e("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",e(kn.a,null,Rn(i()))," variabile in base alla temperatura."),e("p",null,e(kn.a,null,Rn(l()))," è costante.")),e(wn.a,{title:"Teoria di Planck per il corpo nero"},e("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),e(wn.a,{title:"Fotone"},e("p",null,"Un onda magnetica con un quanto di energia è detta ",e("i",null,"fotone"),":"),e("p",null,e(kn.a,null,Rn(a())))),e(wn.a,{title:"Effetto fotoelettrico"},e("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),e("p",null,"Perchè avvenga, la 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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","import style from \"./todo.css\";\nimport { Component } from 'preact';\n\nexport default class Todo extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (

{this.props.title}

);\n\t\t}\n\n\t\treturn (\n\t\t\t
\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
\n\t\t);\n\t}\n}\n","import style from \"./minus.css\";\nimport { Component } from 'preact';\n\nexport default class Minus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","import { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Plus from '../components/plus';\nimport Minus from '../components/minus';\nimport Todo from '../components/todo';\n\nconst r = String.raw;\n\nexport default class Fisica extends Component {\n\trender() {\n return (\n
\n

Fisica

\n \n \n

\n Usa le regole base della trigonometria:\n

\n

\n {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n

\n

\n {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n

\n

\n {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n

\n \n \n

\n Scomponi in componenti, poi sommali:\n

\n

\n {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n

\n

\n Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n

\n \n \n

\n Alla fine è sempre una somma:\n

\n

\n {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n

\n

\n Produce il vettore che parte da w e arriva a v.\n

\n \n \n

\n Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n

\n

\n {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n

\n

\n Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n

\n \n \n

\n Si chiama vettoriale perchè il risultato è un altro vettore.\n

\n
    \n
  • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
    • \n
  • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
    • \n
  • Regola della mano destra
    • \n
\n

\n Non è commutativo!\n

\n \n \n \n \n

\n Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n

\n \n \n

\n La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n

\n

\n {r`\\Sigma \\vec{F} = m \\vec{a}`}\n

\n \n \n

\n Due corpi esercitano forze uguali e opposte uno sull'altro.\n

\n

\n {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n

\n \n \n \n \n

\n Due corpi puntiformi si attirano uno verso l'altro con forza:\n

\n

\n {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n

\n

\n G è la costante di gravitazione universale e vale:\n

\n

\n {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n

\n \n \n

\n Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n g è la costante di gravità della Terra, e vale:\n

\n

\n {r`g = 9.81 \\frac{m}{s^2}`}\n

\n \n \n

\n Per pianeti diversi dalla Terra vale la stessa regola:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n L'unica differenza è che cambia la costante di gravità:\n

\n

\n {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n

\n

\n {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n

\n \n \n \n \n

\n Si oppone alle forze applicate alla superficie di contatto.\n

\n

\n Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere.\n

\n \n \n

\n Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n E' forza trasmessa tra due estremi di una fune.\n

\n

\n Può essere redirezionata per mezzo di carrucole.\n

\n \n \n

\n Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n

\n

\n {r`F = -k x`}\n

\n

\n (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n

\n \n \n \n \n

\n È un vettore che indica la posizione di un corpo rispetto a un'origine.\n

\n

\n {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n

\n \n \n

\n È un vettore che misura la variazione di posizione nel tempo.\n

\n

\n {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n

\n

\n {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n

\n \n \n

\n È un vettore che misura la variazione di velocità nel tempo.\n

\n

\n {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n

\n

\n {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n

\n \n Quantità di moto (momento lineare)}>\n

\n La quantità di moto è una proprietà vettoriale dei corpi:\n

\n

\n {r`\\vec{p} = m \\vec{v}`}\n

\n

\n Se la forza risultante è nulla, la quantità di moto non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n

\n \n \n \n \n

\n La legge oraria è:\n

\n

\n {r`s(t) = v \\cdot \\Delta t + s(0)`}\n

\n \n \n

\n È costante:\n

\n

\n {r`v(t) = k`}\n

\n \n \n

\n La velocità non varia:\n

\n

\n {r`a(t) = 0`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = 0\n

\n \n \n \n \n

\n La legge oraria è:\n

\n

\n {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n

\n \n \n

\n È una retta:\n

\n

\n {r`v(t) = a \\Delta t + v(0)`}\n

\n \n \n

\n È costante:\n

\n

\n {r`a(t) = k`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n \n \n

\n E' la distanza dal centro massima che raggiunge il corpo.\n

\n

\n (L'ampiezza di una sinusoide.)\n

\n \n \n

\n Indica quanto in fretta cambia la posizione del corpo.\n

\n

\n Dipende dal periodo:\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n E' una sinusoide:\n

\n

\n {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n

\n \n \n

\n E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n

\n

\n {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n

\n \n \n

\n E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n

\n

\n {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n \n \n

\n Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n

\n \n \n

\n Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n

\n \n \n \n \n

\n Velocità angolare\n

\n

\n Quanto cambia la fase nel tempo.\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n

\n

\n Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n

\n \n \n

\n Si applicano le formule per la circonferenza:\n

\n

\n {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n

\n \n \n

\n Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:\n

\n

\n {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n

\n \n \n

\n È verso il centro e si calcola con:\n

\n

\n {r`F = m \\cdot a`}\n

\n \n \n \n \n

\n E' compiuto da una forza che sposta un corpo.\n

\n

\n {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n

\n

\n (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n

\n \n \n

\n Un corpo ha energia cinetica in ogni momento uguale a:\n

\n

\n {r`E_c = \\frac{1}{2} m v^2`}\n

\n

\n Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n

\n

\n {r`\\Delta E_c = W`}\n

\n \n \n

\n Un corpo ha energia potenziale in ogni momento pari a:\n

\n

\n {r`E_{p_g} = m \\cdot g \\cdot h`}\n

\n

\n (Con h uguale a un altezza scelta come punto di riferimento.)\n

\n \n \n

\n Una molla ha sempre energia potenziale elastica pari a:\n

\n

\n {r`E_{p_e} = \\frac{1}{2} k x^2`}\n

\n \n \n

\n Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n

\n

\n Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n

\n

\n Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n

\n

\n {r`E = E_k + E_p`}\n

\n \n \n

\n È la velocità di trasferimento di energia:\n

\n

\n {r`P = \\frac{\\Delta E}{\\Delta t}`}\n

\n \n \n \n \n

\n È una proprietà dei corpi che può essere positiva o negativa.\n

\n

\n Si conserva: in un sistema chiuso la carica totale è costante.\n

\n

\n Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n

\n

\n Cariche opposte si attraggono; cariche uguali si respingono.\n

\n \n \n

\n Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n

\n

\n I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n

\n

\n Il corpo umano è un buon conduttore.\n

\n \n \n \n \n

\n E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n

\n \n \n \n \n

\n Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n

\n \n \n \n \n

\n Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n

\n \n \n

\n Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n

\n \n \n

\n Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n

\n

\n Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n

\n

\n Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n

\n \n \n \n \n

\n Due corpi carichi si attraggono tra loro con forza:\n

\n

\n {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n

\n

\n {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n

\n \n \n

\n La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n

\n

\n {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n

\n

\n {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n

\n \n \n

\n Misura che forza viene applicata in ogni punto su una carica unitaria:\n

\n

\n {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n

\n \n \n

\n È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n

\n

\n In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n

\n

\n {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n

\n

\n Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n

\n

\n {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n

\n

\n Circa. E' una specie di integrale...\n

\n \n \n

\n Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n

\n

\n {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n

\n

\n Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n

\n \n \n \n \n

\n Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n

\n \n \n \n Potenziale elettrico (tensione)}>\n

\n È il valore dell'energia potenziale elettrica per una carica unitaria.\n

\n

\n {r`V = \\frac{U_e}{q}`}\n

\n

\n La sua unità di misura è il Volt ({r`V`}).\n

\n

\n In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n

\n \n Corrente elettrica (intensità)}>\n

\n Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n

\n

\n {r`I = \\frac{\\Delta q}{\\Delta t}`}\n

\n

\n Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n

\n

\n La sua unità di misura è l'Ampere ({r`A`}).\n

\n \n Corrente continua (DC)}>\n

\n Quando in un circuito la direzione della corrente è costante.\n

\n \n Corrente alternata (AC)}>\n

\n Quando in un circuito la direzione della corrente si alterna periodicamente.\n

\n \n \n

\n Possiamo calcolare la potenza di un circuito:\n

\n

\n {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n

\n \n \n \n \n

\n Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n

\n

\n Il potenziale utilizzato è pari a:\n

\n

\n {r`V = R \\cdot I`}\n

\n

\n Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n

\n

\n La resistenza di un conduttore vale:\n

\n

\n {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n

\n

\n {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n

\n

\n {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n

\n \n \n

\n Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n

\n

\n Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n

\n

\n Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n

\n

\n {r`C = \\frac{q_{massima}}{\\Delta V}`}\n

\n

\n Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n

\n

\n La capacità aumenta se viene messo qualcosa tra le armature:\n

\n

\n {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n

\n

\n Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n

\n

\n Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n

\n

\n La sua unità di misura è il Farad ({r`Fa`})\n

\n \n \n

\n Misura la corrente elettrica se messo in serie.\n

\n

\n (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n

\n \n \n

\n Misura la differenza di potenziale se messo in parallelo.\n

\n

\n (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n

\n \n \n \n \n

\n Per nodo si intende un qualsiasi punto del circuito.\n

\n

\n Da un nodo entra ed esce la stessa corrente.\n

\n \n \n

\n Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n

\n

\n In una maglia chiusa, la somma delle differenze di potenziale è 0.\n

\n \n \n \n \n

\n Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n

\n

\n Parti di circuito in serie sono attraversate dalla stessa corrente.\n

\n \n \n

\n Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo.\n

\n

\n Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n

\n \n \n \n \n

\n Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n

\n

\n {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n

\n \n \n

\n Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n

\n

\n {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n

\n \n \n \n \n

\n Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n

\n

\n {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n

\n \n \n

\n Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n

\n

\n {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n

\n \n \n \n \n

\n E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n

\n

\n {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n

\n \n \n

\n Come un campo elettrico, ma per i magneti.\n

\n

\n Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n

\n \n \n

\n È \"quanto\" campo magnetico attraversa un percorso chiuso.\n

\n

\n Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n

\n

\n {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n

\n

\n {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n

\n

\n La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n

\n \n \n

\n Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n

\n

\n Ovvero, non esistono monopoli magnetici.\n

\n \n \n

\n L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n

\n

\n {r`\\Phi_B = \\mu_0 \\cdot I`}\n

\n \n \n \n Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n

\n I campi magnetici applicano una forza sulle cariche vicine:\n

\n

\n {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n

\n

\n Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n

\n

\n Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n

\n

\n In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n

\n \n \n

\n I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n

\n

\n {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n

\n

\n Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n

\n \n \n \n \n

\n Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n

\n \n \n

\n Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n

\n

\n All'interno del solenoide si crea un campo (quasi) uniforme:\n

\n

\n {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n

\n \n \n

\n Caso particolare della Legge di Ampère.\n

\n

\n Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n

\n

\n {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n

\n

\n Il campo magnetico così creato gira attorno al filo in senso antiorario.\n

\n

\n Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n

\n \n \n \n \n

\n Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.\n

\n

\n La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.\n

\n

\n Essa vale:\n

\n

\n {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n

\n

\n Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n

\n \n \n

\n In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n

\n

\n {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n

\n \n \n \n \n

\n Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n

\n

\n {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n

\n

\n Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n

\n \n \n

\n In un solenoide, la forza elettromotrice indotta è uguale a:\n

\n

\n {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n

\n

\n Dove {r`N`} è il numero delle spire del solenoide.\n

\n \n \n

\n Correnti o campi elettrici variabili creano un campo magnetico.\n

\n \n \n \n \n

\n Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n

\n

\n Si dice quindi che sono onde elettromagnetiche.\n

\n

\n Esse sono legate dalla relazione:\n

\n

\n {r`E = c \\cdot B`}\n

\n

\n Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n

\n

\n {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n

\n \n \n

\n {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n

\n

\n Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n

\n \n \n \n \n

\n I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n

\n

\n I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda.\n

\n

\n In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n

\n

\n {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n

\n

\n Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n

\n \n \n

\n Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori.\n

\n

\n Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n

\n

\n Energia, momento angolare e raggio sono quantizzati.\n

\n

\n Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n

\n \n \n \n \n

\n L'energia degli elettroni è quantizzata.\n

\n

\n Inoltre, per essi è valido che:\n

\n

\n {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n

\n

\n Ancora, il raggio delle orbite è uguale a:\n

\n

\n {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n

\n

\n Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n

\n

\n Infine, in ogni stato, l'energia è pari a:\n

\n

\n {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n

\n

\n Due elettroni non possono occupare lo stesso stato.\n

\n

\n Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n

\n \n \n \n \n

\n Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n

\n

\n Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n

\n \n \n \n \n

\n Refactor this\n

\n

\n Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n

\n

\n Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n

\n

\n Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n

\n \n \n

\n Legami in cui mancano elettroni.\n

\n

\n Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n

\n \n \n

\n Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n

\n
    \n
  • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
    • \n
  • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
    • \n
\n

\n Maggiore impurezza porta a maggiore conduttività.\n

\n \n \n

\n Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n

\n \n \n Ottica (non l'abbiamo fatta)}>\n \n

\n I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n

\n \n \n

\n Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n

\n

\n Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n

\n

\n {r`\\lambda_{max} \\cdot T`} è costante.\n

\n \n \n

\n L'energia assorbita e emessa dai corpi neri è quantizzata.\n

\n \n \n

\n Un onda magnetica con un quanto di energia è detta fotone:\n

\n

\n {r`E_{fotone} = h \\cdot f`}\n

\n \n \n

\n A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n

\n

\n Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n

\n

\n Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n

\n

\n Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n

\n \n \n
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\Longleftrightarrow \Delta \vec{p} = 0`)))))),e(o.a,{title:"Moto rettilineo uniforme"},e(t.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(i.a,null,Tl(y||(y=Hl`s(t) = v \cdot \Delta t + s(0)`))))),e(t.a,{title:"Velocità"},e("p",null,"È costante:"),e("p",null,e(i.a,null,Tl(M||(M=Hl`v(t) = k`))))),e(t.a,{title:"Accelerazione"},e("p",null,"La velocità non varia:"),e("p",null,e(i.a,null,Tl(O||(O=Hl`a(t) = 0`))))),e(t.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(i.a,null,"f(t) = 0")))),e(o.a,{title:"Moto rettilineo uniformemente accelerato"},e(t.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(i.a,null,Tl(Q||(Q=Hl`s(t) = \frac{1}{2} a \cdot (\Delta t)^2 + v(0) \cdot (\Delta t) + s(0)`))))),e(t.a,{title:"Velocità"},e("p",null,"È una retta:"),e("p",null,e(i.a,null,Tl(j||(j=Hl`v(t) = a \Delta t + v(0)`))))),e(t.a,{title:"Accelerazione"},e("p",null,"È costante:"),e("p",null,e(i.a,null,Tl(K||(K=Hl`a(t) = k`))))),e(t.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(i.a,null,"f(t) = m a")))),e(o.a,{title:"Moto armonico semplice"},e(t.a,{title:"Ampiezza"},e("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),e("p",null,"(L'ampiezza di una sinusoide.)")),e(t.a,{title:"Velocità angolare"},e("p",null,"Indica quanto in fretta cambia la posizione del corpo."),e("p",null,"Dipende dal periodo:"),e("p",null,e(i.a,null,Tl(G||(G=Hl`\omega = \frac{2 \pi}{T}`))))),e(t.a,{title:"Spostamento"},e("p",null,"E' una sinusoide:"),e("p",null,e(i.a,null,Tl(J||(J=Hl`s(t) = A \sin (\omega \cdot t + \phi)`))))),e(t.a,{title:"Velocità"},e("p",null,"E' la sinusoide dello spostamento, sfasata di ",e(i.a,null,Tl(W||(W=Hl`\frac{\pi}{2}`))),":"),e("p",null,e(i.a,null,Tl(X||(X=Hl`v(t) = A \sin (\omega \cdot t + \phi + \frac{\pi}{2})`))))),e(t.a,{title:"Accelerazione"},e("p",null,"E' la sinusoide della velocità, sfasata di ",e(i.a,null,Tl($||($=Hl`\pi`))),":"),e("p",null,e(i.a,null,Tl(Y||(Y=Hl`a(t) = A \sin (\omega \cdot t + \phi + \pi)`))))),e(t.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(i.a,null,"f(t) = m a")))),e(o.a,{title:"Moti composti"},e(t.a,{title:"Moto parabolico"},e("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),e(t.a,{title:"Moto circolare uniforme"},e("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",e(i.a,null,Tl(Z||(Z=Hl`\frac{\pi}{2}`))),", sull'asse Y."))),e(o.a,{title:"Moto circolare uniforme"},e(t.a,null,e("h3",null,"Velocità angolare"),e("p",null,"Quanto cambia la fase nel tempo."),e("p",null,e(i.a,null,Tl(ee||(ee=Hl`\omega = \frac{2 \pi}{T}`))))),e(t.a,{title:"Fase"},e("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),e("p",null,"Si indica con ",e(i.a,null,Tl(le||(le=Hl`\phi`))),", e generalmente si usa in radianti.")),e(t.a,{title:"Velocità"},e("p",null,"Si applicano le formule per la circonferenza:"),e("p",null,e(i.a,null,Tl(ae||(ae=Hl`v = \frac{\Delta s}{t} = \frac{2 \pi \cdot r}{T} = \omega r`))))),e(t.a,{title:"Accelerazione"},e("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),e("p",null,e(i.a,null,Tl(ne||(ne=Hl`a = \frac{v^2}{r} = r \cdot \omega^2 = v \cdot \omega`))))),e(t.a,{title:"Forza centripeta"},e("p",null,"È verso il centro e si calcola con:"),e("p",null,e(i.a,null,Tl(ie||(ie=Hl`F = m \cdot a`)))))),e(o.a,{title:"Lavoro ed energia"},e(t.a,{title:"Lavoro"},e("p",null,"E' compiuto da una forza che sposta un corpo."),e("p",null,e(i.a,null,Tl(te||(te=Hl`W = \vec{F} \cdot \vec{s} = F \cdot \Delta s \cdot cos(\alpha )`)))),e("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),e(t.a,{title:"Energia cinetica"},e("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),e("p",null,e(i.a,null,Tl(oe||(oe=Hl`E_c = \frac{1}{2} m v^2`)))),e("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),e("p",null,e(i.a,null,Tl(re||(re=Hl`\Delta E_c = W`))))),e(t.a,{title:"Energia potenziale gravitazionale"},e("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),e("p",null,e(i.a,null,Tl(ue||(ue=Hl`E_{p_g} = m \cdot g \cdot h`)))),e("p",null,"(Con ",e(i.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),e(t.a,{title:"Energia potenziale elastica"},e("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),e("p",null,e(i.a,null,Tl(ce||(ce=Hl`E_{p_e} = \frac{1}{2} k x^2`))))),e(t.a,{title:"Forze conservative"},e("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),e("p",null,"Ad esempio, è conservativa la ",e("i",null,"forza di gravità"),", ma ",e("b",null,"non")," è conservativa la forza di attrito."),e("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),e("p",null,e(i.a,null,Tl(se||(se=Hl`E = E_k + E_p`))))),e(t.a,{title:"Potenza"},e("p",null,"È la velocità di trasferimento di energia:"),e("p",null,e(i.a,null,Tl(pe||(pe=Hl`P = \frac{\Delta E}{\Delta t}`)))))),e(o.a,{title:"Elettrostatica"},e(t.a,{title:"Carica elettrica"},e("p",null,"È una proprietà dei corpi che può essere ",e(r.a,null,"positiva")," o ",e(u.a,null,"negativa"),"."),e("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),e("p",null,"Esiste un'unità elementare: ",e(i.a,null,Tl(de||(de=Hl`C_{elettrone} = 1.602 \cdot 10^{-19}`))),"."),e("p",null,"Cariche ",e(r.a,null,"opp"),e(u.a,null,"oste")," si attraggono; cariche ",e(r.a,null,"uguali")," si respingono.")),e(t.a,{title:"Conduttori e isolanti"},e("p",null,"Più ",e("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),e("p",null,"I corpi in cui la carica si muove bene sono ",e("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",e("i",null,"isolanti"),"."),e("p",null,e("i",null,"Il corpo umano è un buon conduttore.")))),e(o.a,{title:"Polarizzazione"},e(t.a,{title:"Polarizzazione"},e("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),e(o.a,null,e(t.a,{title:"Messa a terra"},e("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",e("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",e(r.a,null,"cariche positive")," e ",e(u.a,null,"negative")," all'interno)."))),e(o.a,null,e(t.a,{title:"Polarizzazione per strofinio"},e("p",null,"Strofinando tra loro due corpi isolanti, essi si ",e("i",null,"polarizzeranno per strofinio"),".")),e(t.a,{title:"Polarizzazione per contatto"},e("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",e("i",null,"polarizzarsi per contatto"),".")),e(t.a,{title:"Polarizzazione per induzione"},e("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',e(r.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",e(u.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",e(r.a,null,"stesso segno")," più lontano possibile da esse."),e("p",null,"Mettendo a terra il conduttore, nuove cariche del ",e(u.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),e("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",e(u.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),e(o.a,{title:"Forza elettrica"},e(t.a,{title:"Legge di Coulomb"},e("p",null,"Due corpi carichi si attraggono tra loro con forza:"),e("p",null,e(i.a,null,Tl(me||(me=Hl`\left | \vec{F}_{elettrica} \right | = \frac{-k \cdot q_1 \cdot q_2}{s^2}`)))),e("p",null,e(i.a,null,Tl(ve||(ve=Hl`k`)))," è la ",e("i",null,"costante di Coulomb"),", e vale ",e(i.a,null,Tl(fe||(fe=Hl`k = 8.99 \cdot 10^9 \frac{N \cdot m^2}{C^2}`))),".")),e(t.a,{title:"Permeabilità dello spazio vuoto"},e("p",null,"La costante ",e(i.a,null,Tl(ge||(ge=Hl`k`)))," è in realtà dipendente da un altra costante, ",e(i.a,null,Tl(_e||(_e=Hl`\epsilon_0`))),", la ",e("i",null,"permeabilità del vuoto"),"."),e("p",null,e(i.a,null,Tl(he||(he=Hl`k = \frac{1}{4 \pi \cdot \epsilon_0}`)))),e("p",null,e(i.a,null,Tl(ze||(ze=Hl`\left | \vec{F}_{elettrica} \right | = \frac{q_1 \cdot q_2}{4 \pi \cdot \epsilon_0 \cdot s^2}`))))),e(t.a,{title:"Campo elettrico"},e("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),e("p",null,e(i.a,null,Tl(be||(be=Hl`\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k \cdot q}{s^2}`))))),e(t.a,{title:"Flusso elettrico"},e("p",null,'È la differenza tra "quanto" campo elettrico ',e(r.a,null,"entra")," e quanto campo elettrico ",e(u.a,null,"esce")," da una certa area."),e("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),e("p",null,e(i.a,null,Tl(Le||(Le=Hl`\Phi_E = \vec{E} \cdot \vec{A}`)))),e("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),e("p",null,e(i.a,null,Tl(qe||(qe=Hl`\Phi_E = \vec{E} \cdot \vec{A} = E_\perp \cdot A \cdot \cos(\alpha)`)))),e("p",null,e(c.a,null,"Circa. E' una specie di integrale..."))),e(t.a,{title:"Legge di Gauss per i campi elettrostatici"},e("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),e("p",null,e(i.a,null,Tl(Ce||(Ce=Hl`\Phi_E = 4 \pi \cdot k \cdot q = \frac{q}{\epsilon_0}`)))),e("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),e(o.a,{title:"Energia elettrica"},e(t.a,{title:"Energia potenziale elettrica"},e("p",null,"Un corpo carico vicino ad altre cariche possiede un'",e("i",null,"energia potenziale elettrica")," ",e(i.a,null,Tl(De||(De=Hl`U_e`))),"."))),e(o.a,{title:"Circuiti elettrici"},e(t.a,{title:e("span",null,"Potenziale elettrico ",e("small",null,"(tensione)"))},e("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),e("p",null,e(i.a,null,Tl(Ee||(Ee=Hl`V = \frac{U_e}{q}`)))),e("p",null,"La sua unità di misura è il Volt (",e(i.a,null,Tl(Fe||(Fe=Hl`V`))),")."),e("p",null,"In una batteria è detto ",e("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),e(t.a,{title:e("span",null,"Corrente elettrica ",e("small",null,"(intensità)"))},e("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),e("p",null,e(i.a,null,Tl(Ae||(Ae=Hl`I = \frac{\Delta q}{\Delta t}`)))),e("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),e("p",null,"La sua unità di misura è l'Ampere (",e(i.a,null,Tl(Pe||(Pe=Hl`A`))),").")),e(t.a,{title:e("span",null,"Corrente continua ",e("small",null,"(",e("abbr",{title:"Direct Current"},"DC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente è costante.")),e(t.a,{title:e("span",null,"Corrente alternata ",e("small",null,"(",e("abbr",{title:"Alternate Current"},"AC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),e(t.a,{title:"Potenza elettrica"},e("p",null,"Possiamo calcolare la potenza di un circuito:"),e("p",null,e(i.a,null,Tl(Se||(Se=Hl`P = \frac{\Delta U_e}{\Delta t} = I \cdot \Delta V = I^2 \cdot R = \frac{(\Delta V)^2}{R}`)))))),e(o.a,{title:"Elementi di un circuito"},e(t.a,{title:"Resistore"},e("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),e("p",null,"Il potenziale utilizzato è pari a:"),e("p",null,e(i.a,null,Tl(Ie||(Ie=Hl`V = R \cdot I`)))),e("p",null,"Dove ",e(i.a,null,Tl(we||(we=Hl`R`)))," è una costante detta ",e("i",null,"resistenza")," con unità di misura Ohm (",e(i.a,null,Tl(ke||(ke=Hl`\Omega`))),")."),e("p",null,"La resistenza di un conduttore vale:"),e("p",null,e(i.a,null,Tl(xe||(xe=Hl`R = \rho \frac{L_{unghezza}}{A_{rea}}`)))),e("p",null,e(i.a,null,Tl(Be||(Be=Hl`\rho`)))," è la ",e("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),e("p",null,e(i.a,null,Tl(Ne||(Ne=Hl`\rho = \rho_0 (1 + \alpha(T - T_0))`))))),e(t.a,{title:"Condensatore"},e("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),e("p",null,"Per farlo, cattura cariche ",e(r.a,null,"positive")," e ",e(u.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),e("p",null,"Ha una ",e("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),e("p",null,e(i.a,null,Tl(Ue||(Ue=Hl`C = \frac{q_{massima}}{\Delta V}`)))),e("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),e("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),e("p",null,e(i.a,null,Tl(Ve||(Ve=Hl`C_{nuova} = \kappa \cdot \frac{\epsilon_0 \cdot A}{s}`)))),e("p",null,"Dove ",e(i.a,null,Tl(He||(He=Hl`\kappa`)))," è la ",e("i",null,"costante dielettrica relativa")," del materiale inserito, ",e(i.a,null,Tl(Te||(Te=Hl`A`)))," l'area di una armatura e ",e(i.a,null,Tl(Re||(Re=Hl`s`)))," la distanza tra le due armature."),e("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",e("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",e("i",null,"breakdown"),"."),e("p",null,"La sua unità di misura è il Farad (",e(i.a,null,Tl(ye||(ye=Hl`Fa`))),")")),e(t.a,{title:"Amperometro"},e("p",null,"Misura la corrente elettrica se messo in serie."),e("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),e(t.a,{title:"Voltmetro"},e("p",null,"Misura la differenza di potenziale se messo in parallelo."),e("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),e(o.a,{title:"Principi di Kirchhoff"},e(t.a,{title:"Legge dei nodi"},e("p",null,"Per nodo si intende un qualsiasi punto del circuito."),e("p",null,"Da un nodo entra ed esce la stessa corrente.")),e(t.a,{title:"Legge delle maglie"},e("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),e("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),e(o.a,{title:"Serie e Parallelo"},e(t.a,{title:"Circuito in serie"},e("p",null,"Più parti di circuito sono ",e("i",null,"in serie")," se sono consecutive e senza biforcazioni."),e("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),e(t.a,{title:"Circuito in parallelo"},e("p",null,"Più parti di circuito sono ",e("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),e("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),e(o.a,{title:"Resistenze equivalenti"},e(t.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),e("p",null,e(i.a,null,Tl(Me||(Me=Hl`R_{serie} = \sum_{i=1}^{n} R_i`))))),e(t.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),e("p",null,e(i.a,null,Tl(Oe||(Oe=Hl`R_{parallelo} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}}`)))))),e(o.a,{title:"Condensatori equivalenti"},e(t.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),e("p",null,e(i.a,null,Tl(Qe||(Qe=Hl`C_{serie} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}`))))),e(t.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),e("p",null,e(i.a,null,Tl(je||(je=Hl`C_{parallelo} = \sum_{i=1}^{n} C_n`)))))),e(o.a,{title:"Magnetismo"},e(t.a,{title:"Permeabilità magnetica dello spazio vuoto"},e("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),e("p",null,e(i.a,null,Tl(Ke||(Ke=Hl`\mu_0 = 4 \pi \cdot 10^{-7} \frac{H}{m}`)))," (",e(i.a,null,Tl(Ge||(Ge=Hl`\frac{N}{A^2}`))),")")),e(t.a,{title:"Campo magnetico"},e("p",null,"Come un campo elettrico, ma per i magneti."),e("p",null,"Il suo simbolo è ",e(i.a,null,Tl(Je||(Je=Hl`B`))),", e la sua unità di misura è il Tesla (",e(i.a,null,"T"),").")),e(t.a,{title:"Flusso magnetico"},e("p",null,'È "quanto" campo magnetico ',e("b",null,"attraversa")," un percorso chiuso."),e("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),e("p",null,e(i.a,null,Tl(We||(We=Hl`\Phi_{B_{i}} = \vec{B} \cdot \vec{L}_n = B \cdot L_i \cdot \sin(\alpha) = B_\parallel \cdot L_i`)))),e("p",null,e(i.a,null,Tl(Xe||(Xe=Hl`\Phi_{B} = \sum_{i=0}^{n_{lati}} \Phi_{Bn}`)))),e("p",null,"La sua unità di misura è il Weber (",e(i.a,null,Tl($e||($e=Hl`Wb = T \cdot m^2`))),").")),e(t.a,{title:"Legge di Gauss per i campi magnetici"},e("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),e("p",null,"Ovvero, non esistono monopoli magnetici.")),e(t.a,{title:"Legge di Ampère"},e("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),e("p",null,e(i.a,null,Tl(Ye||(Ye=Hl`\Phi_B = \mu_0 \cdot I`)))))),e(o.a,{title:"Forze magnetiche"},e(t.a,{title:e("span",null,"Forza magnetica su carica puntiforme ",e("small",null,"(Forza di Lorentz)"))},e("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),e("p",null,e(i.a,null,Tl(Ze||(Ze=Hl`\vec{F}_{B} = q \cdot (\vec{v} \times \vec{B})`)))),e("p",null,"Dove ",e(i.a,null,Tl(el||(el=Hl`\vec{B}`)))," è l'intensità del campo magnetico e ",e(i.a,null,Tl(ll||(ll=Hl`\vec{v}`)))," la velocità della carica considerata."),e("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),e("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),e(t.a,{title:"Forza magnetica in un filo"},e("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),e("p",null,e(i.a,null,Tl(al||(al=Hl`\vec{F}_{magnetica} = I \cdot (\vec{L} \times \vec{B})`)))," ",e("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),e("p",null,"Dove ",e(i.a,null,Tl(nl||(nl=Hl`I`)))," è la corrente elettrica, ",e(i.a,null,Tl(il||(il=Hl`\vec{L}`)))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),e(o.a,{title:"Campi magnetici"},e(t.a,{title:"Campo magnetico in una spira"},e("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),e(t.a,{title:"Campo magnetico di un solenoide"},e("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),e("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),e("p",null,e(i.a,null,Tl(tl||(tl=Hl`\left | \vec{B} \right | = \mu_0 \cdot I \cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}`))))),e(t.a,{title:"Legge di Oersted"},e("p",null,e("i",null,"Caso particolare della ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),e("p",null,"Il modulo del campo magnetico ",e(i.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",e(i.a,null,"I")," alla distanza ",e(i.a,null,"s")," è:"),e("p",null,e(i.a,null,Tl(ol||(ol=Hl`\left | \vec{B} \right | = \frac{\mu \cdot I}{2 \pi r}`)))),e("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),e("p",null,"Due fili attraversati dalla ",e(r.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",e(r.a,null,"corr"),e(u.a,null,"enti")," ",e(r.a,null,"opp"),e(u.a,null,"oste")," si respingono."))),e(o.a,{title:"Induzione elettromagnetica"},e(t.a,{title:"Forza elettromotrice indotta"},e("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),e("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),e("p",null,"Essa vale:"),e("p",null,e(i.a,null,Tl(rl||(rl=Hl`\Delta V_{indotta} = v \cdot B \cdot L`)))),e("p",null,"Dove ",e(i.a,null,"v")," è la velocità del conduttore, ",e(i.a,null,"B")," è l'intensità del campo magnetico ed ",e(i.a,null,"L")," è la lunghezza del conduttore.")),e(t.a,{title:"Flusso magnetico in una spira"},e("p",null,"In un campo magnetico ",e(i.a,null,Tl(ul||(ul=Hl`B`)))," uniforme e perpendicolare al piano di una spira di area ",e(i.a,null,Tl(cl||(cl=Hl`A`))),", il flusso magnetico si può determinare con la ",e("i",null,"Legge di Faraday-Neumann-Lenz"),":"),e("p",null,e(i.a,null,Tl(sl||(sl=Hl`\Phi_B = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos(\alpha)`)))))),e(o.a,null,e(t.a,{title:"Legge di Faraday-Neumann-Lenz"},e("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),e("p",null,e(i.a,null,Tl(pl||(pl=Hl`\Delta V_{indotta} = - \frac{\Delta \Phi_B}{\Delta t}`)))),e("p",null,"Il meno è dovuto alla ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),e(t.a,{title:"Faraday in un solenoide"},e("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),e("p",null,e(i.a,null,Tl(dl||(dl=Hl`\Delta V_{indotta} = - \frac{N \cdot \Delta \Phi_{B_{spira}}}{\Delta t} = - \frac{N \cdot B \cdot A \cdot cos(\alpha)}{\Delta t}`)))),e("p",null,"Dove ",e(i.a,null,Tl(ml||(ml=Hl`N`)))," è il numero delle spire del solenoide.")),e(t.a,{title:"Legge di Ampère-Maxwell"},e("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),e(o.a,{title:"Elettromagnetismo"},e(t.a,{title:"Onde elettromagnetiche"},e("p",null,"Nel vuoto, il campo elettrico ",e(i.a,null,Tl(vl||(vl=Hl`E`)))," e il campo magnetico ",e(i.a,null,Tl(fl||(fl=Hl`B`)))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),e("p",null,"Si dice quindi che sono ",e("i",null,"onde elettromagnetiche"),"."),e("p",null,"Esse sono legate dalla relazione:"),e("p",null,e(i.a,null,Tl(gl||(gl=Hl`E = c \cdot B`)))),e("p",null,"Dove ",e(i.a,null,Tl(_l||(_l=Hl`c`)))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),e("p",null,e(i.a,null,Tl(hl||(hl=Hl`c = \frac{1}{\sqrt{\epsilon_0 \cdot \mu_0}} = 3.00 \cdot 10^8 \frac{m}{s}`))))),e(t.a,{title:"Formula delle onde"},e("p",null,e(i.a,null,Tl(zl||(zl=Hl`A(t) = A_{max} \cdot \sin \left ( \frac{2 \pi}{\lambda} - \omega t + \phi \right )`)))),e("p",null,"Dove ",e(i.a,null,Tl(bl||(bl=Hl`A_{max}`)))," è l'ampiezza massima che può avere l'onda, ",e(i.a,null,Tl(Ll||(Ll=Hl`\frac{2 \pi}{\lambda} = \left | \vec{k} \right |`)))," è il vettore d'onda, ",e(i.a,null,Tl(ql||(ql=Hl`\omega`)))," la frequenza angolare e ",e(i.a,null,Tl(Cl||(Cl=Hl`\phi`)))," la fase."))),e(o.a,{title:"Spettroscopia"},e(t.a,{title:"Emissione"},e("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",e("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),e("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),e("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),e("p",null,e(i.a,null,Tl(Dl||(Dl=Hl`\frac{1}{\lambda} = R \left ( \frac{1}{4} - \frac{1}{n^2} \right )`)))),e("p",null,"Con ",e(i.a,null,Tl(El||(El=Hl`R = 1.097 \cdot 10^7 \frac{1}{m}`))),", detta costante di Rydberg, e ",e(i.a,null,Tl(Fl||(Fl=Hl`n`)))," un numero intero.")),e(t.a,{title:"Grandezza quantizzata"},e("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),e("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),e("p",null,"Energia, momento angolare e raggio sono quantizzati."),e("p",null,"Nota costante quantica è ",e(i.a,null,Tl(Al||(Al=Hl`h`))),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",e(i.a,null,Tl(Pl||(Pl=Hl`\hbar = \left ( \frac{h}{2 \pi} \right )`))),"."))),e(o.a,null,e(t.a,{title:"Modello di Bohr"},e("p",null,"L'energia degli elettroni è quantizzata."),e("p",null,"Inoltre, per essi è valido che:"),e("p",null,e(i.a,null,Tl(Sl||(Sl=Hl`m \cdot v_n \cdot 2 \pi \cdot r = n \cdot h`)))),e("p",null,"Ancora, il raggio delle orbite è uguale a:"),e("p",null,e(i.a,null,Tl(Il||(Il=Hl`r_n = n^2 \cdot a_0 = n^2 \cdot \frac{\hbar}{m_{elettrone} \cdot k \cdot e^2} `)))),e("p",null,"Con ",e(i.a,null,Tl(wl||(wl=Hl`a_0 = \left ( \frac{h}{2 \pi} \right )^2 \cdot \frac{1}{m_{elettrone} \cdot k \cdot e^2} = 5.29 \cdot 10^{-11} m`))),"."),e("p",null,"Infine, in ogni stato, l'energia è pari a:"),e("p",null,e(i.a,null,Tl(kl||(kl=Hl`E_n = \frac{1}{n^2} \cdot E_1 = - \frac{1}{n^2} \cdot \frac{a_0^2}{2 \cdot m \cdot \hbar^4} = - \frac{1}{n^2} \cdot \frac{m_{elettrone} \cdot k^2 \cdot e^4}{2 \cdot \hbar^2}`)))),e("p",null,"Due elettroni non possono occupare lo stesso stato."),e("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),e(o.a,null,e(t.a,{title:"Nei solidi"},e("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),e("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),e(o.a,{title:"Semiconduttori"},e(t.a,{title:"Semiconduttori"},e("p",null,e(c.a,null,"Refactor this")),e("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",e(i.a,null,Tl(xl||(xl=Hl`10^1 eV`))),", allora il corpo è un isolante."),e("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),e("p",null,"Se il gap è invece dell'ordine di grandezza di ",e(i.a,null,Tl(Bl||(Bl=Hl`1 eV`))),", allora il corpo è un semiconduttore.")),e(t.a,{title:"Lacune"},e("p",null,"Legami in cui ",e(r.a,null,"mancano elettroni"),"."),e("p",null,e(u.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",e(r.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),e(t.a,{title:"Accettori e donori"},e("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),e("ul",null,e("li",null,"Con numero atomico maggiore, un semiconduttore di ",e(u.a,null,"tipo N")," con ",e(u.a,null,"elettroni in eccesso")," liberi di scorrere."),e("li",null,"Con numero atomico minore, un semiconduttore di ",e(r.a,null,"tipo P")," con ",e(r.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),e("p",null,"Maggiore impurezza porta a maggiore conduttività.")),e(t.a,{title:"Temperatura"},e("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",e(u.a,null,"elettroni")," e ",e(r.a,null,"lacune"),"."))),e(o.a,{title:e("span",null,"Ottica ",e("small",null,"(non l'abbiamo fatta)"))},e(t.a,{title:"Assorbimento e riflessione"},e("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),e(t.a,{title:"Corpo nero"},e("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),e("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",e(i.a,null,Tl(Nl||(Nl=Hl`\lambda`)))," variabile in base alla temperatura."),e("p",null,e(i.a,null,Tl(Ul||(Ul=Hl`\lambda_{max} \cdot T`)))," è costante.")),e(t.a,{title:"Teoria di Planck per il corpo nero"},e("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),e(t.a,{title:"Fotone"},e("p",null,"Un onda magnetica con un quanto di energia è detta ",e("i",null,"fotone"),":"),e("p",null,e(i.a,null,Tl(Vl||(Vl=Hl`E_{fotone} = h \cdot f`))))),e(t.a,{title:"Effetto fotoelettrico"},e("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),e("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),e("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),e("p",null,"Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.")))))}}}.call(this,a("hosL").h)},eCjK:function(e){e.exports={split:"split__3dL9r",splitparent:"splitparent__2H-vS",splitchild:"splitchild__1B-Jt"}},h7i1:function(e,l,a){"use strict";(function(e){a.d(l,"a",(function(){return o}));var n=a("56OW"),i=a.n(n),t=a("hosL");class o extends t.Component{render(){return e("span",{class:i.a.plus},this.props.children)}}}).call(this,a("hosL").h)},jXlC:function(e,l,a){"use strict";(function(e){a.d(l,"a",(function(){return o}));var n=a("3k98"),i=a.n(n),t=a("hosL");class o extends t.Component{render(){return 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(\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)`)))),l("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),l(t.a,{title:"Differenza"},l("p",null,"Alla fine è sempre una somma:"),l("p",null,l(n.a,null,Me(v||(v=Ve`\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)`)))),l("p",null,"Produce il vettore che parte da ",l(n.a,null,"w")," e arriva a ",l(n.a,null,"v"),".")),l(t.a,{title:"Prodotto scalare"},l("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),l("p",null,l(n.a,null,Me(g||(g=Ve`\vec{v} \cdot \vec{w} = \left | \vec{v} \right | \left | \vec{w} \right | \cos \alpha`)))),l("p",null,"Produce il modulo della proiezione di ",l(n.a,null,Me(f||(f=Ve`\vec{a}`)))," su ",l(n.a,null,Me(h||(h=Ve`\vec{b}`))),".")),l(t.a,{title:"Prodotto vettoriale"},l("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),l("ul",null,l("li",null,l(n.a,null,Me(z||(z=Ve`\vec{c} = \vec{a} \times \vec{b}`)))),l("li",null,l(n.a,null,Me(_||(_=Ve`\left | \vec{c} \right | = \left | \vec{a} \right | \cdot \left | \vec{b} \right | \cdot \sin(\alpha)`)))),l("li",null,l("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),l("p",null,"Non è commutativo!"))),l(o.a,{title:"Leggi di Newton"},l(t.a,{title:"1ᵃ: Inerzia"},l("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),l("p",null,l(n.a,null,Me(b||(b=Ve`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta v = 0`))))),l(t.a,{title:"2ᵃ: Proporzionalità"},l("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",l("i",null,"massa"),"."),l("p",null,l(n.a,null,Me(L||(L=Ve`\Sigma \vec{F} = m \vec{a}`))))),l(t.a,{title:"3ᵃ: Azione e reazione"},l("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),l("p",null,l(n.a,null,Me(q||(q=Ve`\vec{F}_{21} = -\vec{F}_{12}`)))))),l(o.a,{title:"Forza di gravità"},l(t.a,{title:"Tra due corpi"},l("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),l("p",null,l(n.a,null,Me(C||(C=Ve`\left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}`)))),l("p",null,l(n.a,null,"G")," è la ",l("i",null,"costante di gravitazione universale")," e vale:"),l("p",null,l(n.a,null,Me(D||(D=Ve`G = 6.67 \cdot 10^{-11} \frac{N m^2}{{kg}^2}`))))),l(t.a,{title:"Verso la Terra"},l("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",l("i",null,"peso")," uguale a:"),l("p",null,l(n.a,null,Me(P||(P=Ve`\left | \vec{F} \right | = g m`)))),l("p",null,l(n.a,null,"g")," è la ",l("i",null,"costante di gravità")," della Terra, e vale:"),l("p",null,l(n.a,null,Me(A||(A=Ve`g = 9.81 \frac{m}{s^2}`))))),l(t.a,{title:"Su pianeti diversi"},l("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),l("p",null,l(n.a,null,Me(F||(F=Ve`\left | \vec{F} \right | = g m`)))),l("p",null,"L'unica differenza è che cambia la ",l("i",null,"costante di gravità"),":"),l("p",null,l(n.a,null,Me(E||(E=Ve`g_{luna} = 1.62 \frac{m}{s^2}`)))),l("p",null,l(n.a,null,Me(S||(S=Ve`g_{marte} = 3.71 \frac{m}{s^2}`)))))),l(o.a,{title:"Forze di contatto"},l(t.a,{title:"Normale"},l("p",null,"Si oppone alle forze applicate alla superficie di contatto."),l("p",null,"Un libro appoggiato su un tavolo ha la ",l("b",null,"forza di gravità")," che lo attira verso il terreno e la ",l("b",null,"forza normale")," che lo trattiene dal cadere.")),l(t.a,{title:"Attrito statico"},l("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),l("p",null,l(n.a,null,Me(I||(I=Ve`\left | \vec{F} \right | \leq \mu_{s} \left | \vec{F}_{normale} \right |`))))),l(t.a,{title:"Attrito dinamico"},l("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),l("p",null,l(n.a,null,Me(k||(k=Ve`\left | \vec{F} \right | \leq \mu_{d} \left | \vec{F}_{normale} \right |`))))),l(t.a,{title:"Tensione"},l("p",null,"E' forza trasmessa tra due estremi di una fune."),l("p",null,"Può essere redirezionata per mezzo di carrucole.")),l(t.a,{title:"Elastica"},l("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),l("p",null,l(n.a,null,Me(w||(w=Ve`F = -k x`)))),l("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),l(o.a,{title:"Cinematica"},l(t.a,{title:"Spostamento"},l("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),l("p",null,l(n.a,null,Me(x||(x=Ve`\Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)`))))),l(t.a,{title:"Velocità"},l("p",null,"È un vettore che misura la variazione di posizione nel tempo."),l("p",null,l(n.a,null,Me(B||(B=Ve`\vec{v} = \frac{\Delta \vec{s}}{\Delta t}`)))),l("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",l("i",null,"velocità istantanea"),":"),l("p",null,l(n.a,null,Me(N||(N=Ve`\vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{s}}{\Delta t} = \frac{d \vec{s}}{dt}`))))),l(t.a,{title:"Accelerazione"},l("p",null,"È un vettore che misura la variazione di velocità nel tempo."),l("p",null,l(n.a,null,Me(T||(T=Ve`\vec{a} = \frac{\Delta \vec{v}}{\Delta t}`)))),l("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",l("i",null,"accelerazione istantanea"),":"),l("p",null,l(n.a,null,Me(V||(V=Ve`\vec{a} = \lim_{\Delta v \to 0} \frac{\Delta \vec{v}}{\Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}`))))),l(t.a,{title:l("span",null,"Quantità di moto ",l("small",null,"(momento lineare)"))},l("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),l("p",null,l(n.a,null,Me(M||(M=Ve`\vec{p} = m \vec{v}`)))),l("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),l("p",null,l(n.a,null,Me(R||(R=Ve`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta \vec{p} = 0`)))))),l(o.a,{title:"Moto rettilineo uniforme"},l(t.a,{title:"Spostamento"},l("p",null,"La ",l("i",null,"legge oraria")," è:"),l("p",null,l(n.a,null,Me(y||(y=Ve`s(t) = v \cdot \Delta t + s(0)`))))),l(t.a,{title:"Velocità"},l("p",null,"È costante:"),l("p",null,l(n.a,null,Me(U||(U=Ve`v(t) = k`))))),l(t.a,{title:"Accelerazione"},l("p",null,"La velocità non varia:"),l("p",null,l(n.a,null,Me(Q||(Q=Ve`a(t) = 0`))))),l(t.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(n.a,null,"f(t) = 0")))),l(o.a,{title:"Moto rettilineo uniformemente accelerato"},l(t.a,{title:"Spostamento"},l("p",null,"La ",l("i",null,"legge oraria")," è:"),l("p",null,l(n.a,null,Me(G||(G=Ve`s(t) = \frac{1}{2} a \cdot (\Delta t)^2 + v(0) \cdot (\Delta t) + s(0)`))))),l(t.a,{title:"Velocità"},l("p",null,"È una retta:"),l("p",null,l(n.a,null,Me(O||(O=Ve`v(t) = a \Delta t + v(0)`))))),l(t.a,{title:"Accelerazione"},l("p",null,"È costante:"),l("p",null,l(n.a,null,Me(W||(W=Ve`a(t) = k`))))),l(t.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(n.a,null,"f(t) = m a")))),l(o.a,{title:"Moto armonico semplice"},l(t.a,{title:"Ampiezza"},l("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),l("p",null,"(L'ampiezza di una sinusoide.)")),l(t.a,{title:"Velocità angolare"},l("p",null,"Indica quanto in fretta cambia la posizione del corpo."),l("p",null,"Dipende dal periodo:"),l("p",null,l(n.a,null,Me(J||(J=Ve`\omega = \frac{2 \pi}{T}`))))),l(t.a,{title:"Spostamento"},l("p",null,"E' una sinusoide:"),l("p",null,l(n.a,null,Me(K||(K=Ve`s(t) = A \sin (\omega \cdot t + \phi)`))))),l(t.a,{title:"Velocità"},l("p",null,"E' la sinusoide dello spostamento, sfasata di ",l(n.a,null,Me(X||(X=Ve`\frac{\pi}{2}`))),":"),l("p",null,l(n.a,null,Me(j||(j=Ve`v(t) = A \sin (\omega \cdot t + \phi + \frac{\pi}{2})`))))),l(t.a,{title:"Accelerazione"},l("p",null,"E' la sinusoide della velocità, sfasata di ",l(n.a,null,Me(H||(H=Ve`\pi`))),":"),l("p",null,l(n.a,null,Me(Y||(Y=Ve`a(t) = A \sin (\omega \cdot t + \phi + \pi)`))))),l(t.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(n.a,null,"f(t) = m a")))),l(o.a,{title:"Moti composti"},l(t.a,{title:"Moto parabolico"},l("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),l(t.a,{title:"Moto circolare uniforme"},l("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",l(n.a,null,Me(Z||(Z=Ve`\frac{\pi}{2}`))),", sull'asse Y."))),l(o.a,{title:"Moto circolare uniforme"},l(t.a,null,l("h3",null,"Velocità angolare"),l("p",null,"Quanto cambia la fase nel tempo."),l("p",null,l(n.a,null,Me($||($=Ve`\omega = \frac{2 \pi}{T}`))))),l(t.a,{title:"Fase"},l("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),l("p",null,"Si indica con ",l(n.a,null,Me(ll||(ll=Ve`\phi`))),", e generalmente si usa in radianti.")),l(t.a,{title:"Velocità"},l("p",null,"Si applicano le formule per la circonferenza:"),l("p",null,l(n.a,null,Me(el||(el=Ve`v = \frac{\Delta s}{t} = \frac{2 \pi \cdot r}{T} = \omega r`))))),l(t.a,{title:"Accelerazione"},l("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),l("p",null,l(n.a,null,Me(al||(al=Ve`a = \frac{v^2}{r} = r \cdot \omega^2 = v \cdot \omega`))))),l(t.a,{title:"Forza centripeta"},l("p",null,"È verso il centro e si calcola con:"),l("p",null,l(n.a,null,Me(il||(il=Ve`F = m \cdot a`)))))),l(o.a,{title:"Lavoro ed energia"},l(t.a,{title:"Lavoro"},l("p",null,"E' compiuto da una forza che sposta un corpo."),l("p",null,l(n.a,null,Me(nl||(nl=Ve`W = \vec{F} \cdot \vec{s} = F \cdot \Delta s \cdot cos(\alpha )`)))),l("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),l(t.a,{title:"Energia cinetica"},l("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),l("p",null,l(n.a,null,Me(tl||(tl=Ve`E_c = \frac{1}{2} m v^2`)))),l("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),l("p",null,l(n.a,null,Me(ol||(ol=Ve`\Delta E_c = W`))))),l(t.a,{title:"Energia potenziale gravitazionale"},l("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),l("p",null,l(n.a,null,Me(rl||(rl=Ve`E_{p_g} = m \cdot g \cdot h`)))),l("p",null,"(Con ",l(n.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),l(t.a,{title:"Energia potenziale elastica"},l("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),l("p",null,l(n.a,null,Me(ul||(ul=Ve`E_{p_e} = \frac{1}{2} k x^2`))))),l(t.a,{title:"Forze conservative"},l("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),l("p",null,"Ad esempio, è conservativa la ",l("i",null,"forza di gravità"),", ma ",l("b",null,"non")," è conservativa la forza di attrito."),l("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),l("p",null,l(n.a,null,Me(cl||(cl=Ve`E = E_k + E_p`))))),l(t.a,{title:"Potenza"},l("p",null,"È la velocità di trasferimento di energia:"),l("p",null,l(n.a,null,Me(sl||(sl=Ve`P = \frac{\Delta E}{\Delta t}`)))))),l(o.a,{title:"Elettrostatica"},l(t.a,{title:"Carica elettrica"},l("p",null,"È una proprietà dei corpi che può essere ",l(r.a,null,"positiva")," o ",l(u.a,null,"negativa"),"."),l("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),l("p",null,"Esiste un'unità elementare: ",l(n.a,null,Me(pl||(pl=Ve`C_{elettrone} = 1.602 \cdot 10^{-19}`))),"."),l("p",null,"Cariche ",l(r.a,null,"opp"),l(u.a,null,"oste")," si attraggono; cariche ",l(r.a,null,"uguali")," si respingono.")),l(t.a,{title:"Conduttori e isolanti"},l("p",null,"Più ",l("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),l("p",null,"I corpi in cui la carica si muove bene sono ",l("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",l("i",null,"isolanti"),"."),l("p",null,l("i",null,"Il corpo umano è un buon conduttore.")))),l(o.a,{title:"Polarizzazione"},l(t.a,{title:"Polarizzazione"},l("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),l(o.a,null,l(t.a,{title:"Messa a terra"},l("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",l("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",l(r.a,null,"cariche positive")," e ",l(u.a,null,"negative")," all'interno)."))),l(o.a,null,l(t.a,{title:"Polarizzazione per strofinio"},l("p",null,"Strofinando tra loro due corpi isolanti, essi si ",l("i",null,"polarizzeranno per strofinio"),".")),l(t.a,{title:"Polarizzazione per contatto"},l("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",l("i",null,"polarizzarsi per contatto"),".")),l(t.a,{title:"Polarizzazione per induzione"},l("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',l(r.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",l(u.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",l(r.a,null,"stesso segno")," più lontano possibile da esse."),l("p",null,"Mettendo a terra il conduttore, nuove cariche del ",l(u.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),l("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",l(u.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),l(o.a,{title:"Forza elettrica"},l(t.a,{title:"Legge di Coulomb"},l("p",null,"Due corpi carichi si attraggono tra loro con forza:"),l("p",null,l(n.a,null,Me(dl||(dl=Ve`\left | \vec{F}_{elettrica} \right | = \frac{-k \cdot q_1 \cdot q_2}{s^2}`)))),l("p",null,l(n.a,null,Me(ml||(ml=Ve`k`)))," è la ",l("i",null,"costante di Coulomb"),", e vale ",l(n.a,null,Me(vl||(vl=Ve`k = 8.99 \cdot 10^9 \frac{N \cdot m^2}{C^2}`))),".")),l(t.a,{title:"Permeabilità dello spazio vuoto"},l("p",null,"La costante ",l(n.a,null,Me(gl||(gl=Ve`k`)))," è in realtà dipendente da un altra costante, ",l(n.a,null,Me(fl||(fl=Ve`\epsilon_0`))),", la ",l("i",null,"permeabilità del vuoto"),"."),l("p",null,l(n.a,null,Me(hl||(hl=Ve`k = \frac{1}{4 \pi \cdot \epsilon_0}`)))),l("p",null,l(n.a,null,Me(zl||(zl=Ve`\left | \vec{F}_{elettrica} \right | = \frac{q_1 \cdot q_2}{4 \pi \cdot \epsilon_0 \cdot s^2}`))))),l(t.a,{title:"Campo elettrico"},l("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),l("p",null,l(n.a,null,Me(_l||(_l=Ve`\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k \cdot q}{s^2}`))))),l(t.a,{title:"Flusso elettrico"},l("p",null,'È la differenza tra "quanto" campo elettrico ',l(r.a,null,"entra")," e quanto campo elettrico ",l(u.a,null,"esce")," da una certa area."),l("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),l("p",null,l(n.a,null,Me(bl||(bl=Ve`\Phi_E = \vec{E} \cdot \vec{A}`)))),l("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),l("p",null,l(n.a,null,Me(Ll||(Ll=Ve`\Phi_E = \vec{E} \cdot \vec{A} = E_\perp \cdot A \cdot \cos(\alpha)`)))),l("p",null,l(c.a,null,"Circa. E' una specie di integrale..."))),l(t.a,{title:"Legge di Gauss per i campi elettrostatici"},l("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),l("p",null,l(n.a,null,Me(ql||(ql=Ve`\Phi_E = 4 \pi \cdot k \cdot q = \frac{q}{\epsilon_0}`)))),l("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),l(o.a,{title:"Energia elettrica"},l(t.a,{title:"Energia potenziale elettrica"},l("p",null,"Un corpo carico vicino ad altre cariche possiede un'",l("i",null,"energia potenziale elettrica")," ",l(n.a,null,Me(Cl||(Cl=Ve`U_e`))),"."))),l(o.a,{title:"Circuiti elettrici"},l(t.a,{title:l("span",null,"Potenziale elettrico ",l("small",null,"(tensione)"))},l("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),l("p",null,l(n.a,null,Me(Dl||(Dl=Ve`V = \frac{U_e}{q}`)))),l("p",null,"La sua unità di misura è il Volt (",l(n.a,null,Me(Pl||(Pl=Ve`V`))),")."),l("p",null,"In una batteria è detto ",l("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),l(t.a,{title:l("span",null,"Corrente elettrica ",l("small",null,"(intensità)"))},l("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),l("p",null,l(n.a,null,Me(Al||(Al=Ve`I = \frac{\Delta q}{\Delta t}`)))),l("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),l("p",null,"La sua unità di misura è l'Ampere (",l(n.a,null,Me(Fl||(Fl=Ve`A`))),").")),l(t.a,{title:l("span",null,"Corrente continua ",l("small",null,"(",l("abbr",{title:"Direct Current"},"DC"),")"))},l("p",null,"Quando in un circuito la direzione della corrente è costante.")),l(t.a,{title:l("span",null,"Corrente alternata ",l("small",null,"(",l("abbr",{title:"Alternate Current"},"AC"),")"))},l("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),l(t.a,{title:"Potenza elettrica"},l("p",null,"Possiamo calcolare la potenza di un circuito:"),l("p",null,l(n.a,null,Me(El||(El=Ve`P = \frac{\Delta U_e}{\Delta t} = I \cdot \Delta V = I^2 \cdot R = \frac{(\Delta V)^2}{R}`)))))),l(o.a,{title:"Elementi di un circuito"},l(t.a,{title:"Resistore"},l("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),l("p",null,"Il potenziale utilizzato è pari a:"),l("p",null,l(n.a,null,Me(Sl||(Sl=Ve`V = R \cdot I`)))),l("p",null,"Dove ",l(n.a,null,Me(Il||(Il=Ve`R`)))," è una costante detta ",l("i",null,"resistenza")," con unità di misura Ohm (",l(n.a,null,Me(kl||(kl=Ve`\Omega`))),")."),l("p",null,"La resistenza di un conduttore vale:"),l("p",null,l(n.a,null,Me(wl||(wl=Ve`R = \rho \frac{L_{unghezza}}{A_{rea}}`)))),l("p",null,l(n.a,null,Me(xl||(xl=Ve`\rho`)))," è la ",l("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),l("p",null,l(n.a,null,Me(Bl||(Bl=Ve`\rho = \rho_0 (1 + \alpha(T - T_0))`))))),l(t.a,{title:"Condensatore"},l("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),l("p",null,"Per farlo, cattura cariche ",l(r.a,null,"positive")," e ",l(u.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),l("p",null,"Ha una ",l("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),l("p",null,l(n.a,null,Me(Nl||(Nl=Ve`C = \frac{q_{massima}}{\Delta V}`)))),l("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),l("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),l("p",null,l(n.a,null,Me(Tl||(Tl=Ve`C_{nuova} = \kappa \cdot \frac{\epsilon_0 \cdot A}{s}`)))),l("p",null,"Dove ",l(n.a,null,Me(Vl||(Vl=Ve`\kappa`)))," è la ",l("i",null,"costante dielettrica relativa")," del materiale inserito, ",l(n.a,null,Me(Ml||(Ml=Ve`A`)))," l'area di una armatura e ",l(n.a,null,Me(Rl||(Rl=Ve`s`)))," la distanza tra le due armature."),l("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",l("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",l("i",null,"breakdown"),"."),l("p",null,"La sua unità di misura è il Farad (",l(n.a,null,Me(yl||(yl=Ve`Fa`))),")")),l(t.a,{title:"Amperometro"},l("p",null,"Misura la corrente elettrica se messo in serie."),l("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),l(t.a,{title:"Voltmetro"},l("p",null,"Misura la differenza di potenziale se messo in parallelo."),l("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),l(o.a,{title:"Principi di Kirchhoff"},l(t.a,{title:"Legge dei nodi"},l("p",null,"Per nodo si intende un qualsiasi punto del circuito."),l("p",null,"Da un nodo entra ed esce la stessa corrente.")),l(t.a,{title:"Legge delle maglie"},l("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),l("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),l(o.a,{title:"Serie e Parallelo"},l(t.a,{title:"Circuito in serie"},l("p",null,"Più parti di circuito sono ",l("i",null,"in serie")," se sono consecutive e senza biforcazioni."),l("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),l(t.a,{title:"Circuito in parallelo"},l("p",null,"Più parti di circuito sono ",l("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),l("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),l(o.a,{title:"Resistenze equivalenti"},l(t.a,{title:"Circuiti in serie"},l("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),l("p",null,l(n.a,null,Me(Ul||(Ul=Ve`R_{serie} = \sum_{i=1}^{n} R_i`))))),l(t.a,{title:"Circuiti in parallelo"},l("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),l("p",null,l(n.a,null,Me(Ql||(Ql=Ve`R_{parallelo} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}}`)))))),l(o.a,{title:"Condensatori equivalenti"},l(t.a,{title:"Circuiti in serie"},l("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),l("p",null,l(n.a,null,Me(Gl||(Gl=Ve`C_{serie} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}`))))),l(t.a,{title:"Circuiti in parallelo"},l("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),l("p",null,l(n.a,null,Me(Ol||(Ol=Ve`C_{parallelo} = \sum_{i=1}^{n} C_n`)))))),l(o.a,{title:"Magnetismo"},l(t.a,{title:"Permeabilità magnetica dello spazio vuoto"},l("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),l("p",null,l(n.a,null,Me(Wl||(Wl=Ve`\mu_0 = 4 \pi \cdot 10^{-7} \frac{H}{m}`)))," (",l(n.a,null,Me(Jl||(Jl=Ve`\frac{N}{A^2}`))),")")),l(t.a,{title:"Campo magnetico"},l("p",null,"Come un campo elettrico, ma per i magneti."),l("p",null,"Il suo simbolo è ",l(n.a,null,Me(Kl||(Kl=Ve`B`))),", e la sua unità di misura è il Tesla (",l(n.a,null,"T"),").")),l(t.a,{title:"Flusso magnetico"},l("p",null,'È "quanto" campo magnetico ',l("b",null,"attraversa")," un percorso chiuso."),l("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),l("p",null,l(n.a,null,Me(Xl||(Xl=Ve`\Phi_{B_{i}} = \vec{B} \cdot \vec{L}_n = B \cdot L_i \cdot \sin(\alpha) = B_\parallel \cdot L_i`)))),l("p",null,l(n.a,null,Me(jl||(jl=Ve`\Phi_{B} = \sum_{i=0}^{n_{lati}} \Phi_{Bn}`)))),l("p",null,"La sua unità di misura è il Weber (",l(n.a,null,Me(Hl||(Hl=Ve`Wb = T \cdot m^2`))),").")),l(t.a,{title:"Legge di Gauss per i campi magnetici"},l("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),l("p",null,"Ovvero, non esistono monopoli magnetici.")),l(t.a,{title:"Legge di Ampère"},l("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),l("p",null,l(n.a,null,Me(Yl||(Yl=Ve`\Phi_B = \mu_0 \cdot I`)))))),l(o.a,{title:"Forze magnetiche"},l(t.a,{title:l("span",null,"Forza magnetica su carica puntiforme ",l("small",null,"(Forza di Lorentz)"))},l("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),l("p",null,l(n.a,null,Me(Zl||(Zl=Ve`\vec{F}_{B} = q \cdot (\vec{v} \times \vec{B})`)))),l("p",null,"Dove ",l(n.a,null,Me($l||($l=Ve`\vec{B}`)))," è l'intensità del campo magnetico e ",l(n.a,null,Me(le||(le=Ve`\vec{v}`)))," la velocità della carica considerata."),l("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),l("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),l(t.a,{title:"Forza magnetica in un filo"},l("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),l("p",null,l(n.a,null,Me(ee||(ee=Ve`\vec{F}_{magnetica} = I \cdot (\vec{L} \times \vec{B})`)))," ",l("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),l("p",null,"Dove ",l(n.a,null,Me(ae||(ae=Ve`I`)))," è la corrente elettrica, ",l(n.a,null,Me(ie||(ie=Ve`\vec{L}`)))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),l(o.a,{title:"Campi magnetici"},l(t.a,{title:"Campo magnetico in una spira"},l("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),l(t.a,{title:"Campo magnetico di un solenoide"},l("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),l("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),l("p",null,l(n.a,null,Me(ne||(ne=Ve`\left | \vec{B} \right | = \mu_0 \cdot I \cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}`))))),l(t.a,{title:"Legge di Oersted"},l("p",null,l("i",null,"Caso particolare della ",l("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),l("p",null,"Il modulo del campo magnetico ",l(n.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",l(n.a,null,"I")," alla distanza ",l(n.a,null,"s")," è:"),l("p",null,l(n.a,null,Me(te||(te=Ve`\left | \vec{B} \right | = \frac{\mu \cdot I}{2 \pi r}`)))),l("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),l("p",null,"Due fili attraversati dalla ",l(r.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",l(r.a,null,"corr"),l(u.a,null,"enti")," ",l(r.a,null,"opp"),l(u.a,null,"oste")," si respingono."))),l(o.a,{title:"Induzione elettromagnetica"},l(t.a,{title:"Forza elettromotrice indotta"},l("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),l("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),l("p",null,"Essa vale:"),l("p",null,l(n.a,null,Me(oe||(oe=Ve`\Delta V_{indotta} = v \cdot B \cdot L`)))),l("p",null,"Dove ",l(n.a,null,"v")," è la velocità del conduttore, ",l(n.a,null,"B")," è l'intensità del campo magnetico ed ",l(n.a,null,"L")," è la lunghezza del conduttore.")),l(t.a,{title:"Flusso magnetico in una spira"},l("p",null,"In un campo magnetico ",l(n.a,null,Me(re||(re=Ve`B`)))," uniforme e perpendicolare al piano di una spira di area ",l(n.a,null,Me(ue||(ue=Ve`A`))),", il flusso magnetico si può determinare con la ",l("i",null,"Legge di Faraday-Neumann-Lenz"),":"),l("p",null,l(n.a,null,Me(ce||(ce=Ve`\Phi_B = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos(\alpha)`)))))),l(o.a,null,l(t.a,{title:"Legge di Faraday-Neumann-Lenz"},l("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),l("p",null,l(n.a,null,Me(se||(se=Ve`\Delta V_{indotta} = - \frac{\Delta \Phi_B}{\Delta t}`)))),l("p",null,"Il meno è dovuto alla ",l("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),l(t.a,{title:"Faraday in un solenoide"},l("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),l("p",null,l(n.a,null,Me(pe||(pe=Ve`\Delta V_{indotta} = - \frac{N \cdot \Delta \Phi_{B_{spira}}}{\Delta t} = - \frac{N \cdot B \cdot A \cdot cos(\alpha)}{\Delta t}`)))),l("p",null,"Dove ",l(n.a,null,Me(de||(de=Ve`N`)))," è il numero delle spire del solenoide.")),l(t.a,{title:"Legge di Ampère-Maxwell"},l("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),l(o.a,{title:"Elettromagnetismo"},l(t.a,{title:"Onde elettromagnetiche"},l("p",null,"Nel vuoto, il campo elettrico ",l(n.a,null,Me(me||(me=Ve`E`)))," e il campo magnetico ",l(n.a,null,Me(ve||(ve=Ve`B`)))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),l("p",null,"Si dice quindi che sono ",l("i",null,"onde elettromagnetiche"),"."),l("p",null,"Esse sono legate dalla relazione:"),l("p",null,l(n.a,null,Me(ge||(ge=Ve`E = c \cdot B`)))),l("p",null,"Dove ",l(n.a,null,Me(fe||(fe=Ve`c`)))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),l("p",null,l(n.a,null,Me(he||(he=Ve`c = \frac{1}{\sqrt{\epsilon_0 \cdot \mu_0}} = 3.00 \cdot 10^8 \frac{m}{s}`))))),l(t.a,{title:"Formula delle onde"},l("p",null,l(n.a,null,Me(ze||(ze=Ve`A(t) = A_{max} \cdot \sin \left ( \frac{2 \pi}{\lambda} - \omega t + \phi \right )`)))),l("p",null,"Dove ",l(n.a,null,Me(_e||(_e=Ve`A_{max}`)))," è l'ampiezza massima che può avere l'onda, ",l(n.a,null,Me(be||(be=Ve`\frac{2 \pi}{\lambda} = \left | \vec{k} \right |`)))," è il vettore d'onda, ",l(n.a,null,Me(Le||(Le=Ve`\omega`)))," la frequenza angolare e ",l(n.a,null,Me(qe||(qe=Ve`\phi`)))," la fase."))),l(o.a,{title:"Spettroscopia"},l(t.a,{title:"Emissione"},l("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",l("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),l("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),l("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),l("p",null,l(n.a,null,Me(Ce||(Ce=Ve`\frac{1}{\lambda} = R \left ( \frac{1}{4} - \frac{1}{n^2} \right )`)))),l("p",null,"Con ",l(n.a,null,Me(De||(De=Ve`R = 1.097 \cdot 10^7 \frac{1}{m}`))),", detta costante di Rydberg, e ",l(n.a,null,Me(Pe||(Pe=Ve`n`)))," un numero intero.")),l(t.a,{title:"Grandezza quantizzata"},l("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),l("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),l("p",null,"Energia, momento angolare e raggio sono quantizzati."),l("p",null,"Nota costante quantica è ",l(n.a,null,Me(Ae||(Ae=Ve`h`))),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",l(n.a,null,Me(Fe||(Fe=Ve`\hbar = \left ( \frac{h}{2 \pi} \right )`))),"."))),l(o.a,null,l(t.a,{title:"Modello di Bohr"},l("p",null,"L'energia degli elettroni è quantizzata."),l("p",null,"Inoltre, per essi è valido che:"),l("p",null,l(n.a,null,Me(Ee||(Ee=Ve`m \cdot v_n \cdot 2 \pi \cdot r = n \cdot h`)))),l("p",null,"Ancora, il raggio delle orbite è uguale a:"),l("p",null,l(n.a,null,Me(Se||(Se=Ve`r_n = n^2 \cdot a_0 = n^2 \cdot \frac{\hbar}{m_{elettrone} \cdot k \cdot e^2} `)))),l("p",null,"Con ",l(n.a,null,Me(Ie||(Ie=Ve`a_0 = \left ( \frac{h}{2 \pi} \right )^2 \cdot \frac{1}{m_{elettrone} \cdot k \cdot e^2} = 5.29 \cdot 10^{-11} m`))),"."),l("p",null,"Infine, in ogni stato, l'energia è pari a:"),l("p",null,l(n.a,null,Me(ke||(ke=Ve`E_n = \frac{1}{n^2} \cdot E_1 = - \frac{1}{n^2} \cdot \frac{a_0^2}{2 \cdot m \cdot \hbar^4} = - \frac{1}{n^2} \cdot \frac{m_{elettrone} \cdot k^2 \cdot e^4}{2 \cdot \hbar^2}`)))),l("p",null,"Due elettroni non possono occupare lo stesso stato."),l("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),l(o.a,null,l(t.a,{title:"Nei solidi"},l("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),l("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),l(o.a,{title:"Semiconduttori"},l(t.a,{title:"Semiconduttori"},l("p",null,l(c.a,null,"Refactor this")),l("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",l(n.a,null,Me(we||(we=Ve`10^1 eV`))),", allora il corpo è un isolante."),l("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),l("p",null,"Se il gap è invece dell'ordine di grandezza di ",l(n.a,null,Me(xe||(xe=Ve`1 eV`))),", allora il corpo è un semiconduttore.")),l(t.a,{title:"Lacune"},l("p",null,"Legami in cui ",l(r.a,null,"mancano 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de=function(){return n},n}function fe(){var n=Se(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return fe=function(){return n},n}function ve(){var n=Se(["g = 9.81 \frac{m}{s^2}"],["g = 9.81 \\frac{m}{s^2}"]);return ve=function(){return n},n}function me(){var n=Se(["left | \vec{F} \right | = g m"],["\\left | \\vec{F} \\right | = g m"]);return me=function(){return n},n}function _e(){var n=Se(["G = 6.67 cdot 10^{-11} \frac{N m^2}{{kg}^2}"],["G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}"]);return _e=function(){return n},n}function he(){var n=Se(["left | \vec{F} \right | = G \frac{m_1 m_2}{s^2}"],["\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}"]);return he=function(){return n},n}function ge(){var n=Se(["\vec{F}_{21} = -\vec{F}_{12}"],["\\vec{F}_{21} = -\\vec{F}_{12}"]);return ge=function(){return n},n}function ze(){var n=Se(["Sigma \vec{F} = m \vec{a}"],["\\Sigma \\vec{F} = m \\vec{a}"]);return ze=function(){return n},n}function be(){var n=Se(["Sigma 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(\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)"],["\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]);return Ce=function(){return n},n}function Ae(){var n=Se(["\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)"],["\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)"]);return Ae=function(){return n},n}function Pe(){var n=Se(["left | \vec{v}_y \right | = left | \vec{v} \right | cos alpha"],["\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha"]);return Pe=function(){return n},n}function ye(){var n=Se(["left | \vec{v}_x \right | = left | \vec{v} \right | sin alpha"],["\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha"]);return ye=function(){return n},n}function we(){var n=Se(["\vec{v} = \vec{v}_x + \vec{v}_y"],["\\vec{v} = \\vec{v}_x + \\vec{v}_y"]);return we=function(){return n},n}function Se(n,e){return e||(e=n.slice(0)),n.raw=e,n}t.d(e,"default",(function(){return He}));var Ie=t("hosL"),ke=t("OMhl"),Be=t("HKwK"),xe=t("lL4N"),Ve=t("h7i1"),Re=t("UEJU"),Ne=t("jXlC"),Te=t("wQ73"),Ue=String.raw,He=function(e){function t(){return e.apply(this,arguments)||this}var Se,Ie;return Ie=e,(Se=t).prototype=Object.create(Ie.prototype),Se.prototype.constructor=Se,Se.__proto__=Ie,t.prototype.render=function(){return n(Te.a.Provider,{value:!1},n("div",null,n("h1",null,"Fisica"),n(xe.a,{title:"Vettori"},n(Be.a,{title:"Componenti cartesiane"},n("p",null,"Usa le regole base della trigonometria:"),n("p",null,n(ke.a,null,Ue(we()))),n("p",null,n(ke.a,null,Ue(ye()))),n("p",null,n(ke.a,null,Ue(Pe())))),n(Be.a,{title:"Somma"},n("p",null,"Scomponi in componenti, poi sommali:"),n("p",null,n(ke.a,null,Ue(Ae()))),n("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),n(Be.a,{title:"Differenza"},n("p",null,"Alla fine è sempre una somma:"),n("p",null,n(ke.a,null,Ue(Ce()))),n("p",null,"Produce il vettore che parte da ",n(ke.a,null,"w")," e arriva a ",n(ke.a,null,"v"),".")),n(Be.a,{title:"Prodotto scalare"},n("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),n("p",null,n(ke.a,null,Ue(Fe()))),n("p",null,"Produce il modulo della proiezione di ",n(ke.a,null,Ue(Ee()))," su ",n(ke.a,null,Ue(qe())),".")),n(Be.a,{title:"Prodotto vettoriale"},n("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),n("ul",null,n("li",null,n(ke.a,null,Ue(Le()))),n("li",null,n(ke.a,null,Ue(De()))),n("li",null,n("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),n("p",null,"Non è commutativo!"))),n(xe.a,{title:"Leggi di Newton"},n(Be.a,{title:"1ᵃ: Inerzia"},n("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),n("p",null,n(ke.a,null,Ue(be())))),n(Be.a,{title:"2ᵃ: Proporzionalità"},n("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",n("i",null,"massa"),"."),n("p",null,n(ke.a,null,Ue(ze())))),n(Be.a,{title:"3ᵃ: Azione e reazione"},n("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),n("p",null,n(ke.a,null,Ue(ge()))))),n(xe.a,{title:"Forza di gravità"},n(Be.a,{title:"Tra due corpi"},n("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),n("p",null,n(ke.a,null,Ue(he()))),n("p",null,n(ke.a,null,"G")," è la ",n("i",null,"costante di gravitazione universale")," e vale:"),n("p",null,n(ke.a,null,Ue(_e())))),n(Be.a,{title:"Verso la Terra"},n("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",n("i",null,"peso")," uguale a:"),n("p",null,n(ke.a,null,Ue(me()))),n("p",null,n(ke.a,null,"g")," è la ",n("i",null,"costante di gravità")," della Terra, e vale:"),n("p",null,n(ke.a,null,Ue(ve())))),n(Be.a,{title:"Su pianeti diversi"},n("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),n("p",null,n(ke.a,null,Ue(fe()))),n("p",null,"L'unica differenza è che cambia la ",n("i",null,"costante di gravità"),":"),n("p",null,n(ke.a,null,Ue(de()))),n("p",null,n(ke.a,null,Ue(pe()))))),n(xe.a,{title:"Forze di contatto"},n(Be.a,{title:"Normale"},n("p",null,"Si oppone alle forze applicate alla superficie di contatto."),n("p",null,"Un libro appoggiato su un tavolo ha la ",n("b",null,"forza di gravità")," che lo attira verso il terreno e la ",n("b",null,"forza normale")," che lo trattiene dal cadere.")),n(Be.a,{title:"Attrito statico"},n("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),n("p",null,n(ke.a,null,Ue(se())))),n(Be.a,{title:"Attrito dinamico"},n("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),n("p",null,n(ke.a,null,Ue(ce())))),n(Be.a,{title:"Tensione"},n("p",null,"E' forza trasmessa tra due estremi di una fune."),n("p",null,"Può essere redirezionata per mezzo di carrucole.")),n(Be.a,{title:"Elastica"},n("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),n("p",null,n(ke.a,null,Ue(ue()))),n("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),n(xe.a,{title:"Cinematica"},n(Be.a,{title:"Spostamento"},n("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),n("p",null,n(ke.a,null,Ue(oe())))),n(Be.a,{title:"Velocità"},n("p",null,"È un vettore che misura la variazione di posizione nel tempo."),n("p",null,n(ke.a,null,Ue(re()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"velocità istantanea"),":"),n("p",null,n(ke.a,null,Ue(ie())))),n(Be.a,{title:"Accelerazione"},n("p",null,"È un vettore che misura la variazione di velocità nel tempo."),n("p",null,n(ke.a,null,Ue(le()))),n("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",n("i",null,"accelerazione istantanea"),":"),n("p",null,n(ke.a,null,Ue(ae())))),n(Be.a,{title:n("span",null,"Quantità di moto ",n("small",null,"(momento lineare)"))},n("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),n("p",null,n(ke.a,null,Ue(te()))),n("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),n("p",null,n(ke.a,null,Ue(ee()))))),n(xe.a,{title:"Moto rettilineo uniforme"},n(Be.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(ke.a,null,Ue(ne())))),n(Be.a,{title:"Velocità"},n("p",null,"È costante:"),n("p",null,n(ke.a,null,Ue($n())))),n(Be.a,{title:"Accelerazione"},n("p",null,"La velocità non varia:"),n("p",null,n(ke.a,null,Ue(Zn())))),n(Be.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(ke.a,null,"f(t) = 0")))),n(xe.a,{title:"Moto rettilineo uniformemente accelerato"},n(Be.a,{title:"Spostamento"},n("p",null,"La ",n("i",null,"legge oraria")," è:"),n("p",null,n(ke.a,null,Ue(Yn())))),n(Be.a,{title:"Velocità"},n("p",null,"È una retta:"),n("p",null,n(ke.a,null,Ue(Xn())))),n(Be.a,{title:"Accelerazione"},n("p",null,"È costante:"),n("p",null,n(ke.a,null,Ue(Jn())))),n(Be.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(ke.a,null,"f(t) = m a")))),n(xe.a,{title:"Moto armonico semplice"},n(Be.a,{title:"Ampiezza"},n("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),n("p",null,"(L'ampiezza di una sinusoide.)")),n(Be.a,{title:"Velocità angolare"},n("p",null,"Indica quanto in fretta cambia la posizione del corpo."),n("p",null,"Dipende dal periodo:"),n("p",null,n(ke.a,null,Ue(Kn())))),n(Be.a,{title:"Spostamento"},n("p",null,"E' una sinusoide:"),n("p",null,n(ke.a,null,Ue(Gn())))),n(Be.a,{title:"Velocità"},n("p",null,"E' la sinusoide dello spostamento, sfasata di ",n(ke.a,null,Ue(Wn())),":"),n("p",null,n(ke.a,null,Ue(Qn())))),n(Be.a,{title:"Accelerazione"},n("p",null,"E' la sinusoide della velocità, sfasata di ",n(ke.a,null,Ue(jn())),":"),n("p",null,n(ke.a,null,Ue(Mn())))),n(Be.a,{title:"Forze"},n("p",null,"Si applica la prima legge di Newton:"),n("p",null,n(ke.a,null,"f(t) = m a")))),n(xe.a,{title:"Moti composti"},n(Be.a,{title:"Moto parabolico"},n("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),n(Be.a,{title:"Moto circolare uniforme"},n("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",n(ke.a,null,Ue(On())),", sull'asse Y."))),n(xe.a,{title:"Moto circolare uniforme"},n(Be.a,null,n("h3",null,"Velocità angolare"),n("p",null,"Quanto cambia la fase nel tempo."),n("p",null,n(ke.a,null,Ue(Hn())))),n(Be.a,{title:"Fase"},n("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),n("p",null,"Si indica con ",n(ke.a,null,Ue(Un())),", e generalmente si usa in radianti.")),n(Be.a,{title:"Velocità"},n("p",null,"Si applicano le formule per la circonferenza:"),n("p",null,n(ke.a,null,Ue(Tn())))),n(Be.a,{title:"Accelerazione"},n("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),n("p",null,n(ke.a,null,Ue(Nn())))),n(Be.a,{title:"Forza centripeta"},n("p",null,"È verso il centro e si calcola con:"),n("p",null,n(ke.a,null,Ue(Rn()))))),n(xe.a,{title:"Lavoro ed energia"},n(Be.a,{title:"Lavoro"},n("p",null,"E' compiuto da una forza che sposta un corpo."),n("p",null,n(ke.a,null,Ue(Vn()))),n("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),n(Be.a,{title:"Energia cinetica"},n("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),n("p",null,n(ke.a,null,Ue(xn()))),n("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),n("p",null,n(ke.a,null,Ue(Bn())))),n(Be.a,{title:"Energia potenziale gravitazionale"},n("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),n("p",null,n(ke.a,null,Ue(kn()))),n("p",null,"(Con ",n(ke.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),n(Be.a,{title:"Energia potenziale elastica"},n("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),n("p",null,n(ke.a,null,Ue(In())))),n(Be.a,{title:"Forze conservative"},n("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),n("p",null,"Ad esempio, è conservativa la ",n("i",null,"forza di gravità"),", ma ",n("b",null,"non")," è conservativa la forza di attrito."),n("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),n("p",null,n(ke.a,null,Ue(Sn())))),n(Be.a,{title:"Potenza"},n("p",null,"È la velocità di trasferimento di energia:"),n("p",null,n(ke.a,null,Ue(wn()))))),n(xe.a,{title:"Elettrostatica"},n(Be.a,{title:"Carica elettrica"},n("p",null,"È una proprietà dei corpi che può essere ",n(Ve.a,null,"positiva")," o ",n(Re.a,null,"negativa"),"."),n("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),n("p",null,"Esiste un'unità elementare: ",n(ke.a,null,Ue(yn())),"."),n("p",null,"Cariche ",n(Ve.a,null,"opp"),n(Re.a,null,"oste")," si attraggono; cariche ",n(Ve.a,null,"uguali")," si respingono.")),n(Be.a,{title:"Conduttori e isolanti"},n("p",null,"Più ",n("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),n("p",null,"I corpi in cui la carica si muove bene sono ",n("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",n("i",null,"isolanti"),"."),n("p",null,n("i",null,"Il corpo umano è un buon conduttore.")))),n(xe.a,{title:"Polarizzazione"},n(Be.a,{title:"Polarizzazione"},n("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),n(xe.a,null,n(Be.a,{title:"Messa a terra"},n("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",n("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",n(Ve.a,null,"cariche positive")," e ",n(Re.a,null,"negative")," all'interno)."))),n(xe.a,null,n(Be.a,{title:"Polarizzazione per strofinio"},n("p",null,"Strofinando tra loro due corpi isolanti, essi si ",n("i",null,"polarizzeranno per strofinio"),".")),n(Be.a,{title:"Polarizzazione per contatto"},n("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",n("i",null,"polarizzarsi per contatto"),".")),n(Be.a,{title:"Polarizzazione per induzione"},n("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',n(Ve.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",n(Re.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",n(Ve.a,null,"stesso segno")," più lontano possibile da esse."),n("p",null,"Mettendo a terra il conduttore, nuove cariche del ",n(Re.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),n("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",n(Re.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),n(xe.a,{title:"Forza elettrica"},n(Be.a,{title:"Legge di Coulomb"},n("p",null,"Due corpi carichi si attraggono tra loro con forza:"),n("p",null,n(ke.a,null,Ue(Pn()))),n("p",null,n(ke.a,null,Ue(An()))," è la ",n("i",null,"costante di Coulomb"),", e vale ",n(ke.a,null,Ue(Cn())),".")),n(Be.a,{title:"Permeabilità dello spazio vuoto"},n("p",null,"La costante ",n(ke.a,null,Ue(Fn()))," è in realtà dipendente da un altra costante, ",n(ke.a,null,Ue(En())),", la ",n("i",null,"permeabilità del vuoto"),"."),n("p",null,n(ke.a,null,Ue(qn()))),n("p",null,n(ke.a,null,Ue(Ln())))),n(Be.a,{title:"Campo elettrico"},n("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),n("p",null,n(ke.a,null,Ue(Dn())))),n(Be.a,{title:"Flusso elettrico"},n("p",null,'È la differenza tra "quanto" campo elettrico ',n(Ve.a,null,"entra")," e quanto campo elettrico ",n(Re.a,null,"esce")," da una certa area."),n("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),n("p",null,n(ke.a,null,Ue(bn()))),n("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),n("p",null,n(ke.a,null,Ue(zn()))),n("p",null,n(Ne.a,null,"Circa. E' una specie di integrale..."))),n(Be.a,{title:"Legge di Gauss per i campi elettrostatici"},n("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),n("p",null,n(ke.a,null,Ue(gn()))),n("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),n(xe.a,{title:"Energia elettrica"},n(Be.a,{title:"Energia potenziale elettrica"},n("p",null,"Un corpo carico vicino ad altre cariche possiede un'",n("i",null,"energia potenziale elettrica")," ",n(ke.a,null,Ue(hn())),"."))),n(xe.a,{title:"Circuiti elettrici"},n(Be.a,{title:n("span",null,"Potenziale elettrico ",n("small",null,"(tensione)"))},n("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),n("p",null,n(ke.a,null,Ue(_n()))),n("p",null,"La sua unità di misura è il Volt (",n(ke.a,null,Ue(mn())),")."),n("p",null,"In una batteria è detto ",n("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),n(Be.a,{title:n("span",null,"Corrente elettrica ",n("small",null,"(intensità)"))},n("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),n("p",null,n(ke.a,null,Ue(vn()))),n("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),n("p",null,"La sua unità di misura è l'Ampere (",n(ke.a,null,Ue(fn())),").")),n(Be.a,{title:n("span",null,"Corrente continua ",n("small",null,"(",n("abbr",{title:"Direct Current"},"DC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente è costante.")),n(Be.a,{title:n("span",null,"Corrente alternata ",n("small",null,"(",n("abbr",{title:"Alternate Current"},"AC"),")"))},n("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),n(Be.a,{title:"Potenza elettrica"},n("p",null,"Possiamo calcolare la potenza di un circuito:"),n("p",null,n(ke.a,null,Ue(dn()))))),n(xe.a,{title:"Elementi di un circuito"},n(Be.a,{title:"Resistore"},n("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),n("p",null,"Il potenziale utilizzato è pari a:"),n("p",null,n(ke.a,null,Ue(pn()))),n("p",null,"Dove ",n(ke.a,null,Ue(sn()))," è una costante detta ",n("i",null,"resistenza")," con unità di misura Ohm (",n(ke.a,null,Ue(cn())),")."),n("p",null,"La resistenza di un conduttore vale:"),n("p",null,n(ke.a,null,Ue(un()))),n("p",null,n(ke.a,null,Ue(on()))," è la ",n("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),n("p",null,n(ke.a,null,Ue(rn())))),n(Be.a,{title:"Condensatore"},n("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),n("p",null,"Per farlo, cattura cariche ",n(Ve.a,null,"positive")," e ",n(Re.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),n("p",null,"Ha una ",n("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),n("p",null,n(ke.a,null,Ue(ln()))),n("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),n("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),n("p",null,n(ke.a,null,Ue(an()))),n("p",null,"Dove ",n(ke.a,null,Ue(tn()))," è la ",n("i",null,"costante dielettrica relativa")," del materiale inserito, ",n(ke.a,null,Ue(en()))," l'area di una armatura e ",n(ke.a,null,Ue(nn()))," la distanza tra le due armature."),n("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",n("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",n("i",null,"breakdown"),"."),n("p",null,"La sua unità di misura è il Farad (",n(ke.a,null,Ue($())),")")),n(Be.a,{title:"Amperometro"},n("p",null,"Misura la corrente elettrica se messo in serie."),n("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),n(Be.a,{title:"Voltmetro"},n("p",null,"Misura la differenza di potenziale se messo in parallelo."),n("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),n(xe.a,{title:"Principi di Kirchhoff"},n(Be.a,{title:"Legge dei nodi"},n("p",null,"Per nodo si intende un qualsiasi punto del circuito."),n("p",null,"Da un nodo entra ed esce la stessa corrente.")),n(Be.a,{title:"Legge delle maglie"},n("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),n("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),n(xe.a,{title:"Serie e Parallelo"},n(Be.a,{title:"Circuito in serie"},n("p",null,"Più parti di circuito sono ",n("i",null,"in serie")," se sono consecutive e senza biforcazioni."),n("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),n(Be.a,{title:"Circuito in parallelo"},n("p",null,"Più parti di circuito sono ",n("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),n("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),n(xe.a,{title:"Resistenze equivalenti"},n(Be.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),n("p",null,n(ke.a,null,Ue(Z())))),n(Be.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),n("p",null,n(ke.a,null,Ue(Y()))))),n(xe.a,{title:"Condensatori equivalenti"},n(Be.a,{title:"Circuiti in serie"},n("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),n("p",null,n(ke.a,null,Ue(X())))),n(Be.a,{title:"Circuiti in parallelo"},n("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),n("p",null,n(ke.a,null,Ue(J()))))),n(xe.a,{title:"Magnetismo"},n(Be.a,{title:"Permeabilità magnetica dello spazio vuoto"},n("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),n("p",null,n(ke.a,null,Ue(K()))," (",n(ke.a,null,Ue(G())),")")),n(Be.a,{title:"Campo magnetico"},n("p",null,"Come un campo elettrico, ma per i magneti."),n("p",null,"Il suo simbolo è ",n(ke.a,null,Ue(W())),", e la sua unità di misura è il Tesla (",n(ke.a,null,"T"),").")),n(Be.a,{title:"Flusso magnetico"},n("p",null,'È "quanto" campo magnetico ',n("b",null,"attraversa")," un percorso chiuso."),n("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),n("p",null,n(ke.a,null,Ue(Q()))),n("p",null,n(ke.a,null,Ue(j()))),n("p",null,"La sua unità di misura è il Weber (",n(ke.a,null,Ue(M())),").")),n(Be.a,{title:"Legge di Gauss per i campi magnetici"},n("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),n("p",null,"Ovvero, non esistono monopoli magnetici.")),n(Be.a,{title:"Legge di Ampère"},n("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),n("p",null,n(ke.a,null,Ue(O()))))),n(xe.a,{title:"Forze magnetiche"},n(Be.a,{title:n("span",null,"Forza magnetica su carica puntiforme ",n("small",null,"(Forza di Lorentz)"))},n("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),n("p",null,n(ke.a,null,Ue(H()))),n("p",null,"Dove ",n(ke.a,null,Ue(U()))," è l'intensità del campo magnetico e ",n(ke.a,null,Ue(T()))," la velocità della carica considerata."),n("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),n("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),n(Be.a,{title:"Forza magnetica in un filo"},n("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),n("p",null,n(ke.a,null,Ue(N()))," ",n("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),n("p",null,"Dove ",n(ke.a,null,Ue(R()))," è la corrente elettrica, ",n(ke.a,null,Ue(V()))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),n(xe.a,{title:"Campi magnetici"},n(Be.a,{title:"Campo magnetico in una spira"},n("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),n(Be.a,{title:"Campo magnetico di un solenoide"},n("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),n("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),n("p",null,n(ke.a,null,Ue(x())))),n(Be.a,{title:"Legge di Oersted"},n("p",null,n("i",null,"Caso particolare della ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),n("p",null,"Il modulo del campo magnetico ",n(ke.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",n(ke.a,null,"I")," alla distanza ",n(ke.a,null,"s")," è:"),n("p",null,n(ke.a,null,Ue(B()))),n("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),n("p",null,"Due fili attraversati dalla ",n(Ve.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",n(Ve.a,null,"corr"),n(Re.a,null,"enti")," ",n(Ve.a,null,"opp"),n(Re.a,null,"oste")," si respingono."))),n(xe.a,{title:"Induzione elettromagnetica"},n(Be.a,{title:"Forza elettromotrice indotta"},n("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),n("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),n("p",null,"Essa vale:"),n("p",null,n(ke.a,null,Ue(k()))),n("p",null,"Dove ",n(ke.a,null,"v")," è la velocità del conduttore, ",n(ke.a,null,"B")," è l'intensità del campo magnetico ed ",n(ke.a,null,"L")," è la lunghezza del conduttore.")),n(Be.a,{title:"Flusso magnetico in una spira"},n("p",null,"In un campo magnetico ",n(ke.a,null,Ue(I()))," uniforme e perpendicolare al piano di una spira di area ",n(ke.a,null,Ue(S())),", il flusso magnetico si può determinare con la ",n("i",null,"Legge di Faraday-Neumann-Lenz"),":"),n("p",null,n(ke.a,null,Ue(w()))))),n(xe.a,null,n(Be.a,{title:"Legge di Faraday-Neumann-Lenz"},n("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),n("p",null,n(ke.a,null,Ue(y()))),n("p",null,"Il meno è dovuto alla ",n("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),n(Be.a,{title:"Faraday in un solenoide"},n("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),n("p",null,n(ke.a,null,Ue(P()))),n("p",null,"Dove ",n(ke.a,null,Ue(A()))," è il numero delle spire del solenoide.")),n(Be.a,{title:"Legge di Ampère-Maxwell"},n("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),n(xe.a,{title:"Elettromagnetismo"},n(Be.a,{title:"Onde elettromagnetiche"},n("p",null,"Nel vuoto, il campo elettrico ",n(ke.a,null,Ue(C()))," e il campo magnetico ",n(ke.a,null,Ue(F()))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),n("p",null,"Si dice quindi che sono ",n("i",null,"onde elettromagnetiche"),"."),n("p",null,"Esse sono legate dalla relazione:"),n("p",null,n(ke.a,null,Ue(E()))),n("p",null,"Dove ",n(ke.a,null,Ue(q()))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),n("p",null,n(ke.a,null,Ue(L())))),n(Be.a,{title:"Formula delle onde"},n("p",null,n(ke.a,null,Ue(D()))),n("p",null,"Dove ",n(ke.a,null,Ue(b()))," è l'ampiezza massima che può avere l'onda, ",n(ke.a,null,Ue(z()))," è il vettore d'onda, ",n(ke.a,null,Ue(g()))," la frequenza angolare e ",n(ke.a,null,Ue(h()))," la fase."))),n(xe.a,{title:"Spettroscopia"},n(Be.a,{title:"Emissione"},n("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",n("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),n("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),n("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),n("p",null,n(ke.a,null,Ue(_()))),n("p",null,"Con ",n(ke.a,null,Ue(m())),", detta costante di Rydberg, e ",n(ke.a,null,Ue(v()))," un numero intero.")),n(Be.a,{title:"Grandezza quantizzata"},n("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),n("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),n("p",null,"Energia, momento angolare e raggio sono quantizzati."),n("p",null,"Nota costante quantica è ",n(ke.a,null,Ue(f())),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",n(ke.a,null,Ue(d())),"."))),n(xe.a,null,n(Be.a,{title:"Modello di Bohr"},n("p",null,"L'energia degli elettroni è quantizzata."),n("p",null,"Inoltre, per essi è valido che:"),n("p",null,n(ke.a,null,Ue(p()))),n("p",null,"Ancora, il raggio delle orbite è uguale a:"),n("p",null,n(ke.a,null,Ue(s()))),n("p",null,"Con ",n(ke.a,null,Ue(c())),"."),n("p",null,"Infine, in ogni stato, l'energia è pari a:"),n("p",null,n(ke.a,null,Ue(u()))),n("p",null,"Due elettroni non possono occupare lo stesso stato."),n("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),n(xe.a,null,n(Be.a,{title:"Nei solidi"},n("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),n("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),n(xe.a,{title:"Semiconduttori"},n(Be.a,{title:"Semiconduttori"},n("p",null,n(Ne.a,null,"Refactor this")),n("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",n(ke.a,null,Ue(o())),", allora il corpo è un isolante."),n("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),n("p",null,"Se il gap è invece dell'ordine di grandezza di ",n(ke.a,null,Ue(r())),", allora il corpo è un semiconduttore.")),n(Be.a,{title:"Lacune"},n("p",null,"Legami in cui ",n(Ve.a,null,"mancano elettroni"),"."),n("p",null,n(Re.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",n(Ve.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),n(Be.a,{title:"Accettori e donori"},n("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),n("ul",null,n("li",null,"Con numero atomico maggiore, un semiconduttore di ",n(Re.a,null,"tipo N")," con ",n(Re.a,null,"elettroni in eccesso")," liberi di scorrere."),n("li",null,"Con numero atomico minore, un semiconduttore di ",n(Ve.a,null,"tipo P")," con ",n(Ve.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),n("p",null,"Maggiore impurezza porta a maggiore conduttività.")),n(Be.a,{title:"Temperatura"},n("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",n(Re.a,null,"elettroni")," e ",n(Ve.a,null,"lacune"),"."))),n(xe.a,{title:n("span",null,"Ottica ",n("small",null,"(non l'abbiamo fatta)"))},n(Be.a,{title:"Assorbimento e riflessione"},n("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),n(Be.a,{title:"Corpo nero"},n("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),n("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",n(ke.a,null,Ue(i()))," variabile in base alla temperatura."),n("p",null,n(ke.a,null,Ue(l()))," è costante.")),n(Be.a,{title:"Teoria di Planck per il corpo nero"},n("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),n(Be.a,{title:"Fotone"},n("p",null,"Un onda magnetica con un quanto di energia è detta ",n("i",null,"fotone"),":"),n("p",null,n(ke.a,null,Ue(a())))),n(Be.a,{title:"Effetto fotoelettrico"},n("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),n("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),n("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),n("p",null,"Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.")))))},t}(Ie.Component)}.call(this,t("hosL").h)},eCjK:function(n){n.exports={split:"split__3dL9r",splitparent:"splitparent__2H-vS",splitchild:"splitchild__1B-Jt"}},h7i1:function(n,e,t){"use strict";(function(n){t.d(e,"a",(function(){return i}));var a=t("56OW"),l=t.n(a),i=function(e){function t(){return e.apply(this,arguments)||this}var a,i;return i=e,(a=t).prototype=Object.create(i.prototype),a.prototype.constructor=a,a.__proto__=i,t.prototype.render=function(){return n("span",{class:l.a.plus},this.props.children)},t}(t("hosL").Component)}).call(this,t("hosL").h)},jXlC:function(n,e,t){"use strict";(function(n){t.d(e,"a",(function(){return i}));var a=t("3k98"),l=t.n(a),i=function(e){function 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extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1UVRh\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__2u13i\"};","import style from \"./panel.less\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (

{this.props.title}

);\n\t\t}\n\n\t\treturn (\n\t\t\t
\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
\n\t\t);\n\t}\n}\n","import style from './Latex.css';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nexport default function(props) {\n\t// black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n\tlet renderColor = useContext(LatexRenderColor);\n\tlet defaultInline = useContext(LatexDefaultInline);\n\n\tlet is_inline;\n\tif(props.inline === undefined) {\n\t\tis_inline = defaultInline;\n\t}\n\telse {\n\t\tis_inline = props.inline;\n\t}\n\n\tlet inline = is_inline ? `\\\\inline` : \"\";\n\tlet equation = `${inline} {\\\\color{${renderColor}} ${props.children} }`;\n\n\treturn (\n\t\t{props.children}\n\t\t\t\n\t);\n}\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tif (currentComponent.__hooks) {\n\t\tcurrentComponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\tcurrentComponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\tcurrentComponent.__hooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (!c) return;\n\n\tconst hooks = c.__hooks;\n\tif (hooks) {\n\t\tif (hooks._pendingEffects.length) {\n\t\t\tafterPaint(afterPaintEffects.push(c));\n\t\t}\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (!c) return;\n\n\tconst hooks = c.__hooks;\n\tif (hooks) {\n\t\ttry {\n\t\t\thooks._list.forEach(hook => hook._cleanup && hook._cleanup());\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index) {\n\tif (options._hook) options._hook(currentComponent);\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = { _list: [], _pendingEffects: [] });\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++);\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\tif (!provider) return context._defaultValue;\n\tconst state = getHookState(currentIndex++);\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (hook._cleanup) hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\tconst result = hook._value();\n\tif (typeof result == 'function') hook._cleanup = result;\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./minus.css\";\nimport { Component } from 'preact';\n\nexport default class Minus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import { Component } from 'preact';\nimport Latex from '../components/Latex';\nimport Panel from '../components/old/panel';\nimport Split from '../components/old/split';\nimport Plus from '../components/old/plus';\nimport Minus from '../components/old/minus';\nimport Todo from '../components/old/todo';\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nconst r = String.raw;\n\nexport default class Fisica extends Component {\n\trender() {\n return (\n \n
\n

Fisica

\n \n \n

\n Usa le regole base della trigonometria:\n

\n

\n {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n

\n

\n {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n

\n

\n {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n

\n \n \n

\n Scomponi in componenti, poi sommali:\n

\n

\n {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n

\n

\n Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n

\n \n \n

\n Alla fine è sempre una somma:\n

\n

\n {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n

\n

\n Produce il vettore che parte da w e arriva a v.\n

\n \n \n

\n Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n

\n

\n {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n

\n

\n Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n

\n \n \n

\n Si chiama vettoriale perchè il risultato è un altro vettore.\n

\n
    \n
  • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
    • \n
  • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
    • \n
  • Regola della mano destra
    • \n
\n

\n Non è commutativo!\n

\n \n \n \n \n

\n Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n

\n \n \n

\n La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n

\n

\n {r`\\Sigma \\vec{F} = m \\vec{a}`}\n

\n \n \n

\n Due corpi esercitano forze uguali e opposte uno sull'altro.\n

\n

\n {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n

\n \n \n \n \n

\n Due corpi puntiformi si attirano uno verso l'altro con forza:\n

\n

\n {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n

\n

\n G è la costante di gravitazione universale e vale:\n

\n

\n {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n

\n \n \n

\n Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n g è la costante di gravità della Terra, e vale:\n

\n

\n {r`g = 9.81 \\frac{m}{s^2}`}\n

\n \n \n

\n Per pianeti diversi dalla Terra vale la stessa regola:\n

\n

\n {r`\\left | \\vec{F} \\right | = g m`}\n

\n

\n L'unica differenza è che cambia la costante di gravità:\n

\n

\n {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n

\n

\n {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n

\n \n \n \n \n

\n Si oppone alle forze applicate alla superficie di contatto.\n

\n

\n Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere.\n

\n \n \n

\n Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n

\n

\n {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n

\n \n \n

\n E' forza trasmessa tra due estremi di una fune.\n

\n

\n Può essere redirezionata per mezzo di carrucole.\n

\n \n \n

\n Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n

\n

\n {r`F = -k x`}\n

\n

\n (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n

\n \n \n \n \n

\n È un vettore che indica la posizione di un corpo rispetto a un'origine.\n

\n

\n {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n

\n \n \n

\n È un vettore che misura la variazione di posizione nel tempo.\n

\n

\n {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n

\n

\n {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n

\n \n \n

\n È un vettore che misura la variazione di velocità nel tempo.\n

\n

\n {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n

\n

\n Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n

\n

\n {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n

\n \n Quantità di moto (momento lineare)}>\n

\n La quantità di moto è una proprietà vettoriale dei corpi:\n

\n

\n {r`\\vec{p} = m \\vec{v}`}\n

\n

\n Se la forza risultante è nulla, la quantità di moto non cambia.\n

\n

\n {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n

\n \n \n \n \n

\n La legge oraria è:\n

\n

\n {r`s(t) = v \\cdot \\Delta t + s(0)`}\n

\n \n \n

\n È costante:\n

\n

\n {r`v(t) = k`}\n

\n \n \n

\n La velocità non varia:\n

\n

\n {r`a(t) = 0`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = 0\n

\n \n \n \n \n

\n La legge oraria è:\n

\n

\n {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n

\n \n \n

\n È una retta:\n

\n

\n {r`v(t) = a \\Delta t + v(0)`}\n

\n \n \n

\n È costante:\n

\n

\n {r`a(t) = k`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n \n \n

\n E' la distanza dal centro massima che raggiunge il corpo.\n

\n

\n (L'ampiezza di una sinusoide.)\n

\n \n \n

\n Indica quanto in fretta cambia la posizione del corpo.\n

\n

\n Dipende dal periodo:\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n E' una sinusoide:\n

\n

\n {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n

\n \n \n

\n E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n

\n

\n {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n

\n \n \n

\n E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n

\n

\n {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n

\n \n \n

\n Si applica la prima legge di Newton:\n

\n

\n f(t) = m a\n

\n \n \n \n \n

\n Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n

\n \n \n

\n Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n

\n \n \n \n \n

\n Velocità angolare\n

\n

\n Quanto cambia la fase nel tempo.\n

\n

\n {r`\\omega = \\frac{2 \\pi}{T}`}\n

\n \n \n

\n E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n

\n

\n Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n

\n \n \n

\n Si applicano le formule per la circonferenza:\n

\n

\n {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n

\n \n \n

\n Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:\n

\n

\n {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n

\n \n \n

\n È verso il centro e si calcola con:\n

\n

\n {r`F = m \\cdot a`}\n

\n \n \n \n \n

\n E' compiuto da una forza che sposta un corpo.\n

\n

\n {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n

\n

\n (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n

\n \n \n

\n Un corpo ha energia cinetica in ogni momento uguale a:\n

\n

\n {r`E_c = \\frac{1}{2} m v^2`}\n

\n

\n Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n

\n

\n {r`\\Delta E_c = W`}\n

\n \n \n

\n Un corpo ha energia potenziale in ogni momento pari a:\n

\n

\n {r`E_{p_g} = m \\cdot g \\cdot h`}\n

\n

\n (Con h uguale a un altezza scelta come punto di riferimento.)\n

\n \n \n

\n Una molla ha sempre energia potenziale elastica pari a:\n

\n

\n {r`E_{p_e} = \\frac{1}{2} k x^2`}\n

\n \n \n

\n Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n

\n

\n Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n

\n

\n Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n

\n

\n {r`E = E_k + E_p`}\n

\n \n \n

\n È la velocità di trasferimento di energia:\n

\n

\n {r`P = \\frac{\\Delta E}{\\Delta t}`}\n

\n \n \n \n \n

\n È una proprietà dei corpi che può essere positiva o negativa.\n

\n

\n Si conserva: in un sistema chiuso la carica totale è costante.\n

\n

\n Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n

\n

\n Cariche opposte si attraggono; cariche uguali si respingono.\n

\n \n \n

\n Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n

\n

\n I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n

\n

\n Il corpo umano è un buon conduttore.\n

\n \n \n \n \n

\n E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n

\n \n \n \n \n

\n Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n

\n \n \n \n \n

\n Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n

\n \n \n

\n Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n

\n \n \n

\n Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n

\n

\n Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n

\n

\n Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n

\n \n \n \n \n

\n Due corpi carichi si attraggono tra loro con forza:\n

\n

\n {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n

\n

\n {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n

\n \n \n

\n La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n

\n

\n {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n

\n

\n {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n

\n \n \n

\n Misura che forza viene applicata in ogni punto su una carica unitaria:\n

\n

\n {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n

\n \n \n

\n È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n

\n

\n In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n

\n

\n {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n

\n

\n Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n

\n

\n {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n

\n

\n Circa. E' una specie di integrale...\n

\n \n \n

\n Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n

\n

\n {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n

\n

\n Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n

\n \n \n \n \n

\n Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n

\n \n \n \n Potenziale elettrico (tensione)}>\n

\n È il valore dell'energia potenziale elettrica per una carica unitaria.\n

\n

\n {r`V = \\frac{U_e}{q}`}\n

\n

\n La sua unità di misura è il Volt ({r`V`}).\n

\n

\n In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n

\n \n Corrente elettrica (intensità)}>\n

\n Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n

\n

\n {r`I = \\frac{\\Delta q}{\\Delta t}`}\n

\n

\n Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n

\n

\n La sua unità di misura è l'Ampere ({r`A`}).\n

\n \n Corrente continua (DC)}>\n

\n Quando in un circuito la direzione della corrente è costante.\n

\n \n Corrente alternata (AC)}>\n

\n Quando in un circuito la direzione della corrente si alterna periodicamente.\n

\n \n \n

\n Possiamo calcolare la potenza di un circuito:\n

\n

\n {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n

\n \n \n \n \n

\n Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n

\n

\n Il potenziale utilizzato è pari a:\n

\n

\n {r`V = R \\cdot I`}\n

\n

\n Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n

\n

\n La resistenza di un conduttore vale:\n

\n

\n {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n

\n

\n {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n

\n

\n {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n

\n \n \n

\n Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n

\n

\n Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n

\n

\n Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n

\n

\n {r`C = \\frac{q_{massima}}{\\Delta V}`}\n

\n

\n Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n

\n

\n La capacità aumenta se viene messo qualcosa tra le armature:\n

\n

\n {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n

\n

\n Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n

\n

\n Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n

\n

\n La sua unità di misura è il Farad ({r`Fa`})\n

\n \n \n

\n Misura la corrente elettrica se messo in serie.\n

\n

\n (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n

\n \n \n

\n Misura la differenza di potenziale se messo in parallelo.\n

\n

\n (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n

\n \n \n \n \n

\n Per nodo si intende un qualsiasi punto del circuito.\n

\n

\n Da un nodo entra ed esce la stessa corrente.\n

\n \n \n

\n Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n

\n

\n In una maglia chiusa, la somma delle differenze di potenziale è 0.\n

\n \n \n \n \n

\n Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n

\n

\n Parti di circuito in serie sono attraversate dalla stessa corrente.\n

\n \n \n

\n Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo.\n

\n

\n Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n

\n \n \n \n \n

\n Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n

\n

\n {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n

\n \n \n

\n Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n

\n

\n {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n

\n \n \n \n \n

\n Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n

\n

\n {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n

\n \n \n

\n Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n

\n

\n {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n

\n \n \n \n \n

\n E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n

\n

\n {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n

\n \n \n

\n Come un campo elettrico, ma per i magneti.\n

\n

\n Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n

\n \n \n

\n È \"quanto\" campo magnetico attraversa un percorso chiuso.\n

\n

\n Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n

\n

\n {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n

\n

\n {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n

\n

\n La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n

\n \n \n

\n Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n

\n

\n Ovvero, non esistono monopoli magnetici.\n

\n \n \n

\n L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n

\n

\n {r`\\Phi_B = \\mu_0 \\cdot I`}\n

\n \n \n \n Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n

\n I campi magnetici applicano una forza sulle cariche vicine:\n

\n

\n {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n

\n

\n Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n

\n

\n Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n

\n

\n In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n

\n \n \n

\n I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n

\n

\n {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n

\n

\n Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n

\n \n \n \n \n

\n Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n

\n \n \n

\n Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n

\n

\n All'interno del solenoide si crea un campo (quasi) uniforme:\n

\n

\n {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n

\n \n \n

\n Caso particolare della Legge di Ampère.\n

\n

\n Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n

\n

\n {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n

\n

\n Il campo magnetico così creato gira attorno al filo in senso antiorario.\n

\n

\n Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n

\n \n \n \n \n

\n Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.\n

\n

\n La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.\n

\n

\n Essa vale:\n

\n

\n {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n

\n

\n Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n

\n \n \n

\n In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n

\n

\n {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n

\n \n \n \n \n

\n Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n

\n

\n {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n

\n

\n Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n

\n \n \n

\n In un solenoide, la forza elettromotrice indotta è uguale a:\n

\n

\n {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n

\n

\n Dove {r`N`} è il numero delle spire del solenoide.\n

\n \n \n

\n Correnti o campi elettrici variabili creano un campo magnetico.\n

\n \n \n \n \n

\n Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n

\n

\n Si dice quindi che sono onde elettromagnetiche.\n

\n

\n Esse sono legate dalla relazione:\n

\n

\n {r`E = c \\cdot B`}\n

\n

\n Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n

\n

\n {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n

\n \n \n

\n {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n

\n

\n Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n

\n \n \n \n \n

\n I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n

\n

\n I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda.\n

\n

\n In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n

\n

\n {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n

\n

\n Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n

\n \n \n

\n Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori.\n

\n

\n Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n

\n

\n Energia, momento angolare e raggio sono quantizzati.\n

\n

\n Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n

\n \n \n \n \n

\n L'energia degli elettroni è quantizzata.\n

\n

\n Inoltre, per essi è valido che:\n

\n

\n {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n

\n

\n Ancora, il raggio delle orbite è uguale a:\n

\n

\n {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n

\n

\n Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n

\n

\n Infine, in ogni stato, l'energia è pari a:\n

\n

\n {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n

\n

\n Due elettroni non possono occupare lo stesso stato.\n

\n

\n Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n

\n \n \n \n \n

\n Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n

\n

\n Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n

\n \n \n \n \n

\n Refactor this\n

\n

\n Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n

\n

\n Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n

\n

\n Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n

\n \n \n

\n Legami in cui mancano elettroni.\n

\n

\n Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n

\n \n \n

\n Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n

\n
    \n
  • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
    • \n
  • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
    • \n
\n

\n Maggiore impurezza porta a maggiore conduttività.\n

\n \n \n

\n Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n

\n \n \n Ottica (non l'abbiamo fatta)}>\n \n

\n I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n

\n \n \n

\n Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n

\n

\n Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n

\n

\n {r`\\lambda_{max} \\cdot T`} è costante.\n

\n \n \n

\n L'energia assorbita e emessa dai corpi neri è quantizzata.\n

\n \n \n

\n Un onda magnetica con un quanto di energia è detta fotone:\n

\n

\n {r`E_{fotone} = h \\cdot f`}\n

\n \n \n

\n A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n

\n

\n Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n

\n

\n Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n

\n

\n Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n

\n \n \n
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Indice

\n \n Apprendimento ed evoluzione in sistemi artificiali}>\n

\n Appunti scritti mentre studiavo per l'esame di Apprendimento ed evoluzione in sistemi artificiali del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Basi di dati}>\n

\n Appunti scritti mentre studiavo per l'esame di Basi di dati del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Calcolo Numerico}>\n

\n Appunti scritti mentre studiavo per l'esame di Calcolo Numerico del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Ottimizzazione lineare intera}>\n

\n Appunti scritti mentre studiavo per l'esame di Ottimizzazione lineare intera del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n \n \n Statistica ed elementi di probabilità}>\n

\n Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\n

\n \n Cleaver}>\n

\n Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\n

\n \n Fisica}>\n

\n Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\n

\n \n Sistemi Operativi}>\n

\n Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\n

\n \n Algoritmi e Strutture Dati}>\n

\n Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\n

\n \n Videolezioni di Geometria}>\n

\n Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\n

\n \n Come installare MinGW}>\n

\n Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\n

\n \n \n \n @unimoreinfo}>\n

\n Il gruppo Telegram del corso di Informatica dell'Unimore!\n

\n \n Calendario Lezioni}>\n

\n Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\n

\n \n Erre2}>\n

\n Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\n

\n \n vezzalinistefano/Appunti-Algoritmi}>\n

\n Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\n

\n \n \n
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\n

Indice

\n \n Apprendimento ed evoluzione in sistemi artificiali}>\n

\n Appunti scritti mentre studiavo per l'esame di Apprendimento ed evoluzione in sistemi artificiali del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Basi di dati}>\n

\n Appunti scritti mentre studiavo per l'esame di Basi di dati del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Calcolo Numerico}>\n

\n Appunti scritti mentre studiavo per l'esame di Calcolo Numerico del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n Ottimizzazione lineare intera}>\n

\n Appunti scritti mentre studiavo per l'esame di Ottimizzazione lineare intera del corso triennale di Informatica all'Unimore.\n

\n

\n TODO: Il semestre è ancora in corso!\n

\n \n \n \n Statistica ed elementi di probabilità}>\n

\n Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\n

\n \n Cleaver}>\n

\n Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\n

\n \n Fisica}>\n

\n Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\n

\n \n Sistemi Operativi}>\n

\n Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\n

\n \n Algoritmi e Strutture Dati}>\n

\n Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\n

\n \n Videolezioni di Geometria}>\n

\n Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\n

\n \n Come installare MinGW}>\n

\n Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\n

\n \n \n \n @unimoreinfo}>\n

\n Il gruppo Telegram del corso di Informatica dell'Unimore!\n

\n \n Calendario Lezioni}>\n

\n Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\n

\n \n Erre2}>\n

\n Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\n

\n \n vezzalinistefano/Appunti-Algoritmi}>\n

\n Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\n

\n \n \n
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Come installare MinGW

\n \n\t\t\t\t\t

Scaricate l'installer ufficiale,\n\t\t\t\t\t\ted eseguitelo.

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Dovrebbe comparire questa schermata. Cliccate su Install, poi scegliete una cartella di installazione\n\t\t\t\t\t\t(ricordatevela!) e poi Continue. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate,\n\t\t\t\t\t\ttranne For all users, che dovrebbe essere disattivato.

\"\"/\n\t\t\t\t\t

Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\n\t\t\t\t\t\tContinue. Premetelo.

\"\"/\n\t\t\t\t\t

Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.

\"\"/\n\t\t\t\t\t

Nel nostro caso, dovrebbero servirci mingw32-base-bin (per il C e alcune librerie C++) e\n\t\t\t\t\t\tmingw32-gcc-g++-bin (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\n\t\t\t\t\t\tMark for Installation. Dovrebbe comparire una freccia gialla sul quadratino.

\"\"/\n\t\t\t\t\t

Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.

\"\"/\n\t\t\t\t\t

Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\n\t\t\t\t\t\tdopo circa 10 minuti.

\"\"/\n\t\t\t\t\t

Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.

\n\t\t\t\t\t\"\"/\n\t\t\t\t\t

Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.

\"\"/\n\t\t\t\t\t

Trovate la variabile d'ambiente globale Path, e fateci doppio click per modificarla.

\"\"/\n\t\t\t\t\t

Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.

\"\"/\n\t\t\t\t\t

Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\n\t\t\t\t\t\tchiudendole.

\n\t\t\t\t\t

Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe!

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);\n\t\t}\n\n\t\treturn (\n\t\t\t
\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
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\n

Come installare MinGW

\n \n\t\t\t\t\t

Scaricate l'installer ufficiale,\n\t\t\t\t\t\ted eseguitelo.

\"\"/\n\t\t\t\t\t

Dovrebbe comparire questa schermata. Cliccate su Install, poi scegliete una cartella di installazione\n\t\t\t\t\t\t(ricordatevela!) e poi Continue. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate,\n\t\t\t\t\t\ttranne For all users, che dovrebbe essere disattivato.

\"\"/\n\t\t\t\t\t

Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\n\t\t\t\t\t\tContinue. Premetelo.

\"\"/\n\t\t\t\t\t

Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.

\"\"/\n\t\t\t\t\t

Nel nostro caso, dovrebbero servirci mingw32-base-bin (per il C e alcune librerie C++) e\n\t\t\t\t\t\tmingw32-gcc-g++-bin (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\n\t\t\t\t\t\tMark for Installation. Dovrebbe comparire una freccia gialla sul quadratino.

\"\"/\n\t\t\t\t\t

Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.

\"\"/\n\t\t\t\t\t

Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\n\t\t\t\t\t\tdopo circa 10 minuti.

\"\"/\n\t\t\t\t\t

Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.

\n\t\t\t\t\t\"\"/\n\t\t\t\t\t

Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.

\"\"/\n\t\t\t\t\t

Trovate la variabile d'ambiente globale Path, e fateci doppio click per modificarla.

\"\"/\n\t\t\t\t\t

Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.

\"\"/\n\t\t\t\t\t

Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\n\t\t\t\t\t\tchiudendole.

\n\t\t\t\t\t

Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe!

\n\t\t\t\t\n\t\t\t
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Cliccate su ",e("code",null,"Install"),", poi scegliete una cartella di installazione (ricordatevela!) e poi ",e("code",null,"Continue"),". Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate, tranne ",e("code",null,"For all users"),", che dovrebbe essere disattivato."),e("img",{src:"https://i.imgur.com/brdw8Xy.png",alt:""}),e("p",null," Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto",e("code",null,"Continue"),". Premetelo."),e("img",{src:"https://i.imgur.com/aPTwrxz.png",alt:""}),e("p",null," Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo ",e("code",null,"apt")," su Ubuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità."),e("img",{src:"https://i.imgur.com/5QLSkFN.png",alt:""}),e("p",null," Nel nostro caso, dovrebbero servirci ",e("code",null,"mingw32-base-bin")," (per il C e alcune librerie C++) e",e("code",null,"mingw32-gcc-g++-bin")," (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete",e("code",null,"Mark for Installation"),". Dovrebbe comparire una freccia gialla sul quadratino."),e("img",{src:"https://i.imgur.com/zP74nks.png",alt:""}),e("p",null," Ora, è il momento di installare i pacchetti. Aprite il menù ",e("code",null,"Installation"),", poi premete",e("code",null,"Apply Changes"),", e di nuovo ",e("code",null,"Apply"),"."),e("img",{src:"https://i.imgur.com/jp4uz5B.png",alt:""}),e("p",null," Lasciate che scarichi, ci vorrà un po'. 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")))}}}.call(this,t("hosL").h)},r4EX:function(e){e.exports={panel:"panel__7bYPC"}}}]); +//# sourceMappingURL=route-mingwinstall.chunk.24a27.esm.js.map \ No newline at end of file diff --git a/docs/route-mingwinstall.chunk.111c3.esm.js.map b/docs/route-mingwinstall.chunk.24a27.esm.js.map similarity index 56% rename from docs/route-mingwinstall.chunk.111c3.esm.js.map rename to docs/route-mingwinstall.chunk.24a27.esm.js.map index 407b168..124558b 100644 --- a/docs/route-mingwinstall.chunk.111c3.esm.js.map +++ b/docs/route-mingwinstall.chunk.24a27.esm.js.map @@ -1 +1 @@ -{"version":3,"sources":[],"names":[],"mappings":"","file":"route-mingwinstall.chunk.111c3.esm.js","sourceRoot":""} \ No newline at end of file +{"version":3,"sources":[],"names":[],"mappings":"","file":"route-mingwinstall.chunk.24a27.esm.js","sourceRoot":""} \ No newline at end of file diff --git a/docs/route-mingwinstall.chunk.4f81b.css b/docs/route-mingwinstall.chunk.4f81b.css deleted file mode 100644 index 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strict";i.r(n),function(l){i.d(n,"default",(function(){return O}));var e=i("hosL"),a=i("lL4N"),t=i("OMhl"),o=i("HKwK"),u=i("PEwj"),s=(i("jXlC"),i("UEJU")),r=i("h7i1"),d=(i("3Gjt"),i("BSmf")),c=i("xY5u");let m,p,h,f,b,v,_,z,g,x,w,q,L,C,U,k,y,S,E,j,T,D,F=l=>l;const M=String.raw;class O extends e.Component{render(){return l("div",null,l("h1",null,"Ottimizzazione lineare intera"),l(a.a,{title:"Unimore"},l(o.a,{title:"Videolezioni su YouTube"},l("p",null,"Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!"),l("p",null,l("b",null,l("a",{href:"https://www.youtube.com/playlist?list=PLh93e8qjTszffkHNn-19CqUOhHFbhBlBh"},"Guardate i video qui!")))),l(o.a,{title:"Prossimi appelli"},l("ol",null,l("li",null,l(d.a,{to:"2020-06-08"})),l("li",null,l(d.a,{to:"2020-06-25"})),l("li",null,l(d.a,{to:"2020-07-14"}))))),l(a.a,{title:"Le basi"},l(o.a,{title:"Funzione obiettivo"},l("p",null,"La funzione obiettivo è la funzione con valore noto 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\n

Ottimizzazione lineare intera

\n \n \n

\n Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!\n

\n

\n Guardate i video qui!\n

\n \n \n \n \n

\n La funzione obiettivo è la funzione con valore noto sconosciuto:\n

\n

\n {r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}\n

\n \n \n

\n Funzione della funzione obiettivo che indica la direzione del suo aumento più veloce.\n

\n

\n {r`\\nabla f = \\frac{\\delta f}{\\delta x_1} e_1 + \\frac{\\delta f}{\\delta x_2} e_2 + \\frac{\\delta f}{\\delta x_n} e_n`}\n

\n

\n {r`e_i`} è la direzione della coordinata i-esima.\n

\n \n Se {r`n = 3`}, allora:\n
    \n
  • {r`e_1 = (1, 0, 0)`}
    • \n
  • {r`e_2 = (0, 1, 0)`}
    • \n
  • {r`e_3 = (0, 0, 1)`}
    • \n
\n \n \n Se la funzione obiettivo è z = 2w + 3x + 4y, il suo gradiente è {r`\\nabla z = (2, 3, 4)`}.\n \n \n \n \n \n
    \n
  • Solo equazioni
    • \n
  • Tutte le variabili maggiori di zero
    • \n
\n \n \n
    \n
  • Equazioni e disequazioni
    • \n
  • Tutte le variabili maggiori di zero
    • \n
\n \n \n
    \n
  • Equazioni e disequazioni
    • \n
  • Variabili con qualsiasi valore
    • \n
\n \n \n \n \n

\n Convertiamo ogni equazione {r`=`} in due disequazioni {r`\\leq`} e {r`\\geq`},\n

\n Why would you ever do that?!\n \n \n

\n Convertiamo le disequazioni in equazioni aggiungendo una variabile slack.\n

\n \n {r`a \\leq 3`} diventa {r`a + s_1 = 3`}.\n \n \n \n

\n Sostituiamo le variabili potenzialmente negative (unconstrained) {r`x_j`} con due variabili {r`x_j^+`} e {r`x_j^-`}.\n

\n \n {r`a \\in \\mathbb{Z}`} diventa {r`a^+ \\in \\mathbb{N}`} e {r`-a^- \\in \\mathbb{N}`}.\n \n \n \n \n \n

\n La funzione da minimizzare/massimizzare, tipicamente indicata con una {r`z`} al termine noto.\n

\n \n \n

\n Un modo per rappresentare sistemi in forma standard, anche noto come matrice equivalente completa del sistema.\n

\n \n Il sistema:

\n {r`\n \\begin{cases}\n 2000A + 1000B = z\\\\\n 1A \\leq 3\\\\\n 1B \\leq 3\\\\\n 2A + 2B \\leq 7\n \\end{cases}\n `}

\n Diventa in forma di tableau:

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
TNABs_1s_2
z2000100000
31010
30101
72200
\n \n \n \n

\n TODO: come spiegarla?\n

\n \n \n \n \n

\n Un algoritmo per massimizzare efficientemente variabili di sistemi lineari, derivato da Gauss-Jordan.\n

\n \n E' spiegato semplicemente qui.\n \n \n \n
    \n
  1. Trasforma il sistema in forma standard.
    2. \n
  2. Finchè ci sono variabili con coefficienti positivi nella funzione obiettivo:\n
      \n
    1. Scegli una variabile della funzione obiettivo, chiamandola variabile entrante. Come? Vedi nel prossimo pannello.
      2. \n
    2. Trova la variabile di base (detta variabile uscente) con il valore minore per questo rapporto: termine noto / coeff. variabile entrante
      3. \n
    3. Riscrivi tutte le funzioni del sistema in termini della variabile entrante.
      4. \n
    \n
    3. \n
  3. Il termine noto della funzione obiettivo è il tuo risultato.
    4. \n
\n \n \n
    \n
  • Coefficiente maggiore nella funzione obiettivo.
    • \n
  • Incremento maggiore della funzione obiettivo.
    • \n
  • A caso.
    • \n
  • Regola di Bland: scegli variabili entranti e uscenti con indice minore. Impedisce cicli infiniti!
    • \n
\n \n \n \n \n

\n Un estensione del Simplex per permettere la risoluzione di problemi con termini noti negativi.\n

\n

\n Prevede l'introduzione di un problema ausiliario.\n

\n \n \n
\n )\n }\n}\n","import style from \"./minus.css\";\nimport { Component } from 'preact';\n\nexport default class Minus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","import style from \"./plus.css\";\nimport { Component } from 'preact';\n\nexport default class Plus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__2Ld4F\"};"],"sourceRoot":""} \ No newline at end of file diff --git a/docs/route-ottimizzazioneLineare.chunk.9e341.js b/docs/route-ottimizzazioneLineare.chunk.9e341.js new file mode 100644 index 0000000..3636c92 --- /dev/null +++ b/docs/route-ottimizzazioneLineare.chunk.9e341.js @@ -0,0 +1,2 @@ +(window.webpackJsonp=window.webpackJsonp||[]).push([[9],{"/fDt":function(n,l,t){"use strict";t.r(l),function(n){function e(){var n=C(["\frac{termine noto}{coeff. variabile entrante}"],["\\frac{termine\\ noto}{coeff.\\ variabile\\ entrante}"]);return e=function(){return n},n}function i(){var n=C(["\n \begin{cases}\n 2000A + 1000B = z\\\n 1A leq 3\\\n 1B leq 3\\\n 2A + 2B leq 7\n end{cases}\n "],["\n \\begin{cases}\n 2000A + 1000B = z\\\\\n 1A \\leq 3\\\\\n 1B \\leq 3\\\\\n 2A + 2B \\leq 7\n \\end{cases}\n "]);return i=function(){return n},n}function a(){var n=C(["z"]);return a=function(){return n},n}function o(){var n=C(["-a^- in mathbb{N}"],["-a^- \\in \\mathbb{N}"]);return o=function(){return n},n}function r(){var n=C(["a^+ in mathbb{N}"],["a^+ \\in \\mathbb{N}"]);return r=function(){return n},n}function u(){var n=C(["a in mathbb{Z}"],["a \\in \\mathbb{Z}"]);return u=function(){return n},n}function s(){var n=C(["x_j^-"]);return s=function(){return n},n}function c(){var n=C(["x_j^+"]);return c=function(){return n},n}function d(){var n=C(["x_j"]);return d=function(){return n},n}function p(){var n=C(["a + s_1 = 3"]);return p=function(){return n},n}function f(){var n=C(["a leq 3"],["a \\leq 3"]);return f=function(){return n},n}function m(){var n=C(["geq"],["\\geq"]);return m=function(){return n},n}function h(){var n=C(["leq"],["\\leq"]);return h=function(){return n},n}function v(){var n=C(["="]);return v=function(){return n},n}function b(){var n=C(["\nabla z = (2, 3, 4)"],["\\nabla z = (2, 3, 4)"]);return b=function(){return n},n}function _(){var n=C(["e_3 = (0, 0, 1)"]);return _=function(){return n},n}function z(){var n=C(["e_2 = (0, 1, 0)"]);return z=function(){return n},n}function g(){var n=C(["e_1 = (1, 0, 0)"]);return g=function(){return n},n}function x(){var n=C(["n = 3"]);return x=function(){return n},n}function y(){var n=C(["e_i"]);return y=function(){return n},n}function w(){var n=C(["\nabla f = \frac{delta f}{delta x_1} e_1 + \frac{delta f}{delta x_2} e_2 + \frac{delta f}{delta x_n} e_n"],["\\nabla f = \\frac{\\delta f}{\\delta x_1} e_1 + \\frac{\\delta f}{\\delta x_2} e_2 + \\frac{\\delta 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",n(j.a,null,T(c()))," e ",n(j.a,null,T(s())),"."),n(O.a,null,n(j.a,null,T(u()))," diventa ",n(j.a,null,T(r()))," e ",n(j.a,null,T(o())),"."))),n(U.a,{title:"La forma standard"},n(k.a,{title:"Funzione obiettivo"},n("p",null,"La funzione da minimizzare/massimizzare, tipicamente indicata con una ",n(j.a,null,T(a()))," al termine noto.")),n(k.a,{title:"Tableu"},n("p",null,"Un modo per rappresentare sistemi in forma standard, anche noto come ",n("b",null,"matrice equivalente completa")," del sistema."),n(O.a,null,"Il sistema:",n("br",null),n("br",null),n(j.a,null,T(i())),n("br",null),n("br",null),"Diventa in forma di tableau:",n("br",null),n("br",null),n("table",{class:"right"},n("thead",null,n("tr",null,n("th",null,n("abbr",{title:"Termine 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{Component} from 'preact'\nimport Split from \"../components/old/split\";\nimport Latex from \"../components/Latex\";\nimport Panel from \"../components/old/panel\";\nimport Example from \"../components/example\";\nimport Todo from \"../components/old/todo\";\nimport Minus from \"../components/old/minus\";\nimport Plus from \"../components/old/plus\";\nimport Code from \"../components/old/code\";\nimport Timer from \"../components/old/timer\";\nimport Image from \"../components/Image\";\n\nconst r = String.raw;\n\nexport default class OttimizzazioneLineare extends Component {\n render() {\n return (\n
\n

Ottimizzazione lineare intera

\n \n \n

\n Ho rimosso il rumore in sottofondo da tutti i video di Ricerca Operativa!\n

\n

\n Guardate i video qui!\n

\n \n \n
    \n
    2. \n
    3. \n
    4. \n
\n \n \n \n \n

\n La funzione obiettivo è la funzione con valore noto sconosciuto:\n

\n

\n {r`z = C_1 \\cdot x_1 + C_2 \\cdot x_2 + C_n \\cdot x_n`}\n

\n \n \n

\n Funzione della funzione obiettivo che indica la direzione del suo aumento più veloce.\n

\n

\n {r`\\nabla f = \\frac{\\delta f}{\\delta x_1} e_1 + \\frac{\\delta f}{\\delta x_2} e_2 + \\frac{\\delta f}{\\delta x_n} e_n`}\n

\n

\n {r`e_i`} è la direzione della coordinata i-esima.\n

\n \n Se {r`n = 3`}, allora:\n
    \n
  • {r`e_1 = (1, 0, 0)`}
    • \n
  • {r`e_2 = (0, 1, 0)`}
    • \n
  • {r`e_3 = (0, 0, 1)`}
    • \n
\n \n \n Se la funzione obiettivo è z = 2w + 3x + 4y, il suo gradiente è {r`\\nabla z = (2, 3, 4)`}.\n \n \n \n \n \n
    \n
  • Solo equazioni
    • \n
  • Tutte le variabili maggiori di zero
    • \n
\n \n \n
    \n
  • Equazioni e disequazioni
    • \n
  • Tutte le variabili maggiori di zero
    • \n
\n \n \n
    \n
  • Equazioni e disequazioni
    • \n
  • Variabili con qualsiasi valore
    • \n
\n \n \n \n \n

\n Convertiamo ogni equazione {r`=`} in due disequazioni {r`\\leq`} e {r`\\geq`},\n

\n Why would you ever do that?!\n \n \n

\n Convertiamo le disequazioni in equazioni aggiungendo una variabile slack.\n

\n \n {r`a \\leq 3`} diventa {r`a + s_1 = 3`}.\n \n \n \n

\n Sostituiamo le variabili potenzialmente negative (unconstrained) {r`x_j`} con due variabili {r`x_j^+`} e {r`x_j^-`}.\n

\n \n {r`a \\in \\mathbb{Z}`} diventa {r`a^+ \\in \\mathbb{N}`} e {r`-a^- \\in \\mathbb{N}`}.\n \n \n \n \n \n

\n La funzione da minimizzare/massimizzare, tipicamente indicata con una {r`z`} al termine noto.\n

\n \n \n

\n Un modo per rappresentare sistemi in forma standard, anche noto come matrice equivalente completa del sistema.\n

\n \n Il sistema:

\n {r`\n \\begin{cases}\n 2000A + 1000B = z\\\\\n 1A \\leq 3\\\\\n 1B \\leq 3\\\\\n 2A + 2B \\leq 7\n \\end{cases}\n `}

\n Diventa in forma di tableau:

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
TNx_1x_2s_1s_2
z2000100000
31010
30101
72200
\n \n \n \n

\n Variabili che hanno tutti 0 e un 1 nella loro colonna del tableu.\n

\n

\n La loro controparte sono le variabili fuori base.\n

\n

\n Un sistema lineare è risolto quando tutte le variabili originali (x_n) sono nella base.\n

\n \n \n \n \n

\n Un algoritmo per massimizzare efficientemente variabili di sistemi lineari, derivato da Gauss-Jordan.\n

\n \n E' spiegato semplicemente qui.\n \n \n \n
    \n
  1. Trasforma il sistema in forma standard.
    2. \n
  2. Finchè ci sono variabili con coefficienti positivi nella funzione obiettivo:\n
      \n
    1. Scegli una variabile della funzione obiettivo, chiamandola variabile entrante. Come? Vedi nel prossimo pannello.
      2. \n
    2. Trova la variabile di base (detta variabile uscente) con il valore minore per il rapporto {r`\\frac{termine\\ noto}{coeff.\\ variabile\\ entrante}`}
      3. \n
    3. Riscrivi tutte le funzioni del sistema in termini della variabile entrante.
      4. \n
    \n
    3. \n
  3. Il termine noto della funzione obiettivo è il tuo risultato.
    4. \n
\n \n \n

\n Se il problema è rappresentato in forma di tableau, allora esso è risolvibile applicando l'algoritmo di Gauss-Jordan, in aggiunta tenendo conto delle regole per la selezione delle variabili entranti e uscenti.\n

\n \n \n
    \n
  • Coefficiente maggiore nella funzione obiettivo.
    • \n
  • Incremento maggiore della funzione obiettivo.
    • \n
  • A caso.
    • \n
  • Regola di Bland: scegli variabili entranti e uscenti con indice minore (ovvero, prendi le prime possibili). È usato nella teoria perchè impedisce i cicli infiniti!
    • \n
\n \n \n \n Ho risolto il problema 3 del file Ex_LP_testo con il Simplex:\n

\n \n

\n \n \n \n \n \n

\n Un estensione del Simplex per permettere la risoluzione di problemi con termini noti negativi.\n

\n

\n Prevede l'introduzione di un problema ausiliario.\n

\n \n \n
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tre..."'),l("p",null,"Un insieme di esiti e eventi:"),l("ul",null,l("li",null,l("b",null,"Finito"),"."),l("li",null,"In cui tutti gli eventi hanno ",l("b",null,"probabilità diversa da 0"),"."),l("li",null,"In cui tutti gli eventi sono ",l("b",null,"mutualmente esclusivi"),"."),l("li",null,"In cui l'unione di tutti i suoi elementi ",l("b",null,"copre lo spazio campionario"),".")),l("p",null,"La partizione ",l(e.a,null,ee(S||(S=ne`E_i`)))," è composta dagli eventi ",l(e.a,null,ee(C||(C=ne`E_1`))),", ",l(e.a,null,ee(I||(I=ne`E_2`))),", ",l(e.a,null,ee(N||(N=ne`E_3`))),", fino a ",l(e.a,null,ee(V||(V=ne`E_n`))),"."),l(u.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),l(o.a,{title:"Assiomi della probabilità"},l(t.a,{title:"Primo assioma della probabilità"},l("p",null,"La probabilità di un evento è un numero tra 0 e 1."),l("p",null,l(e.a,null,ee(Y||(Y=ne`\forall E \in \mathcal{F}, 0 \leq P(E) 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probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),l("p",null,l(e.a,null,ee(B||(B=ne`P(E \cup F) = P(E) + P(F) - P(E \cap F)`)))),l(u.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),l(o.a,{title:"Spazi equiprobabili"},l(t.a,{title:"Cosa sono?"},l("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),l("p",null,l(e.a,null,ee(A||(A=ne`P(E) = \frac{len(E)}{len(\Omega)}`))))),l(t.a,{title:"Spazi equiprobabili geometrici"},l("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",l("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),l(o.a,{title:"Calcolo combinatorio"},l(t.a,{title:"Disposizioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho 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Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,ee(G||(G=ne`\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}`))))),l(t.a,{title:"Disposizioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,ee(T||(T=ne`\boldsymbol{D}^{r}_{n, k} = n^k`))))),l(t.a,{title:"Combinazioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,ee(Q||(Q=ne`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`))))),l(t.a,{title:"Combinazioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,ee(O||(O=ne`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`))))),l(t.a,{title:"Permutazioni"},l("p",null,"Estraggo ",l(e.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),l("p",null,l(e.a,null,ee(R||(R=ne`\boldsymbol{P}_n = n!`)))))),l(o.a,{title:"Probabilità condizionata"},l(t.a,{title:"Eventi condizionati"},l("blockquote",null,'"E dato F"'),l("p",null,"La probabilità che si verifichi ",l(e.a,null,"E")," sapendo che ",l("b",null,"si è già verificato")," ",l(e.a,null,"F"),"."),l("p",null,l(e.a,null,ee(K||(K=ne`P(E|F) = \frac{P(E \cap F)}{P(F)}`)))),l(u.a,null,"Ricorda vagamente le pipe di ",l("code",null,"bash"),", però al contrario...")),l(t.a,{title:"Eventi mutualmente esclusivi"},l("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),l("p",null,l(e.a,null,ee(W||(W=ne`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`)))))),l(o.a,null,l(t.a,{title:"Regola della catena"},l("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),l("p",null,l(e.a,null,ee(j||(j=ne`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`)))))),l(o.a,{title:"Le alternative"},l(t.a,{title:"Legge delle alternative"},l("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),l("p",null,l(e.a,null,ee(Z||(Z=ne`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`))))),l(t.a,{title:"Legge condizionata delle alternative"},l("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",l("b",null,"evento"),":"),l("p",null,l(e.a,null,ee(J||(J=ne`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`))))),l(t.a,{title:"Formula di Bayes"},l("p",null,"Tramite la ",l("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),l("p",null,l(e.a,null,ee(H||(H=ne`P(E_h | F) = \frac{P(F | E_h) \cdot P(E_h)}{P(F)}`)))),l(u.a,null,"In pratica, invertiamo gli eventi."))),l(o.a,{title:"Eventi indipendenti"},l(t.a,{title:"Due eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a due a due"'),l("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),l("p",null,l(e.a,null,ee($||($=ne`P(E \cap F) = P(E) \cdot P(F) \Longleftrightarrow P(E|F) = P(E) \Longleftrightarrow P(F|E) = P(F)`))))),l(t.a,{title:"Più eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),l("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),l("p",null,l(e.a,null,ee(ll||(ll=ne`P(E \cap F \cap G) = P(E) \cdot P(F) \cdot P(G)`)))),l("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),l(t.a,{title:"Famiglia di eventi indipendenti"},l("p",null,"Un insieme di ",l(e.a,null,"n")," eventi è una ",l("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),l(u.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),l(o.a,{title:"Variabili aleatorie"},l(t.a,{title:"Variabile aleatoria"},l("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",l(e.a,null,ee(al||(al=ne`X(\omega) : \Omega \to \mathbb{R}`))),".")),l(t.a,{title:l("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},l("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",l(e.a,null,ee(il||(il=ne`A_t = \{ \omega | X(\omega) \leq t \}`))),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",l(e.a,null,"t"),"."),l("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),l("p",null,l(e.a,null,ee(nl||(nl=ne`\forall t \in \mathbb{R}, A_t \in \mathcal{F}`)))),l(u.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),l(t.a,{title:"Supporto"},l("blockquote",null,'"supporto di X"'),l("p",null,"Il ",l("b",null,"codominio")," della variabile aleatoria è il suo ",l("i",null,"supporto"),"."),l("p",null,"Per indicare che un valore ",l(e.a,null,"x_0")," appartiene al supporto di ",l(e.a,null,"X"),", si usa la notazione ",l(e.a,null,"X \\mapsto x_0"),"."))),l(o.a,{title:"Densità"},l(t.a,{title:"Funzione probabilità"},l("p",null,"La ",l("i",null,"funzione probabilità")," ",l(e.a,null,ee(el||(el=ne`p_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"discreta")," ",l(e.a,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),l("p",null,l(e.a,null,ee(tl||(tl=ne`p_X (x) = \begin{cases} - P([X = x]) \quad se\ X \mapsto x \\ - 0 \qquad \qquad \quad se\ X \not\mapsto x - \end{cases}`))))),l(t.a,{title:"Funzione densità"},l("p",null,"La ",l("i",null,"funzione densità")," ",l(e.a,null,ee(ol||(ol=ne`f_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"continua")," ",l(e.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),l("p",null,l(e.a,null,ee(ul||(ul=ne`P([a < X \leq b]) = \int_a^b f_X (x) dx`)))),l("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",l("b",null,"non esista")," per una certa variabile aleatoria."),l(u.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),l(o.a,{title:"Funzione di ripartizione"},l(t.a,{title:"Definizione"},l("p",null,"Ogni variabile aleatoria ha una ",l("i",null,"funzione di ripartizione")," ",l(e.a,null,ee(rl||(rl=ne`F_X : \mathbb{R} \to [0, 1]`)))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",l(e.a,null,"t"),":"),l("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",l(e.a,null,ee(sl||(sl=ne`A_t`))),":"),l("p",null,l(e.a,null,ee(pl||(pl=ne`F_X (t) = P(A_t) = \begin{cases} - \sum_{i = 0}^{t} p_X (x_i) \quad nel\ discreto\\ - \\ - \int_{-\infty}^t f_X (x) dx \quad nel\ continuo - \end{cases}`))))),l(t.a,{title:"Proprietà della funzione"},l("ul",null,l("li",null,"È sempre ",l("b",null,"monotona crescente")," (non strettamente)."),l("br",null),l("li",null,"Vale ",l("b",null,"0")," a ",l(e.a,null,"-\\infty")," e ",l("b",null,"1")," a ",l(e.a,null,"+\\infty"),"."),l("br",null),l("li",null,"È ",l("b",null,"continua da destra"),": ",l(e.a,null,ee(dl||(dl=ne`\forall x_0 \in \mathbb{R}, F_X (x_0) = \lim_{t \to x^+_0} F_X (t)`)))))),l(t.a,{title:"Probabilità di un valore"},l("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),l("p",null,l(e.a,null,ee(ml||(ml=ne`P([X = x_0]) = \lim_{t \to x^+_0} F_X (t) - \lim_{t \to x^-_0} F_X (t)`)))))),l(o.a,{title:"Trasformazioni di variabili aleatorie"},l(t.a,{title:"Nel discreto"},l("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),l(t.a,{title:"Nel continuo (invertibile)"},l("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),l("p",null,l(e.a,null,ee(cl||(cl=ne`f_Y (y) = \int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`))))),l(t.a,{title:"Nel... digitale"},l("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",l("a",{href:"https://docs.python.org/3/library/random.html#random.random"},l("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),l(o.a,{title:"Informazioni delle variabili aleatorie"},l(t.a,{title:"Media"},l("p",null,"Ogni variabile aleatoria che ha una ",l("b",null,"funzione di ripartizione")," e un ",l("b",null,"supporto finito")," ha anche una ",l("i",null,"media")," (o ",l("i",null,"valore medio")," o ",l("i",null,"atteso"),"):"),l("p",null,l(e.a,null,ee(bl||(bl=ne`E(X) = \int_0^{+infty} (1 - F_X (t)) dt - \int_{-\infty}^{0} F_X (t) dt`)))),l("p",null,"Nel discreto, si può calcolare con:"),l("p",null,l(e.a,null,ee(vl||(vl=ne`E(X) = \sum_i P(X = x_i) \cdot x_i`)))),l("p",null,"Nel continuo, si può calcolare con:"),l("p",null,l(e.a,null,ee(fl||(fl=ne`E(X) = \int_{-\infty}^{+\infty} f_X (x) \cdot x \cdot dx`)))))),l(o.a,null,l(t.a,{title:"Moda"},l("p",null,"Valore per cui la ",l("b",null,"funzione probabilità")," o ",l("b",null,"funzione densità")," è ",l("b",null,"massima"),".")),l(t.a,{title:"Quantili"},l("p",null,"Il ",l("i",null,"quantile")," ",l(e.a,null,ee(hl||(hl=ne`x_{\alpha}`)))," di ordine ",l(e.a,null,ee(gl||(gl=ne`0 \leq \alpha \leq 1`)))," della variabile aleatoria ",l(e.a,null,"X")," è il più piccolo numero tale che:"),l("p",null,l(e.a,null,ee(_l||(_l=ne`P([X < x_{\alpha}]) \leq \alpha \leq P([X \leq x_{\alpha}])`)))),l("p",null),l("p",null,"Il quantile di ordine 0.5 ",l(e.a,null,ee(zl||(zl=ne`x_{0.5}`)))," è detto ",l("i",null,"mediana"),"."),l("p",null,"I quantili di ordine 0.25 ",l(e.a,null,ee(Xl||(Xl=ne`x_{0.25}`)))," e 0.75 ",l(e.a,null,ee(ql||(ql=ne`x_{0.75}`)))," sono detti ",l("i",null,"quartili"),"."),l("p",null,"I quantili di ordine ",l(e.a,null,ee(El||(El=ne`\frac{n}{100}`)))," sono detti ",l("i",null,l(e.a,null,"n"),"-esima percentile"),".")),l(t.a,{title:"Varianza"},l("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),l("p",null,l(e.a,null,ee(Ll||(Ll=ne`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`)))))),l(o.a,{title:"Disuguaglianze notevoli"},l(t.a,{title:"Disuguaglianza di Markov"},l("p",null,"Data una variabile aleatoria non-negativa:"),l("p",null,l(e.a,null,ee(xl||(xl=ne`\forall k > 0, P([X \geq k]) \leq \frac{E(X)}{k}`)))),l("p",null,"Divide in due parti (",l(e.a,null,ee(Pl||(Pl=ne`P(X < k)`)))," e ",l(e.a,null,ee(kl||(kl=ne`P(X \geq k)`))),") la funzione X, la cui media risulterà uguale a:"),l("p",null,l(e.a,null,ee(Fl||(Fl=ne`E(X) = \overline{k} \cdot P(X < k) + k \cdot P(X \geq k)`))))),l(t.a,{title:"Disuguaglianza di Čebyšëv"},l("blockquote",null,'"disuguaglianza di cebicev"'),l("p",null,"Se la variabile aleatoria ",l(e.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",l(e.a,null,ee(yl||(yl=ne`\epsilon`)))," di distanza dal valore medio è minore o uguale a ",l(e.a,null,ee(Sl||(Sl=ne`\frac{Var(X)}{\epsilon^2}`))),"."),l("p",null,l(e.a,null,ee(Cl||(Cl=ne`\forall \epsilon > 0, P([ \left| X - E(X) \right| \geq \epsilon]) \leq \frac{Var(X)}{\epsilon^2}`)))),l("p",null,"E anche:"),l("p",null,l(e.a,null,ee(Il||(Il=ne`\forall \epsilon > 0, P([ \left| X - E(X) \right| < \epsilon]) \geq 1 - \frac{Var(X)}{\epsilon^2}`)))),l(u.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),l(o.a,{title:"Un momento...!"},l(t.a,{title:"Momento"},l("p",null,"Il ",l("i",null,"momento")," ",l(e.a,null,"k"),"-esimo di una variabile aleatoria è:"),l("p",null,l(e.a,null,ee(Nl||(Nl=ne`\mu_k = E ( X^k ) = \begin{cases} - \sum_i x_i^k p_X (x_i) \qquad nel\ discreto\\ - \\ - \int_{-\infty}^{+\infty} x^k f_X (x) dx \qquad nel\ continuo - \end{cases}`)))),l(u.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),l(t.a,{title:"Funzione generatrice dei momenti"},l("p",null,"La ",l("i",null,"funzione generatrice dei momenti")," è:"),l("p",null,l(e.a,null,ee(Vl||(Vl=ne`m_X (t) = E( e^{t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),l(t.a,{title:"Funzione caratteristica"},l("p",null,"La ",l("i",null,"funzione caratteristica")," è:"),l("p",null,l(e.a,null,ee(Yl||(Yl=ne`H_X (t) = E ( e^{i \cdot t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),l(o.a,{title:"Prove e schemi"},l(t.a,{title:"Variabile con distribuzione"},l("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),l("p",null,l(e.a,null,ee(wl||(wl=ne`X \sim Distribuzione()`))))),l(t.a,{title:"Prova di Bernoulli"},l("p",null,"Una prova con solo due possibili esiti: ",l(r.a,null,"successo")," e ",l(s.a,null,"insuccesso"),".")),l(t.a,{title:"Schema di Bernoulli"},l("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),l(o.a,{title:"Bernoulliana"},l(t.a,{title:"Distribuzione bernoulliana"},l("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),l("ul",null,l("li",null,"vale ",l(r.a,null,"1")," in caso di ",l(r.a,null,"successo"),"."),l("li",null,"vale ",l(s.a,null,"0")," in caso di ",l(s.a,null,"insuccesso"),".")),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(Dl||(Dl=ne`Ber(p)`))))),l(t.a,{title:"Densità della bernoulliana"},l("p",null,"La distribuzione bernoulliana ha come densità:"),l("p",null,l(e.a,null,ee(Ul||(Ul=ne`f_X (k) : \{0, 1\} = \begin{cases} - p \quad se\ k = 1\\ - q \quad se\ k = 0\\ - 0 \quad altrimenti - \end{cases} = p^x \cdot q^{1 - k}`)))))),l(o.a,{title:"Binomiale"},l(t.a,{title:"Distribuzione binomiale"},l("p",null,"Una variabile aleatoria che conta il numero di successi di ",l(e.a,null,"n")," prove di uno schema di Bernoulli."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(Ml||(Ml=ne`Bin(n, p)`))),".")),l(t.a,{title:"Densità della binomiale"},l("p",null,"La binomiale ha come densità:"),l("p",null,l(e.a,null,ee(Bl||(Bl=ne`f_X (k) : \{0..n\} = \binom{n}{k} \cdot p^k \cdot q^{n - k}`))))),l(t.a,{title:"Momenti della binomiale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale è:"),l("p",null,l(e.a,null,ee(Al||(Al=ne`m_X (t) = (q + p \cdot e^t) ^ n`)))),l("p",null,"La ",l("b",null,"media")," di una binomiale è:"),l("p",null,l(e.a,null,ee(Gl||(Gl=ne`E(X) = n \cdot p`)))),l("p",null,"La ",l("b",null,"varianza")," di una binomiale è:"),l("p",null,l(e.a,null,ee(Tl||(Tl=ne`Var(X) = n \cdot p \cdot q`)))))),l(o.a,{title:"Geometrica"},l(t.a,{title:"Distribuzione geometrica"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),l("p",null,"Il suo simbolo è ",l(e.a,null,"Geo(p)"),".")),l(t.a,{title:"Densità della geometrica"},l("p",null,"La geometrica ha come densità:"),l("p",null,l(e.a,null,ee(Ql||(Ql=ne`f_X (k) : \mathbb{N} = q^{k - 1} p`))))),l(t.a,{title:"Momenti della geometrica"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica è:"),l("p",null,l(e.a,null,ee(Ol||(Ol=ne`m_X (t) = \frac{p \cdot e^t}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica è:"),l("p",null,l(e.a,null,ee(Rl||(Rl=ne`E(X) = \frac{1}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(e.a,null,ee(Kl||(Kl=ne`Var(X) = \frac{q}{p^2}`))))),l(t.a,{title:"Assenza di memoria della geometrica"},l("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,ee(Wl||(Wl=ne`P([X = i + j | X > i ]) = P([X = j])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Binomiale negativa"},l(t.a,{title:"Distribuzione binomiale negativa"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",l(e.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(jl||(jl=ne`\overline{Bin}(n, p)`))),".")),l(t.a,{title:"Densità della binomiale negativa"},l("p",null,"La binomiale negativa ha come densità:"),l("p",null,l(e.a,null,ee(Zl||(Zl=ne`f_X (k) : \{ n .. +\infty \} \in \mathbb{N} = \binom{k - 1}{n - 1} \cdot p^n \cdot q^{k - n} `))))),l(t.a,{title:"Momenti della binomiale negativa"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),l("p",null,l(e.a,null,ee(Jl||(Jl=ne`m_X (t) : \{ t < ln(\frac{1}{q}) \} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa è:"),l("p",null,l(e.a,null,ee(Hl||(Hl=ne`E(X) = \frac{n}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa è:"),l("p",null,l(e.a,null,ee($l||($l=ne`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(o.a,{title:"Geometrica traslata"},l(t.a,{title:"Distribuzione geometrica traslata"},l("p",null,"Una variabile aleatoria che conta il numero ",l(e.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),l("p",null,"Il suo simbolo rimane ",l(e.a,null,ee(la||(la=ne`Geo(p)`))),".")),l(t.a,{title:"Densità della geometrica tralsata"},l("p",null,"La geometrica traslata ha come densità:"),l("p",null,l(e.a,null,ee(aa||(aa=ne`f_X (k) : \mathbb{N} = p \cdot q^k `))))),l(t.a,{title:"Momenti della geometrica traslata"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),l("p",null,l(e.a,null,ee(ia||(ia=ne`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \frac{p}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica traslata è:"),l("p",null,l(e.a,null,ee(na||(na=ne`E(X) = \frac{q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(e.a,null,ee(ea||(ea=ne`Var(X) = \frac{q}{p^2}`))))),l(t.a,{title:"Assenza di memoria della geometrica traslata"},l("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,ee(ta||(ta=ne`P([X = i + j | X > i ]) = P([X = j])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Binomiale negativa traslata"},l(t.a,{title:"Distribuzione binomiale negativa traslata"},l("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",l(e.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo rimane ",l(e.a,null,ee(oa||(oa=ne`\overline{Bin}(n, p)`))),".")),l(t.a,{title:"Densità della binomiale negativa traslata"},l("p",null,"La binomiale negativa traslata ha come densità:"),l("p",null,l(e.a,null,ee(ua||(ua=ne`f_X (k) : \mathbb{N} = \binom{k + n - 1}{n - 1} \cdot p^n \cdot q^k `))))),l(t.a,{title:"Momenti della binomiale negativa traslata"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,ee(ra||(ra=ne`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,ee(sa||(sa=ne`E(X) = \frac{n \cdot q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,ee(pa||(pa=ne`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(o.a,{title:"Ipergeometrica"},l(t.a,{title:"Distribuzione ipergeometrica"},l("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",l(e.a,null,"K")," e di insuccessi ",l(e.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",l(e.a,null,"n")," in blocco."),l("p",null,"Il suo simbolo è ",l(e.a,null,"Ipe(N, K, n)"),".")),l(t.a,{title:"Densità della ipergeometrica"},l("p",null,"La ipergeometrica ha come densità:"),l("p",null,l(e.a,null,ee(da||(da=ne`f_X (k) : \{0..n\} \in \mathbb{N} = \frac{\binom{K}{k} \cdot \binom{N - K}{n - k}}{\binom{N}{n}}`))))),l(t.a,{title:"Momenti della ipergeometrica"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),l("p",null,"La ",l("b",null,"media")," della ipergeometrica è:"),l("p",null,l(e.a,null,ee(ma||(ma=ne`E(X) = n \cdot \frac{K}{N}`)))),l("p",null,"La ",l("b",null,"varianza")," della ipergeometrica è:"),l("p",null,l(e.a,null,ee(ca||(ca=ne`Var(X) = n \cdot \frac{K}{N} \cdot \frac{N - K}{N} \cdot \frac{N - n}{N - 1}`))))))),l(o.a,{title:"Poissoniana"},l(t.a,{title:"Distribuzione poissoniana"},l("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),l("ul",null,l("li",null,"Binomiale: ",l(e.a,null,ee(ba||(ba=ne`X \sim Bin(n, p)`)))),l("li",null,"Il numero di prove tende a infinito: ",l(e.a,null,ee(va||(va=ne`n \to +\infty`)))),l("li",null,"La probabilità di successo tende a 0: ",l(e.a,null,ee(fa||(fa=ne`p \to 0`)))),l("li",null,"La media è finita: ",l(e.a,null,ee(ha||(ha=ne`E(X) = n \cdot p \to \mu \neq 0`))))),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(ga||(ga=ne`Poi(\mu)`))))),l(t.a,{title:"Densità della poissoniana"},l("p",null,"La poissoniana ha come densità:"),l("p",null,l(e.a,null,ee(_a||(_a=ne`f_X (k) : \mathbb{N} = \frac{e^{-\mu} \cdot \mu^k}{k!}`))))),l(t.a,{title:"Momenti della poissoniana"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),l("p",null,l(e.a,null,ee(za||(za=ne`m_X (t) = e^{\mu \cdot (e^t - 1)}`)))),l("p",null,"La ",l("b",null,"media")," della poissoniana è:"),l("p",null,l(e.a,null,ee(Xa||(Xa=ne`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della poissoniana è:"),l("p",null,l(e.a,null,ee(qa||(qa=ne`Var(X) = \mu`)))),l("p",null,"Gli altri momenti della poissoniana sono:"),l("ol",{start:2},l("li",null,l(e.a,null,ee(Ea||(Ea=ne`E(X^2) = \mu^2 + \mu`)))))))),l(o.a,{title:"Un altro schema"},l(t.a,{title:"Schema di Poisson"},l("p",null,"Una successione di ",l("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),l("ul",null,l("li",null,"non sono sovrapposti."),l("li",null,"hanno intensità ",l(e.a,null,ee(La||(La=ne`\lambda`)))," costante."),l("li",null,"avvengono indipendentemente gli uni dagli altri."))),l(t.a,{title:"Processo di Poisson"},l("p",null,"Una variabile aleatoria ",l(e.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",l(e.a,null,ee(xa||(xa=ne`\lambda`)))," in un intervallo di tempo di durata ",l(e.a,null,"t"),"."),l("p",null,"E' una distribuzione poissoniana con ",l(e.a,null,ee(Pa||(Pa=ne`\mu = t \cdot \lambda`))),": ",l(e.a,null,ee(ka||(ka=ne`Poi(t \cdot \lambda)`)))),l(u.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),l(o.a,{title:"Esponenziale"},l(t.a,{title:"Distribuzione esponenziale"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",l(e.a,null,ee(Fa||(Fa=ne`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(ya||(ya=ne`Esp(\lambda)`))),".")),l(t.a,{title:"Densità dell'esponenziale"},l("p",null,"L'esponenziale ha come ",l("b",null,"densità"),":"),l("p",null,l(e.a,null,ee(Sa||(Sa=ne`f_X (x) = \begin{cases} - 0 \qquad \qquad x < 0\\ - \lambda \cdot e^{-\lambda \cdot x} \quad x > 0 - \end{cases}`)))),l("p",null,"L'esponenziale ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(e.a,null,ee(Ca||(Ca=ne`F_X (t) = \begin{cases} - 0 \qquad \qquad t < 0\\ - 1 - e^{-\lambda \cdot t} \quad t \geq 0 - \end{cases}`))))),l(t.a,{title:"Momenti dell'esponenziale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),l("p",null,l(e.a,null,ee(Ia||(Ia=ne`m_X (t) : \{ t | t < \lambda \} \in \mathbb{R} = \frac{\lambda}{\lambda - t}`)))),l("p",null,"La ",l("b",null,"media")," dell'esponenziale è:"),l("p",null,l(e.a,null,ee(Na||(Na=ne`E(X) = \frac{1}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," dell'esponenziale è:"),l("p",null,l(e.a,null,ee(Va||(Va=ne`Var(X) = \frac{1}{\lambda^2}`))))),l(t.a,{title:"Assenza di memoria della esponenziale"},l("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,ee(Ya||(Ya=ne`P([X > s + t | X > s]) = P([X > t])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Legge gamma"},l(t.a,{title:"Distribuzione gamma"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",l(e.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",l(e.a,null,ee(wa||(wa=ne`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(Da||(Da=ne`\Gamma(n, \lambda)`))),".")),l(t.a,{title:"Densità della legge gamma"},l("p",null,"La legge gamma ha come densità:"),l("p",null,l(e.a,null,ee(Ua||(Ua=ne`f_X (x) = \begin{cases} - 0 \qquad \qquad \qquad \qquad \qquad x < 0\\ - \frac{1}{(n-1)!} \cdot \lambda^n \cdot x^{n-1} \cdot e^{-\lambda \cdot x} \quad k > 0 - \end{cases}`))))),l(t.a,{title:"Momenti della legge gamma"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),l("p",null,l(e.a,null,ee(Ma||(Ma=ne`m_X (t) : ( t < \lambda ) \in \mathbb{R} = \left( \frac{\lambda}{\lambda - t} \right) ^\alpha`)))),l("p",null,"La ",l("b",null,"media")," della legge gamma è:"),l("p",null,l(e.a,null,ee(Ba||(Ba=ne`E(X) = \frac{\alpha}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," della legge gamma è:"),l("p",null,l(e.a,null,ee(Aa||(Aa=ne`Var(X) = \frac{\alpha}{\lambda^2}`))))))),l(o.a,{title:"Uniforme"},l(t.a,{title:"Distribuzione uniforme"},l("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",l(e.a,null,ee(Ga||(Ga=ne`[a, b]`)))," in modo equiprobabile."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(Ta||(Ta=ne`Uni(a, b)`)))),l("p",null,"Su di essa vale la seguente proprietà:"),l("p",null,l(e.a,null,ee(Qa||(Qa=ne`P(X \in (c, d)) = \frac{d - c}{b - a}`))))),l(t.a,{title:"Densità della distribuzione uniforme"},l("p",null,"La distribuzione uniforme ha come ",l("b",null,"densità"),":"),l("p",null,l(e.a,null,ee(Oa||(Oa=ne`f_X (x) = \begin{cases} - \frac{1}{b - a} \qquad a \leq x \leq b\\ - 0 \qquad \quad altrimenti - \end{cases}`)))),l("p",null,"La distribuzione uniforme ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(e.a,null,ee(Ra||(Ra=ne`f_X (x) = \begin{cases} - 0 \qquad \quad x < a - \frac{1}{b - a} \qquad a \leq x \leq b\\ - 1 \qquad \quad x > b - \end{cases}`))))),l(t.a,{title:"Momenti della distribuzione uniforme"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,ee(Ka||(Ka=ne`m_X (t) = \frac{e^{b \cdot t} - e^{a \cdot t}}{(b - a) \cdot t}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,ee(Wa||(Wa=ne`E(X) = \frac{a + b}{2}`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,ee(ja||(ja=ne`Var(X) = \frac{(b - a)^2}{12}`))))))),l(o.a,{title:"Normale o Gaussiana"},l(t.a,{title:"Distribuzione normale"},l("p",null,"Una variabile aleatoria con una specifica distribuzione."),l("p",null,"Il suo simbolo è ",l(e.a,null,ee(Za||(Za=ne`Nor(\mu, \sigma^2)`))),"."),l(u.a,null,l(e.a,null,"\\mu")," e ",l(e.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),l(t.a,{title:"Densità della distribuzione normale"},l("p",null,"La distribuzione normale ha come densità:"),l("p",null,l(e.a,null,ee(Ja||(Ja=ne`f_X (x) = \frac{e^{-\frac{(x - \mu)^2}{2 \sigma^2}}}{\sqrt{2 \pi \cdot \sigma^2}}`))))),l(t.a,{title:"Momenti della distribuzione normale"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),l("p",null,l(e.a,null,ee(Ha||(Ha=ne`m_X (t) = e^{\mu \cdot t + \frac{\sigma^2 \cdot t^2}{2}}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione normale è:"),l("p",null,l(e.a,null,ee($a||($a=ne`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione normale è:"),l("p",null,l(e.a,null,ee(li||(li=ne`Var(X) = \sigma^2`))))))),l(o.a,null,l(t.a,{title:"Trasformazione della normale"},l("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),l("p",null,l(e.a,null,ee(ai||(ai=ne`X \sim Nor(m, v^2) \implies \alpha X + \beta \sim Nor(\alpha m + \beta, (\alpha v)^2)`))))),l(t.a,{title:"Normale standard"},l("p",null,"La distribuzione normale standard ",l(e.a,null,"Z")," è:"),l("p",null,l(e.a,null,"Z \\sim Nor(0, 1)")),l("p",null,"La sua funzione di ripartizione è detta ",l(e.a,null,ee(ii||(ii=ne`\phi(z)`)))," e vale:"),l("p",null,l(e.a,null,ee(ni||(ni=ne`F_Z(z) = \phi(z) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{z} e^{-\frac{x^2}{2}} dx`))))),l(t.a,{title:"Quantili normali"},l("p",null,"Da un quantile ",l(e.a,null,ee(ei||(ei=ne`z_\alpha`)))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),l("p",null,l(e.a,null,ee(ti||(ti=ne`x_\alpha = \mu + z_\alpha \cdot \sqrt{\sigma^2}`)))))),l(o.a,null,l(t.a,{title:"Gamma e normale"},l("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),l("p",null,l(e.a,null,ee(oi||(oi=ne`Z^2 \sim \chi^2 (v = 1)`))))),l(t.a,{title:"La funzione Chi"},l("blockquote",null,'"chi-quadro a un grado di libertà"'),l("p",null,"Esiste una distribuzione Gamma particolare:"),l("p",null,l(e.a,null,ee(ui||(ui=ne`\Gamma \left( \frac{1}{2}, \frac{1}{2} \right) = \chi^2 (v = 1)`)))),l("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),l("p",null,l(e.a,null,ee(ri||(ri=ne`\chi^2 (n) + \chi^2 (m) = \chi^2 (n + m)`))))),l(t.a,{title:"T di Student"},l("p",null,"Un'altra funzione particolare è la funzione T di Student:"),l("p",null,l(e.a,null,ee(si||(si=ne`T(v) = \frac{Nor(0, 1)}{\sqrt{\frac{\chi^2(v)}{v}}}`)))))),l(o.a,{title:"Approssimazioni notevoli"},l(t.a,{title:"Ipergeometrica e binomiale"},l("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",l(e.a,null,"N")," rispetto a ",l(e.a,null,"n"),", si può dire che:"),l("p",null,l(e.a,null,ee(pi||(pi=ne`Ipe(N, K, n) \approx Bin(n, \frac{K}{N})`))))),l(t.a,{title:"Binomiale e poissoniana"},l("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",l(e.a,null,"n")," è grande e ",l(e.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),l("p",null,l(e.a,null,ee(di||(di=ne`Bin(n, p) \approx Poi(n \cdot p)`))))),l(t.a,{title:"Binomiale e normale"},l("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",l(e.a,null,"n")," grande e ",l(e.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),l("p",null,l(e.a,null,ee(mi||(mi=ne`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(t.a,{title:"Correzione di Yates"},l("p",null,"Passando da una variabile discreta ",l(e.a,null,"X")," a una continua ",l(e.a,null,"Y"),", per ogni valore discreto ",l(e.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',l(e.a,null,ee(ci||(ci=ne`(k - \frac{1}{2}, k + \frac{1}{2})`))),":"),l("ul",null,l("li",null,l(e.a,null,ee(bi||(bi=ne`P(X < k) \simeq P(Y \leq k - \frac{1}{2})`)))),l("li",null,l(e.a,null,ee(vi||(vi=ne`P(X \leq k) \simeq P(Y \leq k + \frac{1}{2})`)))),l("li",null,l(e.a,null,ee(fi||(fi=ne`P(X \geq k) \simeq P(Y \geq k - \frac{1}{2})`)))),l("li",null,l(e.a,null,ee(hi||(hi=ne`P(X > k) \simeq P(Y \geq k + \frac{1}{2})`))))))),l(o.a,{title:"Vettori aleatori"},l(t.a,{title:"Vettore aleatorio"},l("p",null,"Un vettore ",l("b",null,"composto da variabili aleatorie"),"."),l("p",null,"Il suo simbolo generalmente è ",l(e.a,null,ee(gi||(gi=ne`\boldsymbol{X}`)))," oppure ",l(e.a,null,ee(_i||(_i=ne`X, Y`))),".")),l(t.a,{title:"Funzioni di ripartizione"},l("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione congiunta"),":"),l("p",null,l(e.a,null,ee(zi||(zi=ne`F_{X, Y} (x, y) = P(X \leq x, Y \leq y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione marginale"),":"),l("p",null,l(e.a,null,ee(Xi||(Xi=ne`F_X (x) = P(X \leq x) = \lim_{y \to +\infty} F_{X, Y} (x, y)`))))),l(t.a,{title:"Densità discreta"},l("p",null,"I vettori aleatori ",l("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità congiunta"),":"),l("p",null,l(e.a,null,ee(qi||(qi=ne`p_{X, Y} (x, y) = P(X = x, Y = y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità marginale"),":"),l("p",null,l(e.a,null,ee(Ei||(Ei=ne`p_X (x) = \sum_j p_{X, Y} (x_i, y_j)`)))))),l(o.a,{title:"Più variabili aleatorie"},l(t.a,{title:"Indipendenza delle variabili aleatorie"},l("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",l(e.a,null,"A_i"),":"),l("p",null,l(e.a,null,ee(Li||(Li=ne`P(X_1 \in A_1, \dots, X_n \in A_n) = P(X_1 \in A_1) \times \dots \times P(X_n \in A_n)`))))),l(t.a,{title:"Media dei vettori aleatori"},l("p",null,"E' possibile calcolare la media di qualsiasi funzione ",l(e.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),l("p",null,l(e.a,null,ee(xi||(xi=ne`E(g(X, Y)) = \sum_{i, j} g(x_i, y_i) \cdot p_{X, Y} (x_i, y_i)`)))),l(u.a,null,"Solitamente si calcola la media di ",l(e.a,null,"x \\cdot y"),"."),l("p",null,"Le medie di più variabili aleatorie si possono sommare:"),l("p",null,l(e.a,null,ee(Pi||(Pi=ne`E(X + Y) = E(X) + E(Y)`)))))),l(o.a,null,l(t.a,{title:"Covarianza"},l("p",null,"Un ",l("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),l("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),l("p",null,l(e.a,null,ee(ki||(ki=ne`Cov(X, Y) = E((X - E(X) \cdot (Y - E(Y)) = E(XY) - E(X) \cdot E(Y)`)))),l("p",null,"Ha diverse proprietà:"),l("ul",null,l("li",null,"Il suo ",l("b",null,"valore nullo")," è 0: ",l(e.a,null,ee(Fi||(Fi=ne`Cov(X, \alpha) = 0`)))),l("li",null,"E' ",l("b",null,"commutativa"),": ",l(e.a,null,ee(yi||(yi=ne`Cov(X, Y) = Cov(Y, X)`)))),l("li",null,"E' ",l("b",null,"semplificabile"),": ",l(e.a,null,ee(Si||(Si=ne`Cov(X, X) = Var(X)`)))),l("li",null,"E' ",l("b",null,"lineare"),": ",l(e.a,null,ee(Ci||(Ci=ne`Cov(\alpha X, \beta Y) = \alpha \cdot \beta \cdot Cov(X, Y)`)))),l("li",null,"E' ",l("b",null,"distributiva"),": ",l(e.a,null,ee(Ii||(Ii=ne`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`)))))),l(t.a,{title:"Variabili incorrelate"},l("p",null,"Due variabili sono ",l("i",null,"variabili incorrelate")," se:"),l("p",null,l(e.a,null,ee(Ni||(Ni=ne`Cov(X, Y) = 0`)))),l("p",null,"Variabili indipendenti sono sempre incorrelate.")),l(t.a,{title:"Matrice di covarianza"},l("p",null,"Una matrice ",l(e.a,null,ee(Vi||(Vi=ne`\boldsymbol{C_X}`)))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",l(e.a,null,ee(Yi||(Yi=ne`\boldsymbol{X}`))),":"),l("p",null,l(e.a,null,ee(wi||(wi=ne` - \boldsymbol{C_X} = - \begin{bmatrix} - Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\ - Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\ - Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3) - \end{bmatrix} - `)))),l("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",l(e.a,null,"\\geq 0"),".")),l(t.a,{title:"Coefficiente di correlazione"},l("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),l("p",null,l(e.a,null,ee(Di||(Di=ne`\rho_{X, Y} = \frac{Cov(X, Y)}{\sqrt{Var(X)} \cdot \sqrt{Var(Y)}}`)))),l("p",null,"E' sempre compreso tra -1 e 1:"),l("p",null,l(e.a,null,ee(Ui||(Ui=ne`-1 \leq \rho_{X, Y} \leq 1`)))),l("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),l("p",null,l(e.a,null,ee(Mi||(Mi=ne`Y = a X + b \Longleftrightarrow | \rho_{X, Y} | = 1`))))),l(t.a,{title:"Varianza di variabili aleatorie sommate"},l("p",null,"La varianza di due variabili aleatorie sommate è:"),l("p",null,l(e.a,null,ee(Bi||(Bi=ne`Var(X + Y) = Var(X) + Var(Y) + 2 \cdot Cov(X, Y)`)))),l(u.a,null,"Si dimostra applicando le proprietà della covarianza!"),l("p",null,"Se più variabili aleatorie ",l(e.a,null,"X_i")," sono ",l("b",null,"indipendenti")," (",l(e.a,null,ee(Ai||(Ai=ne`Cov(X, Y) = 0`))),"), allora:"),l("p",null,l(e.a,null,ee(Gi||(Gi=ne`Var \left( \sum_i X_i \right) = \sum_i Var(X_i)`)))))),l(o.a,{title:"Campioni"},l(t.a,{title:"Campione casuale"},l("p",null,"Una ",l("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",l(e.a,null,"X"),' ("popolazione") ma ',l("b",null,"indipendenti")," tra loro."),l(u.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",l("b",null,"realizzeranno")," nel loro valore.")),l(t.a,{title:"Momento campionario"},l("p",null,"Il valore dato dalla media aritmetica degli ",l(e.a,null,"n")," elementi del campione elevati alla potenza ",l(e.a,null,"k"),":"),l("p",null,l(e.a,null,ee(Ti||(Ti=ne`M^{(k)}_n = \frac{1}{n} \cdot \sum_{i = 1}^n X_i^k `)))),l("p",null,"Il momento campionario di primo ordine è la ",l("i",null,"media campionaria")," ",l(e.a,null,ee(Qi||(Qi=ne`\overline{X}_n`))),".")),l(t.a,{title:"Varianza campionaria"},l("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),l("p",null,"Se è noto il valore medio ",l(e.a,null,ee(Oi||(Oi=ne`m = E(X)`)))," di X:"),l("p",null,l(e.a,null,ee(Ri||(Ri=ne`S_0^2 = \frac{1}{n} \cdot \sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \cdot m \cdot \overline{X}_n + m^2`)))),l("p",null,"Altrimenti:"),l("p",null,l(e.a,null,ee(Ki||(Ki=ne`S_n^2 = \frac{1}{n - 1} \cdot \sum_{i = 1}^n (X_i - \overline{X}_n)^2 = \frac{1}{n - 1} \cdot ( n \cdot M_2^{(2)} - n \cdot \overline{X}_n^2)`)))))),l(o.a,{title:"Media-ception"},l(t.a,{title:"Media campionaria"},l("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),l("p",null,l(e.a,null,ee(Wi||(Wi=ne`E(\overline{X}_n) = E(X)`)))),l(u.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),l(t.a,{title:"Varianza campionaria"},l("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),l("p",null,l(e.a,null,ee(ji||(ji=ne`Var(\overline{X}_n) = \frac{Var(X)}{n}`)))),l(u.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),l(t.a,{title:"Correzione campionaria"},l("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),l("p",null,l(e.a,null,ee(Zi||(Zi=ne`E(S_0^2) = E(S_n^2) = Var(X)`)))),l(u.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),l(o.a,{title:"Campionamento di una distribuzione normale"},l(t.a,{title:"Campionamento di una distribuzione normale"},l("p",null,"Se la popolazione ",l(e.a,null,"X")," ha una distribuzione normale (",l(e.a,null,ee(Ji||(Ji=ne`X \sim Nor(\mu, \sigma^2)`))),")...")),l(t.a,{title:"Distribuzione della media campionaria"},l("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),l("p",null,l(e.a,null,ee(Hi||(Hi=ne`\overline{X}_n \sim Nor \left( \mu, \frac{\sigma^2}{n} \right)`))))),l(t.a,{title:"Distribuzione della varianza campionaria"},l("p",null,"...e anche della varianza campionaria!"),l("p",null,l(e.a,null,ee($i||($i=ne`S_0^2 \sim \frac{\sigma^2}{n} \cdot \chi^2 (n)`)))),l("p",null,l(e.a,null,ee(ln||(ln=ne`S_n^2 \sim \frac{\sigma^2}{n - 1} \cdot \chi^2 (n-1)`))))),l(t.a,{title:"Indipendenza"},l("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),l(o.a,{title:"Quando i campioni hanno dimensioni infinite"},l(t.a,{title:"Convergenza in distribuzione"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa funzione di ripartizione")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge in distribuzione"),"."),l("p",null,l(e.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),l(t.a,{title:"Convergenza in probabilità"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge in probabilità"),"."),l("p",null,l(e.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),l(t.a,{title:"Convergenza quasi certa"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità a ")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge quasi certamente"),"."),l("p",null,l(e.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),l(t.a,{title:"Convergenza in media quadratica"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",l(e.a,null,"X")," ",l("b",null,"uguale a 0"),", allora essa ",l("i",null,"converge in media quadratica"),"."),l("p",null,l(e.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),l(t.a,{title:"Gerarchia delle convergenze"},l("p",null,l(e.a,null,"\n \\begin{matrix}\n X_n \\xrightarrow{mq} X\\\\\n X_n \\xrightarrow{qc} X\n \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),l("p",null,"In più:"),l("p",null,l(e.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),l(o.a,{title:"I grandi numeri"},l(t.a,{title:"Legge debole dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,ee(an||(an=ne`\overline{X}_n`)))," ",l("b",null,"converge in probabilità")," alla media della popolazione ",l(e.a,null,ee(nn||(nn=ne`E(X)`))),", se essa esiste."),l("p",null,l(e.a,null,"\\overline{X}_n \\xrightarrow{p} X")),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,ee(en||(en=ne`\forall \epsilon > 0, \lim_{n \to +\infty} P( | \overline{X}_n - E(X) | < \epsilon) = 1`)))),l("p",null,l(e.a,null,ee(tn||(tn=ne`P( | \overline{X}_n - E(X) | < \epsilon) \to 1`))))),l(t.a,{title:"Legge forte dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,ee(on||(on=ne`\overline{X}_n`)))," ",l("b",null,"converge quasi certamente")," alla media della popolazione ",l(e.a,null,ee(un||(un=ne`E(X)`))),", se essa esiste."),l("p",null,l(e.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,ee(rn||(rn=ne`\forall \epsilon > 0, P \left( \lim_{n \to +\infty} | \overline{X}_n - E(X) | < \epsilon \right) = 1`)))),l(u.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),l(o.a,{title:"Al limite"},l(t.a,{title:"Teorema centrale del limite"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,ee(sn||(sn=ne`\overline{X}_n`)))," ",l("b",null,"converge in distribuzione")," a ",l(e.a,null,ee(pn||(pn=ne`Nor(0, 1) = \Phi()`))),"."),l("p",null,l(e.a,null,ee(dn||(dn=ne`\overline{X}_n \approx Nor \left(E(X), \frac{Var(X)}{n} \right)`)))),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,ee(mn||(mn=ne`\forall x \in \mathbb{R}, \lim_{n \to +\infty} P \left( \frac{\overline{X}_n - E(X)}{\sqrt{\frac{Var(X)}{n}}} \leq x \right) = \Phi(x)`)))))),l(o.a,{title:"Altre approsimazioni"},l(t.a,{title:"Binomiale e normale"},l("p",null,"E' una somma di ",l("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,ee(cn||(cn=ne`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(t.a,{title:"Binomiale negativa e normale"},l("p",null,"E' una somma di ",l("b",null,"geometriche"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,ee(bn||(bn=ne`\overline{Bin} (n, p) \approx Nor \left( \frac{n}{p}, \frac{n \cdot (1 - p)}{p^2} \right)`))))),l(t.a,{title:"Poissoniana e normale"},l("p",null,"E' una somma di altre ",l("b",null,"poissoniane"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,ee(vn||(vn=ne`Poi(\lambda) \approx Nor(\lambda, \lambda)`))))),l(t.a,{title:"Gamma e normale"},l("p",null,"E' una somma di ",l("b",null,"esponenziali"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,ee(fn||(fn=ne`\Gamma (\alpha, \lambda) \approx Nor \left( \frac{\alpha}{\lambda}, \frac{\alpha}{\lambda^2} \right)`))))),l(t.a,{title:"In generale"},l("p",null,"Se ",l(e.a,null,"n")," è grande, allora:"),l("p",null,l(e.a,null,ee(hn||(hn=ne`Y = \sum_{i=1}^{n} X_i`)))))),l(o.a,{title:"Actually statistica"},l(t.a,{title:"Parametri sconosciuti"},l("p",null,"Per indicare parametri sconosciuti di una legge si usa ",l(e.a,null,"\\theta"),".")),l(t.a,{title:"Statistica"},l("p",null,"Una variabile aleatoria funzione di un campione:"),l("p",null,l(e.a,null,ee(gn||(gn=ne`T(\boldsymbol{X})`)))),l(u.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",l(e.a,null,ee(_n||(_n=ne`T(\boldsymbol{X}) = \boldsymbol{X}`))),"."))),l(o.a,{title:"Stimatori"},l(t.a,{title:"Stimatore"},l("p",null,"Una statistica ",l(e.a,null,"T_n")," ottenuta da ",l(e.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),l(t.a,{title:"Corretto"},l("p",null,"Uno stimatore è ",l("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(e.a,null,ee(zn||(zn=ne`E(T_n) = \theta`))))),l(t.a,{title:"Asintoticamente corretto"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(e.a,null,ee(Xn||(Xn=ne`\lim_{n \to +\infty} E(T_n) = \theta`))))),l(t.a,{title:"Consistente in media quadratica"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in media quadratica")," se:"),l("p",null,l(e.a,null,ee(qn||(qn=ne`\lim_{n \to +\infty} E((T_n - \theta)^2) = 0`))))),l(t.a,{title:"Consistente in probabilità"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in probabilità")," se:"),l("p",null,l(e.a,null,ee(En||(En=ne`\forall \epsilon > 0, \lim_{n \to +\infty} P( |T_n - \theta| < \epsilon) = 1`))))),l(t.a,{title:"Asintoticamente normale"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente normale")," se:"),l("p",null,l(e.a,null,ee(Ln||(Ln=ne`\lim_{n \to +\infty} \frac{T_n - E(T_n)}{\sqrt{Var(T_n)}} \sim Nor(0, 1)`)))))),l(o.a,{title:"Metodo dei momenti"},l(t.a,{title:"Metodo dei momenti"},l("p",null,"Si può usare il ",l("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",l(e.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(e.a,null,ee(xn||(xn=ne`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(e.a,null,"M")," a ",l(e.a,null,"\\theta"),": ",l(e.a,null,ee(Pn||(Pn=ne`\widehat{\theta}_M`)))),l("p",null,"Visto che:"),l("ul",null,l("li",null,l(e.a,null,ee(kn||(kn=ne`\theta = g(E(X))`)))),l("li",null,l(e.a,null,ee(Fn||(Fn=ne`\widehat{E(X)} = \overline{X}_n`))))),l("p",null,"Allora:"),l("p",null,l(e.a,null,ee(yn||(yn=ne`\widehat{\theta}_M = g( \overline{X}_n )`)))),l("p",null,"Se ",l(e.a,null,ee(Sn||(Sn=ne`\theta`)))," non è esprimibile in termini di ",l(e.a,null,ee(Cn||(Cn=ne`E(X)`))),", si possono usare i momenti successivi ",l(e.a,null,ee(In||(In=ne`M_n^2`))),", ",l(e.a,null,ee(Nn||(Nn=ne`M_n^3`))),", ",l(e.a,null,ee(Vn||(Vn=ne`M_n^3`))),"..."))),l(o.a,{title:"Metodo della massima verosomiglianza"},l(t.a,{title:"Metodo della massima verosomiglianza"},l("p",null,"Si può usare il ",l("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",l(e.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(e.a,null,ee(Yn||(Yn=ne`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(e.a,null,"L")," a ",l(e.a,null,"\\theta"),": ",l(e.a,null,ee(wn||(wn=ne`\widehat{\theta}_L`)))),l("p",null,"Consiste nel trovare il massimo assoluto ",l(e.a,null,ee(Dn||(Dn=ne`\widehat{\theta}_L`)))," della la funzione di verosomiglianza ",l(e.a,null,ee(Un||(Un=ne`L`))),":"),l("p",null,l(e.a,null,ee(Mn||(Mn=ne`L(x_1, ..., x_n; \theta) = \prod_{i=1}^n f_X(x_i; \theta)`)))),l("p",null,"Gli stimatori di massima verosomiglianza sono ",l("b",null,"asintoticamente corretti"),", ",l("b",null,"consistenti in probabilità")," e ",l("b",null,"asintoticamente normali"),".")),l(t.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},l("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),l("ul",null,l("li",null,"Sono ",l("b",null,"asintoticamente corretti"),"."),l("li",null,"Sono ",l("b",null,"consistenti in probabilità"),"."),l("li",null,"Sono ",l("b",null,"asintoticamente normali"),"."),l("li",null,"Sono ",l("b",null,"invarianti"),": ",l(e.a,null,ee(Bn||(Bn=ne`\widehat{g(\theta)}_L = g(\widehat{\theta}_L)`))))))),l(o.a,{title:"Nuove stime notevoli"},l(t.a,{title:"Stima di una bernoulliana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(e.a,null,ee(An||(An=ne`\widehat{p}_M = \widehat{p}_L = \overline{X}_n`))))),l(t.a,{title:"Stima di una poissoniana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima 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n=Wl(["widehat{\theta}_M"],["\\widehat{\\theta}_M"]);return S=function(){return n},n}function Y(){var n=Wl(["\theta"],["\\theta"]);return Y=function(){return n},n}function w(){var n=Wl(["lim_{n \to +infty} \frac{T_n - E(T_n)}{sqrt{Var(T_n)}} sim Nor(0, 1)"],["\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)"]);return w=function(){return n},n}function I(){var n=Wl(["\forall epsilon > 0, lim_{n \to +infty} P( |T_n - \theta| < epsilon) = 1"],["\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1"]);return I=function(){return n},n}function D(){var n=Wl(["lim_{n \to +infty} E((T_n - \theta)^2) = 0"],["\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0"]);return D=function(){return n},n}function U(){var n=Wl(["lim_{n \to +infty} E(T_n) = \theta"],["\\lim_{n \\to +\\infty} E(T_n) = \\theta"]);return U=function(){return n},n}function M(){var n=Wl(["E(T_n) = \theta"],["E(T_n) = \\theta"]);return M=function(){return n},n}function A(){var n=Wl(["T(\boldsymbol{X}) = \boldsymbol{X}"],["T(\\boldsymbol{X}) = \\boldsymbol{X}"]);return A=function(){return n},n}function B(){var n=Wl(["T(\boldsymbol{X})"],["T(\\boldsymbol{X})"]);return B=function(){return n},n}function T(){var n=Wl(["Y = sum_{i=1}^{n} X_i"],["Y = \\sum_{i=1}^{n} X_i"]);return T=function(){return n},n}function O(){var n=Wl(["Gamma (alpha, lambda) approx Nor left( \frac{alpha}{lambda}, \frac{alpha}{lambda^2} \right)"],["\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)"]);return O=function(){return n},n}function G(){var n=Wl(["Poi(lambda) approx Nor(lambda, lambda)"],["Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)"]);return G=function(){return n},n}function H(){var n=Wl(["overline{Bin} (n, p) approx Nor left( \frac{n}{p}, \frac{n cdot (1 - p)}{p^2} \right)"],["\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)"]);return H=function(){return n},n}function j(){var n=Wl(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return j=function(){return n},n}function K(){var n=Wl(["\forall x in mathbb{R}, lim_{n \to +infty} P left( \frac{overline{X}_n - E(X)}{sqrt{\frac{Var(X)}{n}}} leq x \right) = Phi(x)"],["\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)"]);return K=function(){return n},n}function R(){var n=Wl(["overline{X}_n approx Nor left(E(X), \frac{Var(X)}{n} \right)"],["\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)"]);return R=function(){return n},n}function Q(){var n=Wl(["Nor(0, 1) = Phi()"],["Nor(0, 1) = \\Phi()"]);return Q=function(){return n},n}function W(){var n=Wl(["overline{X}_n"],["\\overline{X}_n"]);return W=function(){return n},n}function Z(){var n=Wl(["\forall epsilon > 0, P left( lim_{n \to +infty} | overline{X}_n - E(X) | < epsilon \right) = 1"],["\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1"]);return Z=function(){return n},n}function J(){var n=Wl(["E(X)"]);return J=function(){return n},n}function $(){var n=Wl(["overline{X}_n"],["\\overline{X}_n"]);return $=function(){return n},n}function nn(){var n=Wl(["P( | overline{X}_n - E(X) | < epsilon) \to 1"],["P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1"]);return nn=function(){return n},n}function an(){var n=Wl(["\forall epsilon > 0, lim_{n \to +infty} P( | overline{X}_n - E(X) | < epsilon) = 1"],["\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1"]);return an=function(){return n},n}function ln(){var n=Wl(["E(X)"]);return ln=function(){return n},n}function en(){var n=Wl(["overline{X}_n"],["\\overline{X}_n"]);return en=function(){return n},n}function tn(){var n=Wl(["S_n^2 sim \frac{sigma^2}{n - 1} cdot chi^2 (n-1)"],["S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)"]);return tn=function(){return n},n}function rn(){var n=Wl(["S_0^2 sim \frac{sigma^2}{n} cdot chi^2 (n)"],["S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)"]);return rn=function(){return n},n}function on(){var n=Wl(["overline{X}_n sim Nor left( mu, \frac{sigma^2}{n} \right)"],["\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)"]);return on=function(){return n},n}function un(){var n=Wl(["X sim Nor(mu, sigma^2)"],["X \\sim Nor(\\mu, \\sigma^2)"]);return un=function(){return n},n}function cn(){var n=Wl(["E(S_0^2) = E(S_n^2) = Var(X)"]);return cn=function(){return n},n}function sn(){var n=Wl(["Var(overline{X}_n) = \frac{Var(X)}{n}"],["Var(\\overline{X}_n) = \\frac{Var(X)}{n}"]);return sn=function(){return n},n}function pn(){var n=Wl(["E(overline{X}_n) = E(X)"],["E(\\overline{X}_n) = E(X)"]);return pn=function(){return n},n}function dn(){var n=Wl(["S_n^2 = \frac{1}{n - 1} cdot sum_{i = 1}^n (X_i - overline{X}_n)^2 = \frac{1}{n - 1} cdot ( n cdot M_2^{(2)} - n cdot overline{X}_n^2)"],["S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)"]);return dn=function(){return n},n}function mn(){var n=Wl(["S_0^2 = \frac{1}{n} cdot sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 cdot m cdot overline{X}_n + m^2"],["S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2"]);return mn=function(){return n},n}function fn(){var n=Wl(["m = E(X)"]);return fn=function(){return n},n}function vn(){var n=Wl(["overline{X}_n"],["\\overline{X}_n"]);return vn=function(){return n},n}function bn(){var n=Wl(["M^{(k)}_n = \frac{1}{n} cdot sum_{i = 1}^n X_i^k "],["M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k "]);return bn=function(){return n},n}function _n(){var n=Wl(["Var left( sum_i X_i \right) = sum_i Var(X_i)"],["Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)"]);return _n=function(){return n},n}function hn(){var n=Wl(["Cov(X, Y) = 0"]);return hn=function(){return n},n}function Xn(){var n=Wl(["Var(X + Y) = Var(X) + Var(Y) + 2 cdot Cov(X, Y)"],["Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)"]);return Xn=function(){return n},n}function gn(){var n=Wl(["Y = a X + b Longleftrightarrow | \rho_{X, Y} | = 1"],["Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1"]);return gn=function(){return n},n}function qn(){var n=Wl(["-1 leq \rho_{X, Y} leq 1"],["-1 \\leq \\rho_{X, Y} \\leq 1"]);return qn=function(){return n},n}function zn(){var n=Wl(["\rho_{X, Y} = \frac{Cov(X, Y)}{sqrt{Var(X)} cdot sqrt{Var(Y)}}"],["\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}"]);return zn=function(){return n},n}function En(){var n=Wl(["\n \boldsymbol{C_X} = \n \begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n end{bmatrix}\n "],["\n \\boldsymbol{C_X} = \n \\begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n \\end{bmatrix}\n "]);return En=function(){return n},n}function Pn(){var n=Wl(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Pn=function(){return n},n}function xn(){var n=Wl(["\boldsymbol{C_X}"],["\\boldsymbol{C_X}"]);return xn=function(){return n},n}function kn(){var n=Wl(["Cov(X, Y) = 0"]);return kn=function(){return n},n}function Ln(){var n=Wl(["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"]);return Ln=function(){return n},n}function yn(){var n=Wl(["Cov(alpha X, \beta Y) = alpha cdot \beta cdot Cov(X, Y)"],["Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)"]);return yn=function(){return n},n}function Fn(){var n=Wl(["Cov(X, X) = Var(X)"]);return Fn=function(){return n},n}function Nn(){var n=Wl(["Cov(X, Y) = Cov(Y, X)"]);return Nn=function(){return n},n}function Vn(){var n=Wl(["Cov(X, alpha) = 0"],["Cov(X, \\alpha) = 0"]);return Vn=function(){return n},n}function Cn(){var n=Wl(["Cov(X, Y) = E((X - E(X) cdot (Y - E(Y)) = E(XY) - E(X) cdot E(Y)"],["Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)"]);return Cn=function(){return n},n}function Sn(){var n=Wl(["E(X + Y) = E(X) + E(Y)"]);return Sn=function(){return n},n}function Yn(){var n=Wl(["E(g(X, Y)) = sum_{i, j} g(x_i, y_i) cdot p_{X, Y} (x_i, y_i)"],["E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)"]);return Yn=function(){return n},n}function wn(){var n=Wl(["P(X_1 in A_1, dots, X_n in A_n) = P(X_1 in A_1) \times dots \times P(X_n in A_n)"],["P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)"]);return wn=function(){return n},n}function In(){var n=Wl(["p_X (x) = sum_j p_{X, Y} (x_i, y_j)"],["p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)"]);return In=function(){return n},n}function Dn(){var n=Wl(["p_{X, Y} (x, y) = P(X = x, Y = y)"]);return Dn=function(){return n},n}function Un(){var n=Wl(["F_X (x) = P(X leq x) = lim_{y \to +infty} F_{X, Y} (x, y)"],["F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)"]);return Un=function(){return n},n}function Mn(){var n=Wl(["F_{X, Y} (x, y) = P(X leq x, Y leq y)"],["F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)"]);return Mn=function(){return n},n}function An(){var n=Wl(["X, Y"]);return An=function(){return n},n}function Bn(){var n=Wl(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Bn=function(){return n},n}function Tn(){var n=Wl(["P(X > k) simeq P(Y geq k + \frac{1}{2})"],["P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})"]);return Tn=function(){return n},n}function On(){var n=Wl(["P(X geq k) simeq P(Y geq k - \frac{1}{2})"],["P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})"]);return On=function(){return n},n}function Gn(){var n=Wl(["P(X leq k) simeq P(Y leq k + \frac{1}{2})"],["P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})"]);return Gn=function(){return n},n}function Hn(){var n=Wl(["P(X < k) simeq P(Y leq k - \frac{1}{2})"],["P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})"]);return Hn=function(){return n},n}function jn(){var n=Wl(["(k - \frac{1}{2}, k + \frac{1}{2})"],["(k - \\frac{1}{2}, k + \\frac{1}{2})"]);return jn=function(){return n},n}function Kn(){var n=Wl(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return Kn=function(){return n},n}function Rn(){var n=Wl(["Bin(n, p) approx Poi(n cdot p)"],["Bin(n, p) \\approx Poi(n \\cdot p)"]);return Rn=function(){return n},n}function Qn(){var n=Wl(["Ipe(N, K, n) approx Bin(n, \frac{K}{N})"],["Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})"]);return Qn=function(){return n},n}function Wn(){var n=Wl(["T(v) = \frac{Nor(0, 1)}{sqrt{\frac{chi^2(v)}{v}}}"],["T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}"]);return Wn=function(){return n},n}function Zn(){var n=Wl(["chi^2 (n) + chi^2 (m) = chi^2 (n + m)"],["\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)"]);return Zn=function(){return n},n}function Jn(){var n=Wl(["Gamma left( \frac{1}{2}, \frac{1}{2} \right) = chi^2 (v = 1)"],["\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)"]);return Jn=function(){return n},n}function $n(){var n=Wl(["Z^2 sim chi^2 (v = 1)"],["Z^2 \\sim \\chi^2 (v = 1)"]);return $n=function(){return n},n}function na(){var n=Wl(["x_alpha = mu + z_alpha cdot sqrt{sigma^2}"],["x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}"]);return na=function(){return n},n}function aa(){var n=Wl(["z_alpha"],["z_\\alpha"]);return aa=function(){return n},n}function ia(){var n=Wl(["F_Z(z) = phi(z) = \frac{1}{sqrt{2 pi}} int_{-infty}^{z} e^{-\frac{x^2}{2}} dx"],["F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx"]);return ia=function(){return n},n}function la(){var n=Wl(["phi(z)"],["\\phi(z)"]);return la=function(){return n},n}function ea(){var n=Wl(["X sim Nor(m, v^2) implies alpha X + \beta sim Nor(alpha m + \beta, (alpha v)^2)"],["X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)"]);return ea=function(){return n},n}function ta(){var n=Wl(["Var(X) = sigma^2"],["Var(X) = \\sigma^2"]);return ta=function(){return n},n}function ra(){var n=Wl(["E(X) = mu"],["E(X) = \\mu"]);return ra=function(){return n},n}function oa(){var n=Wl(["m_X (t) = e^{mu cdot t + \frac{sigma^2 cdot t^2}{2}}"],["m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}"]);return oa=function(){return n},n}function ua(){var n=Wl(["f_X (x) = \frac{e^{-\frac{(x - mu)^2}{2 sigma^2}}}{sqrt{2 pi cdot sigma^2}}"],["f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}"]);return ua=function(){return n},n}function ca(){var n=Wl(["Nor(mu, sigma^2)"],["Nor(\\mu, \\sigma^2)"]);return ca=function(){return n},n}function sa(){var n=Wl(["Var(X) = \frac{(b - a)^2}{12}"],["Var(X) = \\frac{(b - a)^2}{12}"]);return sa=function(){return n},n}function pa(){var n=Wl(["E(X) = \frac{a + b}{2}"],["E(X) = \\frac{a + b}{2}"]);return pa=function(){return n},n}function da(){var n=Wl(["m_X (t) = \frac{e^{b cdot t} - e^{a cdot t}}{(b - a) cdot t}"],["m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}"]);return da=function(){return n},n}function ma(){var n=Wl(["f_X (x) = \begin{cases}\n 0 qquad quad x < a \n \frac{1}{b - a} qquad a leq x leq b\\\n 1 qquad quad x > b\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\quad x < a \n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 1 \\qquad \\quad x > b\n \\end{cases}"]);return ma=function(){return n},n}function fa(){var n=Wl(["f_X (x) = \begin{cases}\n \frac{1}{b - a} qquad a leq x leq b\\\n 0 qquad quad altrimenti \n end{cases}"],["f_X (x) = \\begin{cases}\n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 0 \\qquad \\quad altrimenti \n \\end{cases}"]);return fa=function(){return n},n}function va(){var n=Wl(["P(X in (c, d)) = \frac{d - c}{b - a}"],["P(X \\in (c, d)) = \\frac{d - c}{b - a}"]);return va=function(){return n},n}function ba(){var n=Wl(["Uni(a, b)"]);return ba=function(){return n},n}function _a(){var n=Wl(["[a, b]"]);return _a=function(){return n},n}function ha(){var n=Wl(["Var(X) = \frac{alpha}{lambda^2}"],["Var(X) = \\frac{\\alpha}{\\lambda^2}"]);return ha=function(){return n},n}function Xa(){var n=Wl(["E(X) = \frac{alpha}{lambda}"],["E(X) = \\frac{\\alpha}{\\lambda}"]);return Xa=function(){return n},n}function ga(){var n=Wl(["m_X (t) : ( t < lambda ) in mathbb{R} = left( \frac{lambda}{lambda - t} \right) ^alpha"],["m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha"]);return ga=function(){return n},n}function qa(){var n=Wl(["f_X (x) = \begin{cases}\n 0 qquad qquad qquad qquad qquad x < 0\\\n \frac{1}{(n-1)!} cdot lambda^n cdot x^{n-1} cdot e^{-lambda cdot x} quad k > 0\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n \\end{cases}"]);return qa=function(){return n},n}function za(){var n=Wl(["Gamma(n, lambda)"],["\\Gamma(n, \\lambda)"]);return za=function(){return n},n}function Ea(){var n=Wl(["lambda"],["\\lambda"]);return Ea=function(){return n},n}function Pa(){var n=Wl(["P([X > s + t | X > s]) = P([X > t])"]);return Pa=function(){return n},n}function xa(){var n=Wl(["Var(X) = \frac{1}{lambda^2}"],["Var(X) = \\frac{1}{\\lambda^2}"]);return xa=function(){return n},n}function ka(){var n=Wl(["E(X) = \frac{1}{lambda}"],["E(X) = \\frac{1}{\\lambda}"]);return ka=function(){return n},n}function La(){var n=Wl(["m_X (t) : { t | t < lambda } in mathbb{R} = \frac{lambda}{lambda - t}"],["m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}"]);return La=function(){return n},n}function ya(){var n=Wl(["F_X (t) = \begin{cases}\n 0 qquad qquad t < 0\\\n 1 - e^{-lambda cdot t} quad t geq 0\n end{cases}"],["F_X (t) = \\begin{cases}\n 0 \\qquad \\qquad t < 0\\\\\n 1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n \\end{cases}"]);return ya=function(){return n},n}function Fa(){var n=Wl(["f_X (x) = \begin{cases}\n 0 qquad qquad x < 0\\\n lambda cdot e^{-lambda cdot x} quad x > 0\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad x < 0\\\\\n \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n \\end{cases}"]);return Fa=function(){return n},n}function Na(){var n=Wl(["Esp(lambda)"],["Esp(\\lambda)"]);return Na=function(){return n},n}function Va(){var n=Wl(["lambda"],["\\lambda"]);return Va=function(){return n},n}function Ca(){var n=Wl(["Poi(t cdot lambda)"],["Poi(t \\cdot \\lambda)"]);return Ca=function(){return n},n}function Sa(){var n=Wl(["mu = t cdot lambda"],["\\mu = t \\cdot \\lambda"]);return Sa=function(){return n},n}function Ya(){var n=Wl(["lambda"],["\\lambda"]);return Ya=function(){return n},n}function wa(){var n=Wl(["lambda"],["\\lambda"]);return wa=function(){return n},n}function 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n},n}function Fl(){var n=Wl(["E_i"]);return Fl=function(){return n},n}function Nl(){var n=Wl(["E in mathcal{F} implies mathcal{F} = { emptyset, E, \bar{E}, Omega }"],["E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}"]);return Nl=function(){return n},n}function Vl(){var n=Wl(["(E, F) in mathcal{F} implies (E cup F, E cap F) in mathcal{F}"],["(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}"]);return Vl=function(){return n},n}function Cl(){var n=Wl(["E in mathcal{F} implies \bar{E} in mathcal{F}"],["E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}"]);return Cl=function(){return n},n}function Sl(){var n=Wl(["Omega in mathcal{F}"],["\\Omega \\in \\mathcal{F}"]);return Sl=function(){return n},n}function Yl(){var n=Wl(["sigma"],["\\sigma"]);return Yl=function(){return n},n}function wl(){var n=Wl(["sigma"],["\\sigma"]);return wl=function(){return n},n}function Il(){var n=Wl(["mathcal{F}"],["\\mathcal{F}"]);return 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2 \right }"],["E = \\left \\{ 1, 2 \\right \\}"]);return Hl=function(){return n},n}function jl(){var n=Wl(["omega = 1"],["\\omega = 1"]);return jl=function(){return n},n}function Kl(){var n=Wl(["Omega = left { 1, 2, 3, 4, 5, 6 \right }"],["\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}"]);return Kl=function(){return n},n}function Rl(){var n=Wl(["P(E) = \frac{successi}{prove totali}"],["P(E) = \\frac{successi}{prove\\ totali}"]);return Rl=function(){return n},n}function Ql(){var n=Wl(["P(E) = \frac{casi favorevoli}{casi possibili}"],["P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}"]);return Ql=function(){return n},n}function Wl(n,a){return a||(a=n.slice(0)),n.raw=a,n}i.d(a,"default",(function(){return re}));var Zl=i("hosL"),Jl=i("OMhl"),$l=i("HKwK"),ne=i("lL4N"),ae=i("PEwj"),ie=i("h7i1"),le=i("UEJU"),ee=i("wQ73"),te=String.raw,re=function(a){function i(){return a.apply(this,arguments)||this}var Wl,Zl;return Zl=a,(Wl=i).prototype=Object.create(Zl.prototype),Wl.prototype.constructor=Wl,Wl.__proto__=Zl,i.prototype.render=function(){return n(ee.a.Provider,{value:!1},n("div",null,n("h1",null,"Statistica ed Elementi di Probabilità"),n(ne.a,{title:"Tipi di probabilità"},n($l.a,{title:"Classica"},n("p",null,n(Jl.a,null,te(Ql())))),n($l.a,{title:"Frequentista"},n("p",null,n(Jl.a,null,te(Rl())))),n($l.a,{title:"Soggettiva"},n("p",null,"Il prezzo che un individuo coerente riterrebbe equo per ricevere ",n("b",null,"1")," nel caso l'evento si verificasse e ",n("b",null,"0")," nel caso l'evento non si verificasse."))),n(ne.a,{title:"Linguaggio matematico"},n($l.a,{title:"Spazio campionario"},n("blockquote",null,'"omegone"'),n("p",null,"L'",n("b",null,"insieme")," di tutti gli esiti possibili di un esperimento."),n("p",null,n(Jl.a,null,te(Kl())))),n($l.a,{title:"Esito"},n("blockquote",null,'"omeghino"'),n("p",null,"Un ",n("b",null,"elemento")," dello spazio campionario."),n("p",null,n(Jl.a,null,te(jl())))),n($l.a,{title:"Evento"},n("blockquote",null,'"e"'),n("p",null,"Un ",n("b",null,"sottoinsieme")," dello spazio campionario."),n("p",null,n(Jl.a,null,te(Hl()))),n("p",null,"Lo spazio campionario stesso è un ",n("b",null,"evento certo"),".")),n($l.a,{title:"Not"},n("blockquote",null,'"not e"'),n("p",null,"Il ",n("b",null,"complementare")," di un sottoinsieme."),n("p",null,n(Jl.a,null,te(Gl())))),n($l.a,{title:"And"},n("blockquote",null,'"e intersecato effe"'),n("p",null,"L'",n("b",null,"intersezione")," di più sottoinsiemi."),n("p",null,n(Jl.a,null,te(Ol())))),n($l.a,{title:"Or"},n("blockquote",null,'"e unito a effe"'),n("p",null,"L'",n("b",null,"unione")," di più sottoinsiemi."),n("p",null,n(Jl.a,null,te(Tl())))),n($l.a,{title:"Differenza"},n("blockquote",null,'"e meno effe"'),n("p",null,n(Jl.a,null,te(Bl())))),n($l.a,{title:"Implicazione"},n("blockquote",null,'"e contenuto in effe"'),n("p",null,"L'",n("b",null,"inclusione")," del primo insieme in un altro."),n("p",null,n(Jl.a,null,te(Al()))),n("p",null,"Se si verifica ",n(Jl.a,null,"E"),", allora si verifica anche ",n(Jl.a,null,"F"),".")),n($l.a,{title:"Evento impossibile"},n("blockquote",null,'"e è impossibile"'),n("p",null,"Un sottoinsieme ",n("b",null,"vuoto"),"."),n("p",null,n(Jl.a,null,te(Ml())))),n($l.a,{title:"Mutua esclusione"},n("blockquote",null,'"e ed effe si escludono mutualmente"'),n("p",null,"La ",n("b",null,"disgiunzione")," di due insiemi."),n("p",null,n(Jl.a,null,te(Ul()))))),n(ne.a,null,n($l.a,{title:"Famiglia degli eventi"},n("blockquote",null,'"famiglia effe"'),n("p",null,"I sottoinsiemi dello spazio campionario formano una ",n("b",null,"famiglia")," di sottoinsiemi detta ",n("i",null,"famiglia degli eventi"),"."),n("p",null,n(Jl.a,null,te(Dl()))),n("p",null,"Qualsiasi sottoinsieme appartenente a ",n(Jl.a,null,te(Il()))," è considerato un evento.")),n($l.a,{title:n("span",null,n(Jl.a,null,te(wl())),"-algebra")},n("blockquote",null,'"sigma algebra"'),n("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",n("i",null,n(Jl.a,null,te(Yl())),"-algebra"),":"),n("ol",null,n("li",null,"Lo spazio campionario è un evento: ",n(Jl.a,null,te(Sl()))),n("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",n(Jl.a,null,te(Cl()))),n("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",n(Jl.a,null,te(Vl())))),n("p",null,"Un esempio: ",n(Jl.a,null,te(Nl()))))),n(ne.a,null,n($l.a,{title:"Partizione"},n("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),n("p",null,"Un insieme di esiti e eventi:"),n("ul",null,n("li",null,n("b",null,"Finito"),"."),n("li",null,"In cui tutti gli eventi hanno ",n("b",null,"probabilità diversa da 0"),"."),n("li",null,"In cui tutti gli eventi sono ",n("b",null,"mutualmente esclusivi"),"."),n("li",null,"In cui l'unione di tutti i suoi elementi ",n("b",null,"copre lo spazio campionario"),".")),n("p",null,"La partizione ",n(Jl.a,null,te(Fl()))," è composta dagli eventi ",n(Jl.a,null,te(yl())),", ",n(Jl.a,null,te(Ll())),", ",n(Jl.a,null,te(kl())),", fino a ",n(Jl.a,null,te(xl())),"."),n(ae.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),n(ne.a,{title:"Assiomi della probabilità"},n($l.a,{title:"Primo assioma della probabilità"},n("p",null,"La probabilità di un evento è un numero tra 0 e 1."),n("p",null,n(Jl.a,null,te(Pl())))),n($l.a,{title:"Secondo assioma della probabilità"},n("p",null,"La probabilità dello spazio campionario è sempre 1."),n("p",null,n(Jl.a,null,te(El())))),n($l.a,{title:"Terzo assioma della probabilità"},n("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),n("p",null,n(Jl.a,null,te(zl()))))),n(ne.a,{title:"Conseguenze degli assiomi"},n($l.a,{title:"Probabilità di un evento negato"},n("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),n("p",null,n(Jl.a,null,te(ql())))),n($l.a,{title:"Probabilità di un evento incluso"},n("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),n("p",null,n(Jl.a,null,te(gl())))),n($l.a,{title:"Unione"},n("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),n("p",null,n(Jl.a,null,te(Xl()))),n(ae.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),n(ne.a,{title:"Spazi equiprobabili"},n($l.a,{title:"Cosa sono?"},n("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),n("p",null,n(Jl.a,null,te(hl())))),n($l.a,{title:"Spazi equiprobabili geometrici"},n("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",n("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),n(ne.a,{title:"Calcolo combinatorio"},n($l.a,{title:"Disposizioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Jl.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Jl.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Jl.a,null,te(_l())))),n($l.a,{title:"Disposizioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Jl.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Jl.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Jl.a,null,te(bl())))),n($l.a,{title:"Combinazioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Jl.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Jl.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Jl.a,null,te(vl())))),n($l.a,{title:"Combinazioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Jl.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Jl.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Jl.a,null,te(fl())))),n($l.a,{title:"Permutazioni"},n("p",null,"Estraggo ",n(Jl.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),n("p",null,n(Jl.a,null,te(ml()))))),n(ne.a,{title:"Probabilità condizionata"},n($l.a,{title:"Eventi condizionati"},n("blockquote",null,'"E dato F"'),n("p",null,"La probabilità che si verifichi ",n(Jl.a,null,"E")," sapendo che ",n("b",null,"si è già verificato")," ",n(Jl.a,null,"F"),"."),n("p",null,n(Jl.a,null,te(dl()))),n(ae.a,null,"Ricorda vagamente le pipe di ",n("code",null,"bash"),", però al contrario...")),n($l.a,{title:"Eventi mutualmente esclusivi"},n("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),n("p",null,n(Jl.a,null,te(pl()))))),n(ne.a,null,n($l.a,{title:"Regola della catena"},n("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),n("p",null,n(Jl.a,null,te(sl()))))),n(ne.a,{title:"Le alternative"},n($l.a,{title:"Legge delle alternative"},n("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),n("p",null,n(Jl.a,null,te(cl())))),n($l.a,{title:"Legge condizionata delle alternative"},n("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",n("b",null,"evento"),":"),n("p",null,n(Jl.a,null,te(ul())))),n($l.a,{title:"Formula di Bayes"},n("p",null,"Tramite la ",n("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),n("p",null,n(Jl.a,null,te(ol()))),n(ae.a,null,"In pratica, invertiamo gli eventi."))),n(ne.a,{title:"Eventi indipendenti"},n($l.a,{title:"Due eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a due a due"'),n("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),n("p",null,n(Jl.a,null,te(rl())))),n($l.a,{title:"Più eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),n("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),n("p",null,n(Jl.a,null,te(tl()))),n("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),n($l.a,{title:"Famiglia di eventi indipendenti"},n("p",null,"Un insieme di ",n(Jl.a,null,"n")," eventi è una ",n("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),n(ae.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),n(ne.a,{title:"Variabili aleatorie"},n($l.a,{title:"Variabile aleatoria"},n("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",n(Jl.a,null,te(el())),".")),n($l.a,{title:n("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},n("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",n(Jl.a,null,te(ll())),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",n(Jl.a,null,"t"),"."),n("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),n("p",null,n(Jl.a,null,te(il()))),n(ae.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),n($l.a,{title:"Supporto"},n("blockquote",null,'"supporto di X"'),n("p",null,"Il ",n("b",null,"codominio")," della variabile aleatoria è il suo ",n("i",null,"supporto"),"."),n("p",null,"Per indicare che un valore ",n(Jl.a,null,"x_0")," appartiene al supporto di ",n(Jl.a,null,"X"),", si usa la notazione ",n(Jl.a,null,"X \\mapsto x_0"),"."))),n(ne.a,{title:"Densità"},n($l.a,{title:"Funzione probabilità"},n("p",null,"La ",n("i",null,"funzione probabilità")," ",n(Jl.a,null,te(al()))," di una variabile aleatoria ",n("b",null,"discreta")," ",n(Jl.a,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),n("p",null,n(Jl.a,null,te(nl())))),n($l.a,{title:"Funzione densità"},n("p",null,"La ",n("i",null,"funzione densità")," ",n(Jl.a,null,te($i()))," di una variabile aleatoria ",n("b",null,"continua")," ",n(Jl.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),n("p",null,n(Jl.a,null,te(Ji()))),n("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",n("b",null,"non esista")," per una certa variabile aleatoria."),n(ae.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),n(ne.a,{title:"Funzione di ripartizione"},n($l.a,{title:"Definizione"},n("p",null,"Ogni variabile aleatoria ha una ",n("i",null,"funzione di ripartizione")," ",n(Jl.a,null,te(Zi()))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",n(Jl.a,null,"t"),":"),n("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",n(Jl.a,null,te(Wi())),":"),n("p",null,n(Jl.a,null,te(Qi())))),n($l.a,{title:"Proprietà della funzione"},n("ul",null,n("li",null,"È sempre ",n("b",null,"monotona crescente")," (non strettamente)."),n("br",null),n("li",null,"Vale ",n("b",null,"0")," a ",n(Jl.a,null,"-\\infty")," e ",n("b",null,"1")," a ",n(Jl.a,null,"+\\infty"),"."),n("br",null),n("li",null,"È ",n("b",null,"continua da destra"),": ",n(Jl.a,null,te(Ri()))))),n($l.a,{title:"Probabilità di un valore"},n("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),n("p",null,n(Jl.a,null,te(Ki()))))),n(ne.a,{title:"Trasformazioni di variabili aleatorie"},n($l.a,{title:"Nel discreto"},n("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),n($l.a,{title:"Nel continuo (invertibile)"},n("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),n("p",null,n(Jl.a,null,te(ji())))),n($l.a,{title:"Nel... digitale"},n("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",n("a",{href:"https://docs.python.org/3/library/random.html#random.random"},n("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),n(ne.a,{title:"Informazioni delle variabili aleatorie"},n($l.a,{title:"Media"},n("p",null,"Ogni variabile aleatoria che ha una ",n("b",null,"funzione di ripartizione")," e un ",n("b",null,"supporto finito")," ha anche una ",n("i",null,"media")," (o ",n("i",null,"valore medio")," o ",n("i",null,"atteso"),"):"),n("p",null,n(Jl.a,null,te(Hi()))),n("p",null,"Nel discreto, si può calcolare con:"),n("p",null,n(Jl.a,null,te(Gi()))),n("p",null,"Nel continuo, si può calcolare con:"),n("p",null,n(Jl.a,null,te(Oi()))))),n(ne.a,null,n($l.a,{title:"Moda"},n("p",null,"Valore per cui la ",n("b",null,"funzione probabilità")," o ",n("b",null,"funzione densità")," è ",n("b",null,"massima"),".")),n($l.a,{title:"Quantili"},n("p",null,"Il ",n("i",null,"quantile")," ",n(Jl.a,null,te(Ti()))," di ordine ",n(Jl.a,null,te(Bi()))," della variabile aleatoria ",n(Jl.a,null,"X")," è il più piccolo numero tale che:"),n("p",null,n(Jl.a,null,te(Ai()))),n("p",null),n("p",null,"Il quantile di ordine 0.5 ",n(Jl.a,null,te(Mi()))," è detto ",n("i",null,"mediana"),"."),n("p",null,"I quantili di ordine 0.25 ",n(Jl.a,null,te(Ui()))," e 0.75 ",n(Jl.a,null,te(Di()))," sono detti ",n("i",null,"quartili"),"."),n("p",null,"I quantili di ordine ",n(Jl.a,null,te(Ii()))," sono detti ",n("i",null,n(Jl.a,null,"n"),"-esima percentile"),".")),n($l.a,{title:"Varianza"},n("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),n("p",null,n(Jl.a,null,te(wi()))))),n(ne.a,{title:"Disuguaglianze notevoli"},n($l.a,{title:"Disuguaglianza di Markov"},n("p",null,"Data una variabile aleatoria non-negativa:"),n("p",null,n(Jl.a,null,te(Yi()))),n("p",null,"Divide in due parti (",n(Jl.a,null,te(Si()))," e ",n(Jl.a,null,te(Ci())),") la funzione X, la cui media risulterà uguale a:"),n("p",null,n(Jl.a,null,te(Vi())))),n($l.a,{title:"Disuguaglianza di Čebyšëv"},n("blockquote",null,'"disuguaglianza di cebicev"'),n("p",null,"Se la variabile aleatoria ",n(Jl.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",n(Jl.a,null,te(Ni()))," di distanza dal valore medio è minore o uguale a ",n(Jl.a,null,te(Fi())),"."),n("p",null,n(Jl.a,null,te(yi()))),n("p",null,"E anche:"),n("p",null,n(Jl.a,null,te(Li()))),n(ae.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),n(ne.a,{title:"Un momento...!"},n($l.a,{title:"Momento"},n("p",null,"Il ",n("i",null,"momento")," ",n(Jl.a,null,"k"),"-esimo di una variabile aleatoria è:"),n("p",null,n(Jl.a,null,te(ki()))),n(ae.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),n($l.a,{title:"Funzione generatrice dei momenti"},n("p",null,"La ",n("i",null,"funzione generatrice dei momenti")," è:"),n("p",null,n(Jl.a,null,te(xi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),n($l.a,{title:"Funzione caratteristica"},n("p",null,"La ",n("i",null,"funzione caratteristica")," è:"),n("p",null,n(Jl.a,null,te(Pi()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),n(ne.a,{title:"Prove e schemi"},n($l.a,{title:"Variabile con distribuzione"},n("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),n("p",null,n(Jl.a,null,te(Ei())))),n($l.a,{title:"Prova di Bernoulli"},n("p",null,"Una prova con solo due possibili esiti: ",n(ie.a,null,"successo")," e ",n(le.a,null,"insuccesso"),".")),n($l.a,{title:"Schema di Bernoulli"},n("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),n(ne.a,{title:"Bernoulliana"},n($l.a,{title:"Distribuzione bernoulliana"},n("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),n("ul",null,n("li",null,"vale ",n(ie.a,null,"1")," in caso di ",n(ie.a,null,"successo"),"."),n("li",null,"vale ",n(le.a,null,"0")," in caso di ",n(le.a,null,"insuccesso"),".")),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(zi())))),n($l.a,{title:"Densità della bernoulliana"},n("p",null,"La distribuzione bernoulliana ha come densità:"),n("p",null,n(Jl.a,null,te(qi()))))),n(ne.a,{title:"Binomiale"},n($l.a,{title:"Distribuzione binomiale"},n("p",null,"Una variabile aleatoria che conta il numero di successi di ",n(Jl.a,null,"n")," prove di uno schema di Bernoulli."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(gi())),".")),n($l.a,{title:"Densità della binomiale"},n("p",null,"La binomiale ha come densità:"),n("p",null,n(Jl.a,null,te(Xi())))),n($l.a,{title:"Momenti della binomiale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale è:"),n("p",null,n(Jl.a,null,te(hi()))),n("p",null,"La ",n("b",null,"media")," di una binomiale è:"),n("p",null,n(Jl.a,null,te(_i()))),n("p",null,"La ",n("b",null,"varianza")," di una binomiale è:"),n("p",null,n(Jl.a,null,te(bi()))))),n(ne.a,{title:"Geometrica"},n($l.a,{title:"Distribuzione geometrica"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,"Geo(p)"),".")),n($l.a,{title:"Densità della geometrica"},n("p",null,"La geometrica ha come densità:"),n("p",null,n(Jl.a,null,te(vi())))),n($l.a,{title:"Momenti della geometrica"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica è:"),n("p",null,n(Jl.a,null,te(fi()))),n("p",null,"La ",n("b",null,"media")," della geometrica è:"),n("p",null,n(Jl.a,null,te(mi()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Jl.a,null,te(di())))),n($l.a,{title:"Assenza di memoria della geometrica"},n("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Jl.a,null,te(pi()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Binomiale negativa"},n($l.a,{title:"Distribuzione binomiale negativa"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",n(Jl.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(si())),".")),n($l.a,{title:"Densità della binomiale negativa"},n("p",null,"La binomiale negativa ha come densità:"),n("p",null,n(Jl.a,null,te(ci())))),n($l.a,{title:"Momenti della binomiale negativa"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),n("p",null,n(Jl.a,null,te(ui()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa è:"),n("p",null,n(Jl.a,null,te(oi()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa è:"),n("p",null,n(Jl.a,null,te(ri())))))),n(ne.a,{title:"Geometrica traslata"},n($l.a,{title:"Distribuzione geometrica traslata"},n("p",null,"Una variabile aleatoria che conta il numero ",n(Jl.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),n("p",null,"Il suo simbolo rimane ",n(Jl.a,null,te(ti())),".")),n($l.a,{title:"Densità della geometrica tralsata"},n("p",null,"La geometrica traslata ha come densità:"),n("p",null,n(Jl.a,null,te(ei())))),n($l.a,{title:"Momenti della geometrica traslata"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),n("p",null,n(Jl.a,null,te(li()))),n("p",null,"La ",n("b",null,"media")," della geometrica traslata è:"),n("p",null,n(Jl.a,null,te(ii()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Jl.a,null,te(ai())))),n($l.a,{title:"Assenza di memoria della geometrica traslata"},n("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Jl.a,null,te(ni()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Binomiale negativa traslata"},n($l.a,{title:"Distribuzione binomiale negativa traslata"},n("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",n(Jl.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo rimane ",n(Jl.a,null,te($a())),".")),n($l.a,{title:"Densità della binomiale negativa traslata"},n("p",null,"La binomiale negativa traslata ha come densità:"),n("p",null,n(Jl.a,null,te(Ja())))),n($l.a,{title:"Momenti della binomiale negativa traslata"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),n("p",null,n(Jl.a,null,te(Za()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa traslata è:"),n("p",null,n(Jl.a,null,te(Wa()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa traslata è:"),n("p",null,n(Jl.a,null,te(Qa())))))),n(ne.a,{title:"Ipergeometrica"},n($l.a,{title:"Distribuzione ipergeometrica"},n("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",n(Jl.a,null,"K")," e di insuccessi ",n(Jl.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",n(Jl.a,null,"n")," in blocco."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,"Ipe(N, K, n)"),".")),n($l.a,{title:"Densità della ipergeometrica"},n("p",null,"La ipergeometrica ha come densità:"),n("p",null,n(Jl.a,null,te(Ra())))),n($l.a,{title:"Momenti della ipergeometrica"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),n("p",null,"La ",n("b",null,"media")," della ipergeometrica è:"),n("p",null,n(Jl.a,null,te(Ka()))),n("p",null,"La ",n("b",null,"varianza")," della ipergeometrica è:"),n("p",null,n(Jl.a,null,te(ja())))))),n(ne.a,{title:"Poissoniana"},n($l.a,{title:"Distribuzione poissoniana"},n("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),n("ul",null,n("li",null,"Binomiale: ",n(Jl.a,null,te(Ha()))),n("li",null,"Il numero di prove tende a infinito: ",n(Jl.a,null,te(Ga()))),n("li",null,"La probabilità di successo tende a 0: ",n(Jl.a,null,te(Oa()))),n("li",null,"La media è finita: ",n(Jl.a,null,te(Ta())))),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(Ba())))),n($l.a,{title:"Densità della poissoniana"},n("p",null,"La poissoniana ha come densità:"),n("p",null,n(Jl.a,null,te(Aa())))),n($l.a,{title:"Momenti della poissoniana"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),n("p",null,n(Jl.a,null,te(Ma()))),n("p",null,"La ",n("b",null,"media")," della poissoniana è:"),n("p",null,n(Jl.a,null,te(Ua()))),n("p",null,"La ",n("b",null,"varianza")," della poissoniana è:"),n("p",null,n(Jl.a,null,te(Da()))),n("p",null,"Gli altri momenti della poissoniana sono:"),n("ol",{start:2},n("li",null,n(Jl.a,null,te(Ia()))))))),n(ne.a,{title:"Un altro schema"},n($l.a,{title:"Schema di Poisson"},n("p",null,"Una successione di ",n("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),n("ul",null,n("li",null,"non sono sovrapposti."),n("li",null,"hanno intensità ",n(Jl.a,null,te(wa()))," costante."),n("li",null,"avvengono indipendentemente gli uni dagli altri."))),n($l.a,{title:"Processo di Poisson"},n("p",null,"Una variabile aleatoria ",n(Jl.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",n(Jl.a,null,te(Ya()))," in un intervallo di tempo di durata ",n(Jl.a,null,"t"),"."),n("p",null,"E' una distribuzione poissoniana con ",n(Jl.a,null,te(Sa())),": ",n(Jl.a,null,te(Ca()))),n(ae.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),n(ne.a,{title:"Esponenziale"},n($l.a,{title:"Distribuzione esponenziale"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",n(Jl.a,null,te(Va())),"."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(Na())),".")),n($l.a,{title:"Densità dell'esponenziale"},n("p",null,"L'esponenziale ha come ",n("b",null,"densità"),":"),n("p",null,n(Jl.a,null,te(Fa()))),n("p",null,"L'esponenziale ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Jl.a,null,te(ya())))),n($l.a,{title:"Momenti dell'esponenziale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),n("p",null,n(Jl.a,null,te(La()))),n("p",null,"La ",n("b",null,"media")," dell'esponenziale è:"),n("p",null,n(Jl.a,null,te(ka()))),n("p",null,"La ",n("b",null,"varianza")," dell'esponenziale è:"),n("p",null,n(Jl.a,null,te(xa())))),n($l.a,{title:"Assenza di memoria della esponenziale"},n("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Jl.a,null,te(Pa()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Legge gamma"},n($l.a,{title:"Distribuzione gamma"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",n(Jl.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",n(Jl.a,null,te(Ea())),"."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(za())),".")),n($l.a,{title:"Densità della legge gamma"},n("p",null,"La legge gamma ha come densità:"),n("p",null,n(Jl.a,null,te(qa())))),n($l.a,{title:"Momenti della legge gamma"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),n("p",null,n(Jl.a,null,te(ga()))),n("p",null,"La ",n("b",null,"media")," della legge gamma è:"),n("p",null,n(Jl.a,null,te(Xa()))),n("p",null,"La ",n("b",null,"varianza")," della legge gamma è:"),n("p",null,n(Jl.a,null,te(ha())))))),n(ne.a,{title:"Uniforme"},n($l.a,{title:"Distribuzione uniforme"},n("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",n(Jl.a,null,te(_a()))," in modo equiprobabile."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(ba()))),n("p",null,"Su di essa vale la seguente proprietà:"),n("p",null,n(Jl.a,null,te(va())))),n($l.a,{title:"Densità della distribuzione uniforme"},n("p",null,"La distribuzione uniforme ha come ",n("b",null,"densità"),":"),n("p",null,n(Jl.a,null,te(fa()))),n("p",null,"La distribuzione uniforme ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Jl.a,null,te(ma())))),n($l.a,{title:"Momenti della distribuzione uniforme"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),n("p",null,n(Jl.a,null,te(da()))),n("p",null,"La ",n("b",null,"media")," della distribuzione uniforme è:"),n("p",null,n(Jl.a,null,te(pa()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione uniforme è:"),n("p",null,n(Jl.a,null,te(sa())))))),n(ne.a,{title:"Normale o Gaussiana"},n($l.a,{title:"Distribuzione normale"},n("p",null,"Una variabile aleatoria con una specifica distribuzione."),n("p",null,"Il suo simbolo è ",n(Jl.a,null,te(ca())),"."),n(ae.a,null,n(Jl.a,null,"\\mu")," e ",n(Jl.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),n($l.a,{title:"Densità della distribuzione normale"},n("p",null,"La distribuzione normale ha come densità:"),n("p",null,n(Jl.a,null,te(ua())))),n($l.a,{title:"Momenti della distribuzione normale"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),n("p",null,n(Jl.a,null,te(oa()))),n("p",null,"La ",n("b",null,"media")," della distribuzione normale è:"),n("p",null,n(Jl.a,null,te(ra()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione normale è:"),n("p",null,n(Jl.a,null,te(ta())))))),n(ne.a,null,n($l.a,{title:"Trasformazione della normale"},n("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),n("p",null,n(Jl.a,null,te(ea())))),n($l.a,{title:"Normale standard"},n("p",null,"La distribuzione normale standard ",n(Jl.a,null,"Z")," è:"),n("p",null,n(Jl.a,null,"Z \\sim Nor(0, 1)")),n("p",null,"La sua funzione di ripartizione è detta ",n(Jl.a,null,te(la()))," e vale:"),n("p",null,n(Jl.a,null,te(ia())))),n($l.a,{title:"Quantili normali"},n("p",null,"Da un quantile ",n(Jl.a,null,te(aa()))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),n("p",null,n(Jl.a,null,te(na()))))),n(ne.a,null,n($l.a,{title:"Gamma e normale"},n("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),n("p",null,n(Jl.a,null,te($n())))),n($l.a,{title:"La funzione Chi"},n("blockquote",null,'"chi-quadro a un grado di libertà"'),n("p",null,"Esiste una distribuzione Gamma particolare:"),n("p",null,n(Jl.a,null,te(Jn()))),n("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),n("p",null,n(Jl.a,null,te(Zn())))),n($l.a,{title:"T di Student"},n("p",null,"Un'altra funzione particolare è la funzione T di Student:"),n("p",null,n(Jl.a,null,te(Wn()))))),n(ne.a,{title:"Approssimazioni notevoli"},n($l.a,{title:"Ipergeometrica e binomiale"},n("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",n(Jl.a,null,"N")," rispetto a ",n(Jl.a,null,"n"),", si può dire che:"),n("p",null,n(Jl.a,null,te(Qn())))),n($l.a,{title:"Binomiale e poissoniana"},n("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",n(Jl.a,null,"n")," è grande e ",n(Jl.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),n("p",null,n(Jl.a,null,te(Rn())))),n($l.a,{title:"Binomiale e normale"},n("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",n(Jl.a,null,"n")," grande e ",n(Jl.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),n("p",null,n(Jl.a,null,te(Kn())))),n($l.a,{title:"Correzione di Yates"},n("p",null,"Passando da una variabile discreta ",n(Jl.a,null,"X")," a una continua ",n(Jl.a,null,"Y"),", per ogni valore discreto ",n(Jl.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',n(Jl.a,null,te(jn())),":"),n("ul",null,n("li",null,n(Jl.a,null,te(Hn()))),n("li",null,n(Jl.a,null,te(Gn()))),n("li",null,n(Jl.a,null,te(On()))),n("li",null,n(Jl.a,null,te(Tn())))))),n(ne.a,{title:"Vettori aleatori"},n($l.a,{title:"Vettore aleatorio"},n("p",null,"Un vettore ",n("b",null,"composto da variabili aleatorie"),"."),n("p",null,"Il suo simbolo generalmente è ",n(Jl.a,null,te(Bn()))," oppure ",n(Jl.a,null,te(An())),".")),n($l.a,{title:"Funzioni di ripartizione"},n("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione congiunta"),":"),n("p",null,n(Jl.a,null,te(Mn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione marginale"),":"),n("p",null,n(Jl.a,null,te(Un())))),n($l.a,{title:"Densità discreta"},n("p",null,"I vettori aleatori ",n("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità congiunta"),":"),n("p",null,n(Jl.a,null,te(Dn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità marginale"),":"),n("p",null,n(Jl.a,null,te(In()))))),n(ne.a,{title:"Più variabili aleatorie"},n($l.a,{title:"Indipendenza delle variabili aleatorie"},n("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",n(Jl.a,null,"A_i"),":"),n("p",null,n(Jl.a,null,te(wn())))),n($l.a,{title:"Media dei vettori aleatori"},n("p",null,"E' possibile calcolare la media di qualsiasi funzione ",n(Jl.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),n("p",null,n(Jl.a,null,te(Yn()))),n(ae.a,null,"Solitamente si calcola la media di ",n(Jl.a,null,"x \\cdot y"),"."),n("p",null,"Le medie di più variabili aleatorie si possono sommare:"),n("p",null,n(Jl.a,null,te(Sn()))))),n(ne.a,null,n($l.a,{title:"Covarianza"},n("p",null,"Un ",n("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),n("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),n("p",null,n(Jl.a,null,te(Cn()))),n("p",null,"Ha diverse proprietà:"),n("ul",null,n("li",null,"Il suo ",n("b",null,"valore nullo")," è 0: ",n(Jl.a,null,te(Vn()))),n("li",null,"E' ",n("b",null,"commutativa"),": ",n(Jl.a,null,te(Nn()))),n("li",null,"E' ",n("b",null,"semplificabile"),": ",n(Jl.a,null,te(Fn()))),n("li",null,"E' ",n("b",null,"lineare"),": ",n(Jl.a,null,te(yn()))),n("li",null,"E' ",n("b",null,"distributiva"),": ",n(Jl.a,null,te(Ln()))))),n($l.a,{title:"Variabili incorrelate"},n("p",null,"Due variabili sono ",n("i",null,"variabili incorrelate")," se:"),n("p",null,n(Jl.a,null,te(kn()))),n("p",null,"Variabili indipendenti sono sempre incorrelate.")),n($l.a,{title:"Matrice di covarianza"},n("p",null,"Una matrice ",n(Jl.a,null,te(xn()))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",n(Jl.a,null,te(Pn())),":"),n("p",null,n(Jl.a,null,te(En()))),n("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",n(Jl.a,null,"\\geq 0"),".")),n($l.a,{title:"Coefficiente di correlazione"},n("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),n("p",null,n(Jl.a,null,te(zn()))),n("p",null,"E' sempre compreso tra -1 e 1:"),n("p",null,n(Jl.a,null,te(qn()))),n("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),n("p",null,n(Jl.a,null,te(gn())))),n($l.a,{title:"Varianza di variabili aleatorie sommate"},n("p",null,"La varianza di due variabili aleatorie sommate è:"),n("p",null,n(Jl.a,null,te(Xn()))),n(ae.a,null,"Si dimostra applicando le proprietà della covarianza!"),n("p",null,"Se più variabili aleatorie ",n(Jl.a,null,"X_i")," sono ",n("b",null,"indipendenti")," (",n(Jl.a,null,te(hn())),"), allora:"),n("p",null,n(Jl.a,null,te(_n()))))),n(ne.a,{title:"Campioni"},n($l.a,{title:"Campione casuale"},n("p",null,"Una ",n("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",n(Jl.a,null,"X"),' ("popolazione") ma ',n("b",null,"indipendenti")," tra loro."),n(ae.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",n("b",null,"realizzeranno")," nel loro valore.")),n($l.a,{title:"Momento campionario"},n("p",null,"Il valore dato dalla media aritmetica degli ",n(Jl.a,null,"n")," elementi del campione elevati alla potenza ",n(Jl.a,null,"k"),":"),n("p",null,n(Jl.a,null,te(bn()))),n("p",null,"Il momento campionario di primo ordine è la ",n("i",null,"media campionaria")," ",n(Jl.a,null,te(vn())),".")),n($l.a,{title:"Varianza campionaria"},n("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),n("p",null,"Se è noto il valore medio ",n(Jl.a,null,te(fn()))," di X:"),n("p",null,n(Jl.a,null,te(mn()))),n("p",null,"Altrimenti:"),n("p",null,n(Jl.a,null,te(dn()))))),n(ne.a,{title:"Media-ception"},n($l.a,{title:"Media campionaria"},n("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),n("p",null,n(Jl.a,null,te(pn()))),n(ae.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),n($l.a,{title:"Varianza campionaria"},n("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),n("p",null,n(Jl.a,null,te(sn()))),n(ae.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),n($l.a,{title:"Correzione campionaria"},n("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),n("p",null,n(Jl.a,null,te(cn()))),n(ae.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),n(ne.a,{title:"Campionamento di una distribuzione normale"},n($l.a,{title:"Campionamento di una distribuzione normale"},n("p",null,"Se la popolazione ",n(Jl.a,null,"X")," ha una distribuzione normale (",n(Jl.a,null,te(un())),")...")),n($l.a,{title:"Distribuzione della media campionaria"},n("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),n("p",null,n(Jl.a,null,te(on())))),n($l.a,{title:"Distribuzione della varianza campionaria"},n("p",null,"...e anche della varianza campionaria!"),n("p",null,n(Jl.a,null,te(rn()))),n("p",null,n(Jl.a,null,te(tn())))),n($l.a,{title:"Indipendenza"},n("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),n(ne.a,{title:"Quando i campioni hanno dimensioni infinite"},n($l.a,{title:"Convergenza in distribuzione"},n("p",null,"Se la successione di variabili aleatorie ",n(Jl.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa funzione di ripartizione")," della popolazione ",n(Jl.a,null,"X"),", allora essa ",n("i",null,"converge in distribuzione"),"."),n("p",null,n(Jl.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),n($l.a,{title:"Convergenza in probabilità"},n("p",null,"Se la successione di variabili aleatorie ",n(Jl.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità")," della popolazione ",n(Jl.a,null,"X"),", allora essa ",n("i",null,"converge in probabilità"),"."),n("p",null,n(Jl.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),n($l.a,{title:"Convergenza quasi certa"},n("p",null,"Se la successione di variabili aleatorie ",n(Jl.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità a ")," della popolazione ",n(Jl.a,null,"X"),", allora essa ",n("i",null,"converge quasi certamente"),"."),n("p",null,n(Jl.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),n($l.a,{title:"Convergenza in media quadratica"},n("p",null,"Se la successione di variabili aleatorie ",n(Jl.a,null,"X_n")," all'infinito ha la ",n("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",n(Jl.a,null,"X")," ",n("b",null,"uguale a 0"),", allora essa ",n("i",null,"converge in media quadratica"),"."),n("p",null,n(Jl.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),n($l.a,{title:"Gerarchia delle convergenze"},n("p",null,n(Jl.a,null,"\n \\begin{matrix}\n X_n \\xrightarrow{mq} X\\\\\n X_n \\xrightarrow{qc} X\n \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),n("p",null,"In più:"),n("p",null,n(Jl.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),n(ne.a,{title:"I grandi numeri"},n($l.a,{title:"Legge debole dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Jl.a,null,te(en()))," ",n("b",null,"converge in probabilità")," alla media della popolazione ",n(Jl.a,null,te(ln())),", se essa esiste."),n("p",null,n(Jl.a,null,"\\overline{X}_n \\xrightarrow{p} X")),n("p",null,"Ovvero:"),n("p",null,n(Jl.a,null,te(an()))),n("p",null,n(Jl.a,null,te(nn())))),n($l.a,{title:"Legge forte dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Jl.a,null,te($()))," ",n("b",null,"converge quasi certamente")," alla media della popolazione ",n(Jl.a,null,te(J())),", se essa esiste."),n("p",null,n(Jl.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),n("p",null,"Ovvero:"),n("p",null,n(Jl.a,null,te(Z()))),n(ae.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),n(ne.a,{title:"Al limite"},n($l.a,{title:"Teorema centrale del limite"},n("p",null,"La successione delle medie campionarie ",n(Jl.a,null,te(W()))," ",n("b",null,"converge in distribuzione")," a ",n(Jl.a,null,te(Q())),"."),n("p",null,n(Jl.a,null,te(R()))),n("p",null,"Ovvero:"),n("p",null,n(Jl.a,null,te(K()))))),n(ne.a,{title:"Altre approsimazioni"},n($l.a,{title:"Binomiale e normale"},n("p",null,"E' una somma di ",n("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),n("p",null,n(Jl.a,null,te(j())))),n($l.a,{title:"Binomiale negativa e normale"},n("p",null,"E' una somma di ",n("b",null,"geometriche"),", e quindi si approssima a una normale:"),n("p",null,n(Jl.a,null,te(H())))),n($l.a,{title:"Poissoniana e normale"},n("p",null,"E' una somma di altre ",n("b",null,"poissoniane"),", e quindi si approssima a una normale:"),n("p",null,n(Jl.a,null,te(G())))),n($l.a,{title:"Gamma e normale"},n("p",null,"E' una somma di ",n("b",null,"esponenziali"),", e quindi si approssima a una normale:"),n("p",null,n(Jl.a,null,te(O())))),n($l.a,{title:"In generale"},n("p",null,"Se ",n(Jl.a,null,"n")," è grande, allora:"),n("p",null,n(Jl.a,null,te(T()))))),n(ne.a,{title:"Actually statistica"},n($l.a,{title:"Parametri sconosciuti"},n("p",null,"Per indicare parametri sconosciuti di una legge si usa ",n(Jl.a,null,"\\theta"),".")),n($l.a,{title:"Statistica"},n("p",null,"Una variabile aleatoria funzione di un campione:"),n("p",null,n(Jl.a,null,te(B()))),n(ae.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",n(Jl.a,null,te(A())),"."))),n(ne.a,{title:"Stimatori"},n($l.a,{title:"Stimatore"},n("p",null,"Una statistica ",n(Jl.a,null,"T_n")," ottenuta da ",n(Jl.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),n($l.a,{title:"Corretto"},n("p",null,"Uno stimatore è ",n("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Jl.a,null,te(M())))),n($l.a,{title:"Asintoticamente corretto"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Jl.a,null,te(U())))),n($l.a,{title:"Consistente in media quadratica"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in media quadratica")," se:"),n("p",null,n(Jl.a,null,te(D())))),n($l.a,{title:"Consistente in probabilità"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in probabilità")," se:"),n("p",null,n(Jl.a,null,te(I())))),n($l.a,{title:"Asintoticamente normale"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente normale")," se:"),n("p",null,n(Jl.a,null,te(w()))))),n(ne.a,{title:"Metodo dei momenti"},n($l.a,{title:"Metodo dei momenti"},n("p",null,"Si può usare il ",n("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",n(Jl.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Jl.a,null,te(Y()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Jl.a,null,"M")," a ",n(Jl.a,null,"\\theta"),": ",n(Jl.a,null,te(S()))),n("p",null,"Visto che:"),n("ul",null,n("li",null,n(Jl.a,null,te(C()))),n("li",null,n(Jl.a,null,te(V())))),n("p",null,"Allora:"),n("p",null,n(Jl.a,null,te(N()))),n("p",null,"Se ",n(Jl.a,null,te(F()))," non è esprimibile in termini di ",n(Jl.a,null,te(y())),", si possono usare i momenti successivi ",n(Jl.a,null,te(L())),", ",n(Jl.a,null,te(k())),", ",n(Jl.a,null,te(x())),"..."))),n(ne.a,{title:"Metodo della massima verosomiglianza"},n($l.a,{title:"Metodo della massima verosomiglianza"},n("p",null,"Si può usare il ",n("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",n(Jl.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Jl.a,null,te(P()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Jl.a,null,"L")," a ",n(Jl.a,null,"\\theta"),": ",n(Jl.a,null,te(E()))),n("p",null,"Consiste nel trovare il massimo assoluto ",n(Jl.a,null,te(z()))," della la funzione di verosomiglianza ",n(Jl.a,null,te(q())),":"),n("p",null,n(Jl.a,null,te(g()))),n("p",null,"Gli stimatori di massima verosomiglianza sono ",n("b",null,"asintoticamente corretti"),", ",n("b",null,"consistenti in probabilità")," e ",n("b",null,"asintoticamente normali"),".")),n($l.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},n("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),n("ul",null,n("li",null,"Sono ",n("b",null,"asintoticamente corretti"),"."),n("li",null,"Sono ",n("b",null,"consistenti in probabilità"),"."),n("li",null,"Sono ",n("b",null,"asintoticamente normali"),"."),n("li",null,"Sono ",n("b",null,"invarianti"),": ",n(Jl.a,null,te(X())))))),n(ne.a,{title:"Nuove stime notevoli"},n($l.a,{title:"Stima di una bernoulliana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Jl.a,null,te(h())))),n($l.a,{title:"Stima di una poissoniana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Jl.a,null,te(_())))),n($l.a,{title:"Stima di una esponenziale"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Jl.a,null,te(b())))),n($l.a,{title:"Stima di una normale"},n("p",null,"Per il metodo della massima verosomiglianza:"),n("ul",null,n("li",null,n(Jl.a,null,te(v()))),n("br",null),n("li",null,n(Jl.a,null,te(f())))))),n(ne.a,{title:"Intervalli di confidenza"},n($l.a,{title:"Confidenza"},n("blockquote",null,'"intervallo di confidenza al 95%"'),n("p",null,"L'intervallo di valori di ",n(Jl.a,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),n("p",null,"L'intervallo di confidenza a N della stima ",n(Jl.a,null,te(m()))," è l'intervallo ",n(Jl.a,null,"]a, b[")," tale che:"),n("p",null,n(Jl.a,null,te(d()))),n("p",null,"Può anche essere ",n("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),n(ne.a,{title:"Confidenza nella media di una normale"},n($l.a,{title:"Varianza nota"},n("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Jl.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Jl.a,null,te(p()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Jl.a,null,te(s()))),n("li",null,"Intervallo unilatero da destra: ",n(Jl.a,null,te(c()))))),n($l.a,{title:"Varianza incognita"},n("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Jl.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Jl.a,null,te(u()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Jl.a,null,te(o()))),n("li",null,"Intervallo unilatero da destra: ",n(Jl.a,null,te(r())))),n("p",null,n(Jl.a,null,te(t()))," è un quantile della distribuzione di Student di parametro ",n(Jl.a,null,"v"),"."))),n(ne.a,{title:"Confidenza per la proporzione di una bernoulliana"},n($l.a,{title:"Terzo metodo corretto"},n("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),n("p",null,n(Jl.a,null,te(e()))))),n(ne.a,{title:"Confidenza per la media di qualsiasi popolazione"},n($l.a,{title:"Approssimando con la normale"},n("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),n("p",null,n(Jl.a,null,te(l())))))))},i}(Zl.Component)}.call(this,i("hosL").h)},wQ73:function(n,a,i){"use strict";var l=i("hosL");a.a=Object(l.createContext)(!0)}}]); +//# sourceMappingURL=route-statistica.chunk.67526.js.map \ No newline at end of file diff --git a/docs/route-statistica.chunk.67526.js.map b/docs/route-statistica.chunk.67526.js.map new file mode 100644 index 0000000..a41e904 --- /dev/null +++ b/docs/route-statistica.chunk.67526.js.map @@ -0,0 +1 @@ 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extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__2PzAa\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__2u13i\"};","import style from \"./panel.less\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (

{this.props.title}

);\n\t\t}\n\n\t\treturn (\n\t\t\t
\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
\n\t\t);\n\t}\n}\n","import style from './Latex.css';\nimport {useContext} from \"preact/hooks\";\nimport LatexRenderColor from \"../contexts/LatexRenderColor\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nexport default function(props) {\n\t// black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow\n\tlet renderColor = useContext(LatexRenderColor);\n\tlet defaultInline = useContext(LatexDefaultInline);\n\n\tlet is_inline;\n\tif(props.inline === undefined) {\n\t\tis_inline = defaultInline;\n\t}\n\telse {\n\t\tis_inline = props.inline;\n\t}\n\n\tlet inline = is_inline ? `\\\\inline` : \"\";\n\tlet equation = `${inline} {\\\\color{${renderColor}} ${props.children} }`;\n\n\treturn (\n\t\t{props.children}\n\t\t\t\n\t);\n}\n","import style from \"./Example.less\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default function(props) {\r\n return (\r\n
\r\n {props.children}\r\n
\r\n );\r\n}\r\n","import { options } from 'preact';\n\n/** @type {number} */\nlet currentIndex;\n\n/** @type {import('./internal').Component} */\nlet currentComponent;\n\n/** @type {Array} */\nlet afterPaintEffects = [];\n\nlet oldBeforeRender = options._render;\nlet oldAfterDiff = options.diffed;\nlet oldCommit = options._commit;\nlet oldBeforeUnmount = options.unmount;\n\nconst RAF_TIMEOUT = 100;\nlet prevRaf;\n\noptions._render = vnode => {\n\tif (oldBeforeRender) oldBeforeRender(vnode);\n\n\tcurrentComponent = vnode._component;\n\tcurrentIndex = 0;\n\n\tif (currentComponent.__hooks) {\n\t\tcurrentComponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\tcurrentComponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\tcurrentComponent.__hooks._pendingEffects = [];\n\t}\n};\n\noptions.diffed = vnode => {\n\tif (oldAfterDiff) oldAfterDiff(vnode);\n\n\tconst c = vnode._component;\n\tif (!c) return;\n\n\tconst hooks = c.__hooks;\n\tif (hooks) {\n\t\tif (hooks._pendingEffects.length) {\n\t\t\tafterPaint(afterPaintEffects.push(c));\n\t\t}\n\t}\n};\n\noptions._commit = (vnode, commitQueue) => {\n\tcommitQueue.some(component => {\n\t\ttry {\n\t\t\tcomponent._renderCallbacks.forEach(invokeCleanup);\n\t\t\tcomponent._renderCallbacks = component._renderCallbacks.filter(cb =>\n\t\t\t\tcb._value ? invokeEffect(cb) : true\n\t\t\t);\n\t\t} catch (e) {\n\t\t\tcommitQueue.some(c => {\n\t\t\t\tif (c._renderCallbacks) c._renderCallbacks = [];\n\t\t\t});\n\t\t\tcommitQueue = [];\n\t\t\toptions._catchError(e, component._vnode);\n\t\t}\n\t});\n\n\tif (oldCommit) oldCommit(vnode, commitQueue);\n};\n\noptions.unmount = vnode => {\n\tif (oldBeforeUnmount) oldBeforeUnmount(vnode);\n\n\tconst c = vnode._component;\n\tif (!c) return;\n\n\tconst hooks = c.__hooks;\n\tif (hooks) {\n\t\ttry {\n\t\t\thooks._list.forEach(hook => hook._cleanup && hook._cleanup());\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t}\n};\n\n/**\n * Get a hook's state from the currentComponent\n * @param {number} index The index of the hook to get\n * @returns {import('./internal').HookState}\n */\nfunction getHookState(index) {\n\tif (options._hook) options._hook(currentComponent);\n\t// Largely inspired by:\n\t// * https://github.com/michael-klein/funcy.js/blob/f6be73468e6ec46b0ff5aa3cc4c9baf72a29025a/src/hooks/core_hooks.mjs\n\t// * https://github.com/michael-klein/funcy.js/blob/650beaa58c43c33a74820a3c98b3c7079cf2e333/src/renderer.mjs\n\t// Other implementations to look at:\n\t// * https://codesandbox.io/s/mnox05qp8\n\tconst hooks =\n\t\tcurrentComponent.__hooks ||\n\t\t(currentComponent.__hooks = { _list: [], _pendingEffects: [] });\n\n\tif (index >= hooks._list.length) {\n\t\thooks._list.push({});\n\t}\n\treturn hooks._list[index];\n}\n\n/**\n * @param {import('./index').StateUpdater} initialState\n */\nexport function useState(initialState) {\n\treturn useReducer(invokeOrReturn, initialState);\n}\n\n/**\n * @param {import('./index').Reducer} reducer\n * @param {import('./index').StateUpdater} initialState\n * @param {(initialState: any) => void} [init]\n * @returns {[ any, (state: any) => void ]}\n */\nexport function useReducer(reducer, initialState, init) {\n\t/** @type {import('./internal').ReducerHookState} */\n\tconst hookState = getHookState(currentIndex++);\n\tif (!hookState._component) {\n\t\thookState._component = currentComponent;\n\n\t\thookState._value = [\n\t\t\t!init ? invokeOrReturn(undefined, initialState) : init(initialState),\n\n\t\t\taction => {\n\t\t\t\tconst nextValue = reducer(hookState._value[0], action);\n\t\t\t\tif (hookState._value[0] !== nextValue) {\n\t\t\t\t\thookState._value[0] = nextValue;\n\t\t\t\t\thookState._component.setState({});\n\t\t\t\t}\n\t\t\t}\n\t\t];\n\t}\n\n\treturn hookState._value;\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent.__hooks._pendingEffects.push(state);\n\t}\n}\n\n/**\n * @param {import('./internal').Effect} callback\n * @param {any[]} args\n */\nexport function useLayoutEffect(callback, args) {\n\t/** @type {import('./internal').EffectHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._value = callback;\n\t\tstate._args = args;\n\n\t\tcurrentComponent._renderCallbacks.push(state);\n\t}\n}\n\nexport function useRef(initialValue) {\n\treturn useMemo(() => ({ current: initialValue }), []);\n}\n\n/**\n * @param {object} ref\n * @param {() => object} createHandle\n * @param {any[]} args\n */\nexport function useImperativeHandle(ref, createHandle, args) {\n\tuseLayoutEffect(\n\t\t() => {\n\t\t\tif (typeof ref == 'function') ref(createHandle());\n\t\t\telse if (ref) ref.current = createHandle();\n\t\t},\n\t\targs == null ? args : args.concat(ref)\n\t);\n}\n\n/**\n * @param {() => any} factory\n * @param {any[]} args\n */\nexport function useMemo(factory, args) {\n\t/** @type {import('./internal').MemoHookState} */\n\tconst state = getHookState(currentIndex++);\n\tif (argsChanged(state._args, args)) {\n\t\tstate._args = args;\n\t\tstate._factory = factory;\n\t\treturn (state._value = factory());\n\t}\n\n\treturn state._value;\n}\n\n/**\n * @param {() => void} callback\n * @param {any[]} args\n */\nexport function useCallback(callback, args) {\n\treturn useMemo(() => callback, args);\n}\n\n/**\n * @param {import('./internal').PreactContext} context\n */\nexport function useContext(context) {\n\tconst provider = currentComponent.context[context._id];\n\tif (!provider) return context._defaultValue;\n\tconst state = getHookState(currentIndex++);\n\t// This is probably not safe to convert to \"!\"\n\tif (state._value == null) {\n\t\tstate._value = true;\n\t\tprovider.sub(currentComponent);\n\t}\n\treturn provider.props.value;\n}\n\n/**\n * Display a custom label for a custom hook for the devtools panel\n * @type {(value: T, cb?: (value: T) => string | number) => void}\n */\nexport function useDebugValue(value, formatter) {\n\tif (options.useDebugValue) {\n\t\toptions.useDebugValue(formatter ? formatter(value) : value);\n\t}\n}\n\nexport function useErrorBoundary(cb) {\n\tconst state = getHookState(currentIndex++);\n\tconst errState = useState();\n\tstate._value = cb;\n\tif (!currentComponent.componentDidCatch) {\n\t\tcurrentComponent.componentDidCatch = err => {\n\t\t\tif (state._value) state._value(err);\n\t\t\terrState[1](err);\n\t\t};\n\t}\n\treturn [\n\t\terrState[0],\n\t\t() => {\n\t\t\terrState[1](undefined);\n\t\t}\n\t];\n}\n\n/**\n * After paint effects consumer.\n */\nfunction flushAfterPaintEffects() {\n\tafterPaintEffects.some(component => {\n\t\tif (component._parentDom) {\n\t\t\ttry {\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeCleanup);\n\t\t\t\tcomponent.__hooks._pendingEffects.forEach(invokeEffect);\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t} catch (e) {\n\t\t\t\tcomponent.__hooks._pendingEffects = [];\n\t\t\t\toptions._catchError(e, component._vnode);\n\t\t\t\treturn true;\n\t\t\t}\n\t\t}\n\t});\n\tafterPaintEffects = [];\n}\n\n/**\n * Schedule a callback to be invoked after the browser has a chance to paint a new frame.\n * Do this by combining requestAnimationFrame (rAF) + setTimeout to invoke a callback after\n * the next browser frame.\n *\n * Also, schedule a timeout in parallel to the the rAF to ensure the callback is invoked\n * even if RAF doesn't fire (for example if the browser tab is not visible)\n *\n * @param {() => void} callback\n */\nfunction afterNextFrame(callback) {\n\tconst done = () => {\n\t\tclearTimeout(timeout);\n\t\tcancelAnimationFrame(raf);\n\t\tsetTimeout(callback);\n\t};\n\tconst timeout = setTimeout(done, RAF_TIMEOUT);\n\n\tlet raf;\n\tif (typeof window != 'undefined') {\n\t\traf = requestAnimationFrame(done);\n\t}\n}\n\n// Note: if someone used options.debounceRendering = requestAnimationFrame,\n// then effects will ALWAYS run on the NEXT frame instead of the current one, incurring a ~16ms delay.\n// Perhaps this is not such a big deal.\n/**\n * Schedule afterPaintEffects flush after the browser paints\n * @param {number} newQueueLength\n */\nfunction afterPaint(newQueueLength) {\n\tif (newQueueLength === 1 || prevRaf !== options.requestAnimationFrame) {\n\t\tprevRaf = options.requestAnimationFrame;\n\t\t(prevRaf || afterNextFrame)(flushAfterPaintEffects);\n\t}\n}\n\n/**\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeCleanup(hook) {\n\tif (hook._cleanup) hook._cleanup();\n}\n\n/**\n * Invoke a Hook's effect\n * @param {import('./internal').EffectHookState} hook\n */\nfunction invokeEffect(hook) {\n\tconst result = hook._value();\n\tif (typeof result == 'function') hook._cleanup = result;\n}\n\n/**\n * @param {any[]} oldArgs\n * @param {any[]} newArgs\n */\nfunction argsChanged(oldArgs, newArgs) {\n\treturn !oldArgs || newArgs.some((arg, index) => arg !== oldArgs[index]);\n}\n\nfunction invokeOrReturn(arg, f) {\n\treturn typeof f == 'function' ? f(arg) : f;\n}\n","import style from \"./minus.css\";\nimport { Component } from 'preact';\n\nexport default class Minus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"split\":\"split__3dL9r\",\"splitparent\":\"splitparent__2H-vS\",\"splitchild\":\"splitchild__1B-Jt\"};","import style from \"./plus.css\";\nimport { Component } from 'preact';\n\nexport default class Plus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t let title = null;\n\t if(this.props.title !== undefined) {\n title = (

{this.props.title}

)\n }\n\n let children;\n if(Array.isArray(this.props.children)) {\n children = this.props.children.map(element => {\n return (
{element}
);\n });\n }\n else {\n children =
{this.props.children}
;\n }\n\t\treturn (\n\t
\n {title}\n
{children}
\n
\n );\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__2EaF0\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3zlIu\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__7bYPC\"};","import { Component } from 'preact';\nimport Latex from '../components/Latex';\nimport Panel from '../components/old/panel';\nimport Split from '../components/old/split';\nimport Example from \"../components/example\";\nimport Plus from \"../components/old/plus\";\nimport Minus from \"../components/old/minus\";\nimport LatexDefaultInline from \"../contexts/LatexDefaultInline\";\n\nconst r = String.raw;\n\nexport default class Statistica extends Component {\n\trender() {\n return (\n \n
\n

Statistica ed Elementi di Probabilità

\n \n \n

\n {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n

\n \n \n

\n {r`P(E) = \\frac{successi}{prove\\ totali}`}\n

\n \n \n

\n Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n

\n \n \n \n \n
\n \"omegone\"\n
\n

\n L'insieme di tutti gli esiti possibili di un esperimento.\n

\n

\n {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n

\n \n \n
\n \"omeghino\"\n
\n

\n Un elemento dello spazio campionario.\n

\n

\n {r`\\omega = 1`}\n

\n \n \n
\n \"e\"\n
\n

\n Un sottoinsieme dello spazio campionario.\n

\n

\n {r`E = \\left \\{ 1, 2 \\right \\}`}\n

\n

\n Lo spazio campionario stesso è un evento certo.\n

\n \n \n
\n \"not e\"\n
\n

\n Il complementare di un sottoinsieme.\n

\n

\n {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n

\n \n \n
\n \"e intersecato effe\"\n
\n

\n L'intersezione di più sottoinsiemi.\n

\n

\n {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n

\n \n \n
\n \"e unito a effe\"\n
\n

\n L'unione di più sottoinsiemi.\n

\n

\n {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n

\n \n \n
\n \"e meno effe\"\n
\n

\n {r`E \\setminus F = E \\cap \\bar{F}`}\n

\n \n \n
\n \"e contenuto in effe\"\n
\n

\n L'inclusione del primo insieme in un altro.\n

\n

\n {r`E \\subseteq F`}\n

\n

\n Se si verifica E, allora si verifica anche F.\n

\n \n \n
\n \"e è impossibile\"\n
\n

\n Un sottoinsieme vuoto.\n

\n

\n {r`E = \\emptyset`}\n

\n \n \n
\n \"e ed effe si escludono mutualmente\"\n
\n

\n La disgiunzione di due insiemi.\n

\n

\n {r`E \\cap F = \\emptyset`}\n

\n \n \n \n \n
\n \"famiglia effe\"\n
\n

\n I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n

\n

\n {r`\\mathcal{F}`}\n

\n

\n Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n

\n \n {r`\\sigma`}-algebra}>\n
\n \"sigma algebra\"\n
\n

\n Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n

\n
    \n
  1. \n Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n
    2. \n
  2. \n Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n
    3. \n
  3. \n Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n
    4. \n
\n

\n Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n

\n \n \n \n \n
\n \"la partizione e composta da e uno, e due, e tre...\"\n
\n

\n Un insieme di esiti e eventi:\n

\n
    \n
  • Finito.
    • \n
  • In cui tutti gli eventi hanno probabilità diversa da 0.
    • \n
  • In cui tutti gli eventi sono mutualmente esclusivi.
    • \n
  • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
    • \n
\n

\n La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n

\n \n Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n \n \n \n \n \n

\n La probabilità di un evento è un numero tra 0 e 1.\n

\n

\n {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n

\n \n \n

\n La probabilità dello spazio campionario è sempre 1.\n

\n

\n {r`P(\\Omega) = 1`}\n

\n \n \n

\n La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n

\n

\n {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n

\n \n \n \n \n

\n La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n

\n

\n {r`P(\\bar{E}) = 1 - P({E})`}\n

\n \n \n

\n La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n

\n

\n {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n

\n \n \n

\n La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n

\n

\n {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n

\n \n Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n \n \n \n \n \n

\n Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n

\n

\n {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n

\n \n \n

\n Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n

\n \n \n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n

\n

\n Tengo conto dell'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n

\n

\n Tengo conto dell'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n

\n

\n Non mi interessa l'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n

\n

\n Non mi interessa l'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n

\n \n \n

\n Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n

\n

\n {r`\\boldsymbol{P}_n = n!`}\n

\n \n \n \n \n
\n \"E dato F\"\n
\n

\n La probabilità che si verifichi E sapendo che si è già verificato F.\n

\n

\n {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n

\n \n Ricorda vagamente le pipe di bash, però al contrario...\n \n \n \n

\n Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n

\n

\n {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n

\n \n \n \n \n

\n Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n

\n

\n {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n

\n \n \n \n \n

\n La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n

\n

\n {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n

\n \n \n

\n La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n

\n

\n {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n

\n \n \n

\n Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n

\n

\n {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n

\n \n In pratica, invertiamo gli eventi.\n \n \n \n \n \n
\n \"eventi indipendenti a due a due\"\n
\n

\n Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n

\n

\n {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n

\n \n \n
\n \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n
\n

\n Si può verificare l'indipendenza di più eventi alla volta:\n

\n

\n {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n

\n

\n Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n

\n \n \n

\n Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n

\n \n Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n \n \n \n \n \n

\n Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n

\n \n Insieme di ripartizione}>\n

\n Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n

\n

\n Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n

\n

\n {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n

\n \n All'aumentare di t, l'insieme conterrà sempre più elementi.\n \n \n \n
\n \"supporto di X\"\n
\n

\n Il codominio della variabile aleatoria è il suo supporto.\n

\n

\n Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n

\n \n \n \n \n

\n La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n

\n

\n {r`p_X (x) = \\begin{cases}\n P([X = x]) \\quad se\\ X \\mapsto x \\\\\n 0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n \\end{cases}`}\n

\n \n \n

\n La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n

\n

\n {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n

\n

\n A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n

\n \n Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n \n \n \n \n \n

\n Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n

\n

\n Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n

\n

\n {r`F_X (t) = P(A_t) = \\begin{cases}\n \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n \\end{cases}`}\n

\n \n \n
    \n
  • È sempre monotona crescente (non strettamente).

    • \n
  • Vale 0 a -\\infty e 1 a +\\infty.

    • \n
  • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
    • \n
\n \n \n

\n Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n

\n

\n {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n

\n \n \n \n \n

\n Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n

\n \n \n

\n Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n

\n

\n {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n

\n \n \n

\n Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n

\n \n \n \n \n

\n Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n

\n

\n {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n

\n

\n Nel discreto, si può calcolare con:\n

\n

\n {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n

\n

\n Nel continuo, si può calcolare con:\n

\n

\n {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n

\n \n \n \n \n

\n Valore per cui la funzione probabilità o funzione densità è massima.\n

\n \n \n

\n Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n

\n

\n \n {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n \n

\n

\n\n

\n

\n Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n

\n

\n I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n

\n

\n I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n

\n \n \n

\n È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n

\n

\n {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n

\n \n \n \n \n

\n Data una variabile aleatoria non-negativa:\n

\n

\n {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n

\n

\n Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n

\n

\n {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n

\n \n \n
\n \"disuguaglianza di cebicev\"\n
\n

\n Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n

\n

\n {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n

\n

\n E anche:\n

\n

\n {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n

\n \n Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n \n \n \n \n \n

\n Il momento k-esimo di una variabile aleatoria è:\n

\n

\n \n {r`\\mu_k = E ( X^k ) = \\begin{cases}\n \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n \\end{cases}`}\n \n

\n \n La media di una variabile aleatoria è anche il suo primo momento.\n \n \n \n

\n La funzione generatrice dei momenti è:\n

\n

\n {r`m_X (t) = E( e^{t \\cdot X} )`}\n

\n

\n Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n

\n

\n E' la trasformata di Laplace della variabile aleatoria di X.\n

\n \n \n

\n La funzione caratteristica è:\n

\n

\n {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n

\n

\n Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n

\n

\n E' la trasformata di Fourier della variabile aleatoria di X.\n

\n \n \n \n \n

\n Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n

\n

\n {r`X \\sim Distribuzione()`}\n

\n \n \n

\n Una prova con solo due possibili esiti: successo e insuccesso.\n

\n \n \n

\n Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n

\n \n \n \n \n

\n Una variabile aleatoria che rappresenta una prova di Bernoulli:\n

\n
    \n
  • vale 1 in caso di successo.
    • \n
  • vale 0 in caso di insuccesso.
    • \n
\n

\n Il suo simbolo è {r`Ber(p)`}\n

\n \n \n

\n La distribuzione bernoulliana ha come densità:\n

\n

\n {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n p \\quad se\\ k = 1\\\\\n q \\quad se\\ k = 0\\\\\n 0 \\quad altrimenti\n \\end{cases} = p^x \\cdot q^{1 - k}`}\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n

\n

\n Il suo simbolo è {r`Bin(n, p)`}.\n

\n \n \n

\n La binomiale ha come densità:\n

\n

\n {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n

\n \n \n

\n La funzione generatrice dei momenti della binomiale è:\n

\n

\n {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n

\n

\n La media di una binomiale è:\n

\n

\n {r`E(X) = n \\cdot p`}\n

\n

\n La varianza di una binomiale è:\n

\n

\n {r`Var(X) = n \\cdot p \\cdot q`}\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n

\n

\n Il suo simbolo è Geo(p).\n

\n \n \n

\n La geometrica ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n

\n \n \n

\n La funzione generatrice dei momenti della geometrica è:\n

\n

\n {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n

\n

\n La media della geometrica è:\n

\n

\n {r`E(X) = \\frac{1}{p}`}\n

\n

\n La varianza della geometrica è:\n

\n

\n {r`Var(X) = \\frac{q}{p^2}`}\n

\n \n \n

\n La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X = i + j | X > i ]) = P([X = j])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n

\n

\n Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n

\n \n \n

\n La binomiale negativa ha come densità:\n

\n

\n {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della binomiale negativa è:\n

\n

\n {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n

\n

\n La media della binomiale negativa è:\n

\n

\n {r`E(X) = \\frac{n}{p}`}\n

\n

\n La varianza della binomiale negativa è:\n

\n

\n {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n

\n

\n Il suo simbolo rimane {r`Geo(p)`}.\n

\n \n \n

\n La geometrica traslata ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n

\n \n \n

\n La funzione generatrice dei momenti della geometrica traslata è:\n

\n

\n {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n

\n

\n La media della geometrica traslata è:\n

\n

\n {r`E(X) = \\frac{q}{p}`}\n

\n

\n La varianza della geometrica è:\n

\n

\n {r`Var(X) = \\frac{q}{p^2}`}\n

\n \n \n

\n La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X = i + j | X > i ]) = P([X = j])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n

\n

\n Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n

\n \n \n

\n La binomiale negativa traslata ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della binomiale negativa traslata è:\n

\n

\n {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n

\n

\n La media della binomiale negativa traslata è:\n

\n

\n {r`E(X) = \\frac{n \\cdot q}{p}`}\n

\n

\n La varianza della binomiale negativa traslata è:\n

\n

\n {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n

\n

\n Il suo simbolo è Ipe(N, K, n).\n

\n \n \n

\n La ipergeometrica ha come densità:\n

\n

\n {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n

\n

\n La media della ipergeometrica è:\n

\n

\n {r`E(X) = n \\cdot \\frac{K}{N}`}\n

\n

\n La varianza della ipergeometrica è:\n

\n

\n {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n

\n
    \n
  • Binomiale: {r`X \\sim Bin(n, p)`}
    • \n
  • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
    • \n
  • La probabilità di successo tende a 0: {r`p \\to 0`}
    • \n
  • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
    • \n
\n

\n Il suo simbolo è {r`Poi(\\mu)`}\n

\n \n \n

\n La poissoniana ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della poissoniana è:\n

\n

\n {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n

\n

\n La media della poissoniana è:\n

\n

\n {r`E(X) = \\mu`}\n

\n

\n La varianza della poissoniana è:\n

\n

\n {r`Var(X) = \\mu`}\n

\n

\n Gli altri momenti della poissoniana sono:\n

\n
    \n
  1. {r`E(X^2) = \\mu^2 + \\mu`}
    2. \n
\n

\n \n \n \n \n

\n Una successione di arrivi avvenuti in un certo arco temporale che:\n

\n
    \n
  • non sono sovrapposti.
    • \n
  • hanno intensità {r`\\lambda`} costante.
    • \n
  • avvengono indipendentemente gli uni dagli altri.
    • \n
\n \n \n

\n Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n

\n

\n E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n

\n \n E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n \n \n \n \n \n

\n Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n

\n

\n Il suo simbolo è {r`Esp(\\lambda)`}.\n

\n \n \n

\n L'esponenziale ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad x < 0\\\\\n \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n \\end{cases}`}\n

\n

\n L'esponenziale ha come funzione di ripartizione:\n

\n

\n {r`F_X (t) = \\begin{cases}\n 0 \\qquad \\qquad t < 0\\\\\n 1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n \\end{cases}`}\n

\n \n \n

\n La funzione generatrice dei momenti dell'esponenziale è:\n

\n

\n {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n

\n

\n La media dell'esponenziale è:\n

\n

\n {r`E(X) = \\frac{1}{\\lambda}`}\n

\n

\n La varianza dell'esponenziale è:\n

\n

\n {r`Var(X) = \\frac{1}{\\lambda^2}`}\n

\n \n \n

\n L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X > s + t | X > s]) = P([X > t])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n

\n

\n Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n

\n \n \n

\n La legge gamma ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n \\end{cases}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della legge gamma è:\n

\n

\n {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n

\n

\n La media della legge gamma è:\n

\n

\n {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n

\n

\n La varianza della legge gamma è:\n

\n

\n {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n

\n

\n Il suo simbolo è {r`Uni(a, b)`}\n

\n

\n Su di essa vale la seguente proprietà:\n

\n

\n {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n

\n \n \n

\n La distribuzione uniforme ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 0 \\qquad \\quad altrimenti \n \\end{cases}`}\n

\n

\n La distribuzione uniforme ha come funzione di ripartizione:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\quad x < a \n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 1 \\qquad \\quad x > b\n \\end{cases}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della distribuzione uniforme è:\n

\n

\n {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n

\n

\n La media della distribuzione uniforme è:\n

\n

\n {r`E(X) = \\frac{a + b}{2}`}\n

\n

\n La varianza della distribuzione uniforme è:\n

\n

\n {r`Var(X) = \\frac{(b - a)^2}{12}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria con una specifica distribuzione.\n

\n

\n Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n

\n \n \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n \n \n \n

\n La distribuzione normale ha come densità:\n

\n

\n {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della distribuzione normale è:\n

\n

\n {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n

\n

\n La media della distribuzione normale è:\n

\n

\n {r`E(X) = \\mu`}\n

\n

\n La varianza della distribuzione normale è:\n

\n

\n {r`Var(X) = \\sigma^2`}\n

\n

\n \n \n \n \n

\n Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n

\n

\n {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n

\n \n \n

\n La distribuzione normale standard Z è:\n

\n

\n Z \\sim Nor(0, 1)\n

\n

\n La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n

\n

\n {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n

\n \n \n

\n Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n

\n

\n {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n

\n \n \n \n \n

\n La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n

\n

\n {r`Z^2 \\sim \\chi^2 (v = 1)`}\n

\n \n \n
\n \"chi-quadro a un grado di libertà\"\n
\n

\n Esiste una distribuzione Gamma particolare:\n

\n

\n {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n

\n

\n Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n

\n

\n {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n

\n \n \n

\n Un'altra funzione particolare è la funzione T di Student:\n

\n

\n {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n

\n \n \n \n \n

\n La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n

\n

\n {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n

\n \n \n

\n La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n

\n

\n {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n

\n \n \n

\n Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n

\n

\n {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n

\n \n \n

\n Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n

\n
    \n
  • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
    • \n
  • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
    • \n
  • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
    • \n
  • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
    • \n
\n \n \n \n \n

\n Un vettore composto da variabili aleatorie.\n

\n

\n Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n

\n \n \n

\n I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n

\n

\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n

\n

\n {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n

\n

\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n

\n

\n {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n

\n \n \n

\n I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n

\n

\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n

\n

\n {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n

\n

\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n

\n

\n {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n

\n \n \n \n \n

\n Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n

\n

\n {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n

\n \n \n

\n E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n

\n

\n {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n

\n \n Solitamente si calcola la media di x \\cdot y.\n \n

\n Le medie di più variabili aleatorie si possono sommare:\n

\n

\n {r`E(X + Y) = E(X) + E(Y)`}\n

\n \n \n \n \n

\n Un operatore che misura la correlazione di due variabili aleatorie.\n

\n

\n Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n

\n

\n {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n

\n

\n Ha diverse proprietà:\n

\n
    \n
  • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
    • \n
  • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
    • \n
  • E' semplificabile: {r`Cov(X, X) = Var(X)`}
    • \n
  • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
    • \n
  • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
    • \n
\n \n \n

\n Due variabili sono variabili incorrelate se:\n

\n

\n {r`Cov(X, Y) = 0`}\n

\n

\n Variabili indipendenti sono sempre incorrelate.\n

\n \n \n

\n Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n

\n

\n {r`\n \\boldsymbol{C_X} = \n \\begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n \\end{bmatrix}\n `}\n

\n

\n E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n

\n \n \n

\n Un valore che misura come due variabili aleatorie sono correlate:\n

\n

\n {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n

\n

\n E' sempre compreso tra -1 e 1:\n

\n

\n {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n

\n

\n Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n

\n

\n {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n

\n \n \n

\n La varianza di due variabili aleatorie sommate è:\n

\n

\n {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n

\n \n Si dimostra applicando le proprietà della covarianza!\n \n

\n Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n

\n

\n {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n

\n \n \n \n \n

\n Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n

\n \n Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n \n \n \n

\n Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n

\n

\n {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n

\n

\n Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n

\n \n \n

\n La media aritmetica dello scarto quadratico medio degli elementi del campione.\n

\n

\n Se è noto il valore medio {r`m = E(X)`} di X:\n

\n

\n {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n

\n

\n Altrimenti:\n

\n

\n {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n

\n \n \n \n \n

\n Se calcoliamo la media della media campionaria, risulterà vero che:\n

\n

\n {r`E(\\overline{X}_n) = E(X)`}\n

\n \n Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n \n \n \n

\n Se calcoliamo la varianza della media campionaria, risulterà vero che:\n

\n

\n {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n

\n \n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n \n \n \n

\n Se calcoliamo la media della varianza campionaria, risulterà vero che:\n

\n

\n {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n

\n \n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n \n \n \n \n \n

\n Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n

\n \n \n

\n ...allora sappiamo anche la distribuzione della media campionaria!\n

\n

\n {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n

\n \n \n

\n ...e anche della varianza campionaria!\n

\n

\n {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n

\n

\n {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n

\n \n \n

\n ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n

\n \n \n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n

\n

\n {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n

\n

\n {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a della popolazione X, allora essa converge quasi certamente.\n

\n

\n {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n

\n

\n {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n

\n \n \n

\n {`\n \\\\begin{matrix}\n X_n \\\\xrightarrow{mq} X\\\\\\\\\n X_n \\\\xrightarrow{qc} X\n \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n }\n

\n

\n In più:\n

\n

\n {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n

\n \n \n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n

\n

\n {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n

\n

\n {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n

\n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n

\n

\n {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n

\n \n Dimostra che l'interpretazione frequentista della probabilità è valida!\n \n \n \n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n

\n

\n {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n

\n \n \n \n \n

\n E' una somma di bernoulliane, e quindi si approssima a una normale:\n

\n

\n {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n

\n \n \n

\n E' una somma di geometriche, e quindi si approssima a una normale:\n

\n

\n {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n

\n \n \n

\n E' una somma di altre poissoniane, e quindi si approssima a una normale:\n

\n

\n {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n

\n \n \n

\n E' una somma di esponenziali, e quindi si approssima a una normale:\n

\n

\n {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n

\n \n \n

\n Se n è grande, allora:\n

\n

\n {r`Y = \\sum_{i=1}^{n} X_i`}\n

\n \n \n \n \n

\n Per indicare parametri sconosciuti di una legge si usa \\theta.\n

\n \n \n

\n Una variabile aleatoria funzione di un campione:\n

\n

\n {r`T(\\boldsymbol{X})`}\n

\n \n Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n \n \n \n \n \n

\n Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n

\n \n \n

\n Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n

\n

\n {r`E(T_n) = \\theta`}\n

\n \n \n

\n Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n

\n

\n {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n

\n \n \n

\n Uno stimatore è consistente in media quadratica se:\n

\n

\n {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n

\n \n \n

\n Uno stimatore è consistente in probabilità se:\n

\n

\n {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n

\n \n \n

\n Uno stimatore è asintoticamente normale se:\n

\n

\n {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n

\n \n \n \n \n

\n Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n

\n

\n Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n

\n

\n Visto che:\n

\n
    \n
  • {r`\\theta = g(E(X))`}
    • \n
  • {r`\\widehat{E(X)} = \\overline{X}_n`}
    • \n
\n

\n Allora:\n

\n

\n {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n

\n

\n Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n

\n \n \n \n \n

\n Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n

\n

\n Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n

\n

\n Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n

\n

\n {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n

\n

\n Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n

\n \n \n

\n Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n

\n
    \n
  • Sono asintoticamente corretti.
    • \n
  • Sono consistenti in probabilità.
    • \n
  • Sono asintoticamente normali.
    • \n
  • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
    • \n
\n \n \n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n

\n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n

\n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n

\n \n \n

\n Per il metodo della massima verosomiglianza:\n

\n
    \n
  • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

    • \n
  • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
    • \n
\n \n \n \n \n
\n \"intervallo di confidenza al 95%\"\n
\n

\n L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n

\n

\n L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n

\n

\n {r`P( a < W < b ) = N`}\n

\n

\n Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n

\n \n \n \n \n

\n Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n

\n
    \n
  • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
    • \n
\n \n \n

\n Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n

\n
    \n
  • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
    • \n
\n

\n {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n

\n \n \n \n \n

\n L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n

\n

\n {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n

\n \n \n \n \n

\n L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n

\n

\n {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n

\n \n \n
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(x)"]);return Rl=function(){return n},n}function Kl(){var n=Zi(["P([X = x_0]) = lim_{t \to x^+_0} F_X (t) - lim_{t \to x^-_0} F_X (t)"],["P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)"]);return Kl=function(){return n},n}function Ql(){var n=Zi(["\forall x_0 in mathbb{R}, F_X (x_0) = lim_{t \to x^+_0} F_X (t)"],["\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)"]);return Ql=function(){return n},n}function Wl(){var n=Zi(["F_X (t) = P(A_t) = \begin{cases}\n sum_{i = 0}^{t} p_X (x_i) quad nel discreto\\\n \\\n int_{-infty}^t f_X (x) dx quad nel continuo\n end{cases}"],["F_X (t) = P(A_t) = \\begin{cases}\n \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n \\end{cases}"]);return Wl=function(){return n},n}function Zl(){var n=Zi(["A_t"]);return Zl=function(){return n},n}function Hl(){var n=Zi(["F_X : mathbb{R} \to [0, 1]"],["F_X : \\mathbb{R} \\to [0, 1]"]);return 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ei(){var n=Zi(["X(omega) : Omega \to mathbb{R}"],["X(\\omega) : \\Omega \\to \\mathbb{R}"]);return ei=function(){return n},n}function ti(){var n=Zi(["P(E cap F cap G) = P(E) cdot P(F) cdot P(G)"],["P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)"]);return ti=function(){return n},n}function ri(){var n=Zi(["P(E cap F) = P(E) cdot P(F) Longleftrightarrow P(E|F) = P(E) Longleftrightarrow P(F|E) = P(F)"],["P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)"]);return ri=function(){return n},n}function oi(){var n=Zi(["P(E_h | F) = \frac{P(F | E_h) cdot P(E_h)}{P(F)}"],["P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}"]);return oi=function(){return n},n}function ui(){var n=Zi(["P(F|G) = sum_i P(F|E_i cap G) cdot P(E_i | G)"],["P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)"]);return ui=function(){return n},n}function ci(){var n=Zi(["P(F) = sum_{i} P(F|E_i) cdot P(E_i)"],["P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)"]);return ci=function(){return n},n}function si(){var n=Zi(["P(E_1 cap \times cap E_n) = P(E_1) \times P(E_2 | E_1) \times dots \times P(E_n | E_1 cap E_2 cap dots cap E_{n-1})"],["P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})"]);return si=function(){return n},n}function pi(){var n=Zi(["E cap F = emptyset Longleftrightarrow P(E|F) = P(F|E) = 0"],["E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0"]);return pi=function(){return n},n}function di(){var n=Zi(["P(E|F) = \frac{P(E cap F)}{P(F)}"],["P(E|F) = \\frac{P(E \\cap F)}{P(F)}"]);return di=function(){return n},n}function mi(){var n=Zi(["\boldsymbol{P}_n = n!"],["\\boldsymbol{P}_n = n!"]);return mi=function(){return n},n}function fi(){var n=Zi(["\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! cdot (n - 1)!}"],["\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}"]);return fi=function(){return n},n}function vi(){var n=Zi(["\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! cdot (n - k)!}"],["\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}"]);return vi=function(){return n},n}function bi(){var n=Zi(["\boldsymbol{D}^{r}_{n, k} = n^k"],["\\boldsymbol{D}^{r}_{n, k} = n^k"]);return bi=function(){return n},n}function _i(){var n=Zi(["\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}"],["\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}"]);return _i=function(){return n},n}function hi(){var n=Zi(["P(E) = \frac{len(E)}{len(Omega)}"],["P(E) = \\frac{len(E)}{len(\\Omega)}"]);return hi=function(){return n},n}function Xi(){var n=Zi(["P(E cup F) = P(E) + P(F) - P(E cap F)"],["P(E \\cup F) = P(E) + P(F) - P(E \\cap F)"]);return Xi=function(){return n},n}function gi(){var n=Zi(["F subseteq E implies P(F) leq P(E)"],["F \\subseteq E \\implies P(F) \\leq P(E)"]);return gi=function(){return n},n}function qi(){var n=Zi(["P(\bar{E}) = 1 - P({E})"],["P(\\bar{E}) = 1 - P({E})"]);return qi=function(){return n},n}function zi(){var n=Zi(["P left ( \bigcup_i E_i \right ) = sum_i P ( E_i )"],["P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )"]);return zi=function(){return n},n}function Ei(){var n=Zi(["P(Omega) = 1"],["P(\\Omega) = 1"]);return Ei=function(){return n},n}function Pi(){var n=Zi(["\forall E in mathcal{F}, 0 leq P(E) leq 1"],["\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1"]);return Pi=function(){return n},n}function xi(){var n=Zi(["E_n"]);return xi=function(){return n},n}function ki(){var n=Zi(["E_3"]);return ki=function(){return n},n}function yi(){var n=Zi(["E_2"]);return yi=function(){return n},n}function Li(){var n=Zi(["E_1"]);return Li=function(){return n},n}function Fi(){var n=Zi(["E_i"]);return Fi=function(){return n},n}function Ni(){var n=Zi(["E in mathcal{F} implies mathcal{F} = { emptyset, E, \bar{E}, Omega }"],["E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}"]);return Ni=function(){return n},n}function Vi(){var n=Zi(["(E, F) in mathcal{F} implies (E cup F, E cap F) in mathcal{F}"],["(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}"]);return Vi=function(){return n},n}function Ci(){var n=Zi(["E in mathcal{F} implies \bar{E} in mathcal{F}"],["E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}"]);return Ci=function(){return n},n}function Si(){var n=Zi(["Omega in mathcal{F}"],["\\Omega \\in \\mathcal{F}"]);return Si=function(){return n},n}function Yi(){var n=Zi(["sigma"],["\\sigma"]);return Yi=function(){return n},n}function wi(){var n=Zi(["sigma"],["\\sigma"]);return wi=function(){return n},n}function Ii(){var n=Zi(["mathcal{F}"],["\\mathcal{F}"]);return Ii=function(){return n},n}function Mi(){var n=Zi(["mathcal{F}"],["\\mathcal{F}"]);return Mi=function(){return n},n}function Di(){var n=Zi(["E cap F = emptyset"],["E \\cap F = \\emptyset"]);return Di=function(){return n},n}function Ui(){var n=Zi(["E = emptyset"],["E = \\emptyset"]);return Ui=function(){return n},n}function Bi(){var n=Zi(["E subseteq F"],["E \\subseteq F"]);return Bi=function(){return n},n}function Ai(){var n=Zi(["E setminus F = E cap \bar{F}"],["E \\setminus F = E \\cap \\bar{F}"]);return Ai=function(){return n},n}function Ti(){var n=Zi(["E cup F = left { 1, 2, 3, 4 \right }"],["E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}"]);return Ti=function(){return n},n}function Gi(){var n=Zi(["E cap F = left { 1 \right }"],["E \\cap F = \\left \\{ 1 \\right \\}"]);return Gi=function(){return n},n}function Oi(){var n=Zi(["\bar{E} = left { 3, 4, 5, 6 \right }"],["\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}"]);return Oi=function(){return n},n}function ji(){var n=Zi(["E = left { 1, 2 \right }"],["E = \\left \\{ 1, 2 \\right \\}"]);return ji=function(){return n},n}function Ri(){var n=Zi(["omega = 1"],["\\omega = 1"]);return Ri=function(){return n},n}function Ki(){var n=Zi(["Omega = left { 1, 2, 3, 4, 5, 6 \right }"],["\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}"]);return Ki=function(){return n},n}function Qi(){var n=Zi(["P(E) = \frac{successi}{prove totali}"],["P(E) = \\frac{successi}{prove\\ totali}"]);return Qi=function(){return n},n}function Wi(){var n=Zi(["P(E) = \frac{casi favorevoli}{casi possibili}"],["P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}"]);return Wi=function(){return n},n}function Zi(n,a){return a||(a=n.slice(0)),n.raw=a,n}l.d(a,"default",(function(){return te}));var Hi=l("hosL"),Ji=l("ZsnK"),$i=l("9yVG"),ne=l("ddBW"),ae=(l("7bXG"),l("iBfA"),l("XmE9"),l("0UW7"),l("rIv+"),l("PEwj")),le=l("bQQT"),ie=l("GC6P"),ee=String.raw,te=function(a){function l(){return a.apply(this,arguments)||this}var Zi,Hi;return Hi=a,(Zi=l).prototype=Object.create(Hi.prototype),Zi.prototype.constructor=Zi,Zi.__proto__=Hi,l.prototype.render=function(){return n("div",null,n("h1",null,"Statistica ed Elementi di Probabilità"),n(ne.a,{title:"Tipi di probabilità"},n($i.a,{title:"Classica"},n("p",null,n(Ji.a,null,ee(Wi())))),n($i.a,{title:"Frequentista"},n("p",null,n(Ji.a,null,ee(Qi())))),n($i.a,{title:"Soggettiva"},n("p",null,"Il prezzo che un individuo coerente riterrebbe equo per ricevere ",n("b",null,"1")," nel caso l'evento si verificasse e ",n("b",null,"0")," nel caso l'evento non si verificasse."))),n(ne.a,{title:"Linguaggio matematico"},n($i.a,{title:"Spazio campionario"},n("blockquote",null,'"omegone"'),n("p",null,"L'",n("b",null,"insieme")," di tutti gli esiti possibili di un esperimento."),n("p",null,n(Ji.a,null,ee(Ki())))),n($i.a,{title:"Esito"},n("blockquote",null,'"omeghino"'),n("p",null,"Un ",n("b",null,"elemento")," dello spazio campionario."),n("p",null,n(Ji.a,null,ee(Ri())))),n($i.a,{title:"Evento"},n("blockquote",null,'"e"'),n("p",null,"Un ",n("b",null,"sottoinsieme")," dello spazio campionario."),n("p",null,n(Ji.a,null,ee(ji()))),n("p",null,"Lo spazio campionario stesso è un ",n("b",null,"evento certo"),".")),n($i.a,{title:"Not"},n("blockquote",null,'"not e"'),n("p",null,"Il ",n("b",null,"complementare")," di un sottoinsieme."),n("p",null,n(Ji.a,null,ee(Oi())))),n($i.a,{title:"And"},n("blockquote",null,'"e intersecato effe"'),n("p",null,"L'",n("b",null,"intersezione")," di più sottoinsiemi."),n("p",null,n(Ji.a,null,ee(Gi())))),n($i.a,{title:"Or"},n("blockquote",null,'"e unito a effe"'),n("p",null,"L'",n("b",null,"unione")," di più sottoinsiemi."),n("p",null,n(Ji.a,null,ee(Ti())))),n($i.a,{title:"Differenza"},n("blockquote",null,'"e meno effe"'),n("p",null,n(Ji.a,null,ee(Ai())))),n($i.a,{title:"Implicazione"},n("blockquote",null,'"e contenuto in effe"'),n("p",null,"L'",n("b",null,"inclusione")," del primo insieme in un altro."),n("p",null,n(Ji.a,null,ee(Bi()))),n("p",null,"Se si verifica ",n(Ji.a,null,"E"),", allora si verifica anche ",n(Ji.a,null,"F"),".")),n($i.a,{title:"Evento impossibile"},n("blockquote",null,'"e è impossibile"'),n("p",null,"Un sottoinsieme ",n("b",null,"vuoto"),"."),n("p",null,n(Ji.a,null,ee(Ui())))),n($i.a,{title:"Mutua esclusione"},n("blockquote",null,'"e ed effe si escludono mutualmente"'),n("p",null,"La ",n("b",null,"disgiunzione")," di due insiemi."),n("p",null,n(Ji.a,null,ee(Di()))))),n(ne.a,null,n($i.a,{title:"Famiglia degli eventi"},n("blockquote",null,'"famiglia effe"'),n("p",null,"I sottoinsiemi dello spazio campionario formano una ",n("b",null,"famiglia")," di sottoinsiemi detta ",n("i",null,"famiglia degli eventi"),"."),n("p",null,n(Ji.a,null,ee(Mi()))),n("p",null,"Qualsiasi sottoinsieme appartenente a ",n(Ji.a,null,ee(Ii()))," è considerato un evento.")),n($i.a,{title:n("span",null,n(Ji.a,null,ee(wi())),"-algebra")},n("blockquote",null,'"sigma algebra"'),n("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",n("i",null,n(Ji.a,null,ee(Yi())),"-algebra"),":"),n("ol",null,n("li",null,"Lo spazio campionario è un evento: ",n(Ji.a,null,ee(Si()))),n("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",n(Ji.a,null,ee(Ci()))),n("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",n(Ji.a,null,ee(Vi())))),n("p",null,"Un esempio: ",n(Ji.a,null,ee(Ni()))))),n(ne.a,null,n($i.a,{title:"Partizione"},n("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),n("p",null,"Un insieme di esiti e eventi:"),n("ul",null,n("li",null,n("b",null,"Finito"),"."),n("li",null,"In cui tutti gli eventi hanno ",n("b",null,"probabilità diversa da 0"),"."),n("li",null,"In cui tutti gli eventi sono ",n("b",null,"mutualmente esclusivi"),"."),n("li",null,"In cui l'unione di tutti i suoi elementi ",n("b",null,"copre lo spazio campionario"),".")),n("p",null,"La partizione ",n(Ji.a,null,ee(Fi()))," è composta dagli eventi ",n(Ji.a,null,ee(Li())),", ",n(Ji.a,null,ee(yi())),", ",n(Ji.a,null,ee(ki())),", fino a ",n(Ji.a,null,ee(xi())),"."),n(ae.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),n(ne.a,{title:"Assiomi della probabilità"},n($i.a,{title:"Primo assioma della probabilità"},n("p",null,"La probabilità di un evento è un numero tra 0 e 1."),n("p",null,n(Ji.a,null,ee(Pi())))),n($i.a,{title:"Secondo assioma della probabilità"},n("p",null,"La probabilità dello spazio campionario è sempre 1."),n("p",null,n(Ji.a,null,ee(Ei())))),n($i.a,{title:"Terzo assioma della probabilità"},n("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),n("p",null,n(Ji.a,null,ee(zi()))))),n(ne.a,{title:"Conseguenze degli assiomi"},n($i.a,{title:"Probabilità di un evento negato"},n("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),n("p",null,n(Ji.a,null,ee(qi())))),n($i.a,{title:"Probabilità di un evento incluso"},n("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),n("p",null,n(Ji.a,null,ee(gi())))),n($i.a,{title:"Unione"},n("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),n("p",null,n(Ji.a,null,ee(Xi()))),n(ae.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),n(ne.a,{title:"Spazi equiprobabili"},n($i.a,{title:"Cosa sono?"},n("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),n("p",null,n(Ji.a,null,ee(hi())))),n($i.a,{title:"Spazi equiprobabili geometrici"},n("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",n("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),n(ne.a,{title:"Calcolo combinatorio"},n($i.a,{title:"Disposizioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Ji.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Ji.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Ji.a,null,ee(_i())))),n($i.a,{title:"Disposizioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Ji.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Ji.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(Ji.a,null,ee(bi())))),n($i.a,{title:"Combinazioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Ji.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(Ji.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Ji.a,null,ee(vi())))),n($i.a,{title:"Combinazioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(Ji.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(Ji.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(Ji.a,null,ee(fi())))),n($i.a,{title:"Permutazioni"},n("p",null,"Estraggo ",n(Ji.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),n("p",null,n(Ji.a,null,ee(mi()))))),n(ne.a,{title:"Probabilità condizionata"},n($i.a,{title:"Eventi condizionati"},n("blockquote",null,'"E dato F"'),n("p",null,"La probabilità che si verifichi ",n(Ji.a,null,"E")," sapendo che ",n("b",null,"si è già verificato")," ",n(Ji.a,null,"F"),"."),n("p",null,n(Ji.a,null,ee(di()))),n(ae.a,null,"Ricorda vagamente le pipe di ",n("code",null,"bash"),", però al contrario...")),n($i.a,{title:"Eventi mutualmente esclusivi"},n("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),n("p",null,n(Ji.a,null,ee(pi()))))),n(ne.a,null,n($i.a,{title:"Regola della catena"},n("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),n("p",null,n(Ji.a,null,ee(si()))))),n(ne.a,{title:"Le alternative"},n($i.a,{title:"Legge delle alternative"},n("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),n("p",null,n(Ji.a,null,ee(ci())))),n($i.a,{title:"Legge condizionata delle alternative"},n("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",n("b",null,"evento"),":"),n("p",null,n(Ji.a,null,ee(ui())))),n($i.a,{title:"Formula di Bayes"},n("p",null,"Tramite la ",n("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),n("p",null,n(Ji.a,null,ee(oi()))),n(ae.a,null,"In pratica, invertiamo gli eventi."))),n(ne.a,{title:"Eventi indipendenti"},n($i.a,{title:"Due eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a due a due"'),n("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),n("p",null,n(Ji.a,null,ee(ri())))),n($i.a,{title:"Più eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),n("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),n("p",null,n(Ji.a,null,ee(ti()))),n("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),n($i.a,{title:"Famiglia di eventi indipendenti"},n("p",null,"Un insieme di ",n(Ji.a,null,"n")," eventi è una ",n("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),n(ae.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),n(ne.a,{title:"Variabili aleatorie"},n($i.a,{title:"Variabile aleatoria"},n("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",n(Ji.a,null,ee(ei())),".")),n($i.a,{title:n("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},n("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",n(Ji.a,null,ee(ii())),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",n(Ji.a,null,"t"),"."),n("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),n("p",null,n(Ji.a,null,ee(li()))),n(ae.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),n($i.a,{title:"Supporto"},n("blockquote",null,'"supporto di X"'),n("p",null,"Il ",n("b",null,"codominio")," della variabile aleatoria è il suo ",n("i",null,"supporto"),"."),n("p",null,"Per indicare che un valore ",n(Ji.a,null,"x_0")," appartiene al supporto di ",n(Ji.a,null,"X"),", si usa la notazione ",n(Ji.a,null,"X \\mapsto x_0"),"."))),n(ne.a,{title:"Densità"},n($i.a,{title:"Funzione probabilità"},n("p",null,"La ",n("i",null,"funzione probabilità")," ",n(Ji.a,null,ee(ai()))," di una variabile aleatoria ",n("b",null,"discreta")," ",n(Ji.a,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),n("p",null,n(Ji.a,null,ee(ni())))),n($i.a,{title:"Funzione densità"},n("p",null,"La ",n("i",null,"funzione densità")," ",n(Ji.a,null,ee($l()))," di una variabile aleatoria ",n("b",null,"continua")," ",n(Ji.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),n("p",null,n(Ji.a,null,ee(Jl()))),n("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",n("b",null,"non esista")," per una certa variabile aleatoria."),n(ae.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),n(ne.a,{title:"Funzione di ripartizione"},n($i.a,{title:"Definizione"},n("p",null,"Ogni variabile aleatoria ha una ",n("i",null,"funzione di ripartizione")," ",n(Ji.a,null,ee(Hl()))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",n(Ji.a,null,"t"),":"),n("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",n(Ji.a,null,ee(Zl())),":"),n("p",null,n(Ji.a,null,ee(Wl())))),n($i.a,{title:"Proprietà della funzione"},n("ul",null,n("li",null,"È sempre ",n("b",null,"monotona crescente")," (non strettamente)."),n("br",null),n("li",null,"Vale ",n("b",null,"0")," a ",n(Ji.a,null,"-\\infty")," e ",n("b",null,"1")," a ",n(Ji.a,null,"+\\infty"),"."),n("br",null),n("li",null,"È ",n("b",null,"continua da destra"),": ",n(Ji.a,null,ee(Ql()))))),n($i.a,{title:"Probabilità di un valore"},n("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),n("p",null,n(Ji.a,null,ee(Kl()))))),n(ne.a,{title:"Trasformazioni di variabili aleatorie"},n($i.a,{title:"Nel discreto"},n("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),n($i.a,{title:"Nel continuo (invertibile)"},n("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),n("p",null,n(Ji.a,null,ee(Rl())))),n($i.a,{title:"Nel... digitale"},n("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",n("a",{href:"https://docs.python.org/3/library/random.html#random.random"},n("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),n(ne.a,{title:"Informazioni delle variabili aleatorie"},n($i.a,{title:"Media"},n("p",null,"Ogni variabile aleatoria che ha una ",n("b",null,"funzione di ripartizione")," e un ",n("b",null,"supporto finito")," ha anche una ",n("i",null,"media")," (o ",n("i",null,"valore medio")," o ",n("i",null,"atteso"),"):"),n("p",null,n(Ji.a,null,ee(jl()))),n("p",null,"Nel discreto, si può calcolare con:"),n("p",null,n(Ji.a,null,ee(Ol()))),n("p",null,"Nel continuo, si può calcolare con:"),n("p",null,n(Ji.a,null,ee(Gl()))))),n(ne.a,null,n($i.a,{title:"Moda"},n("p",null,"Valore per cui la ",n("b",null,"funzione probabilità")," o ",n("b",null,"funzione densità")," è ",n("b",null,"massima"),".")),n($i.a,{title:"Quantili"},n("p",null,"Il ",n("i",null,"quantile")," ",n(Ji.a,null,ee(Tl()))," di ordine ",n(Ji.a,null,ee(Al()))," della variabile aleatoria ",n(Ji.a,null,"X")," è il più piccolo numero tale che:"),n("p",null,n(Ji.a,null,ee(Bl()))),n("p",null),n("p",null,"Il quantile di ordine 0.5 ",n(Ji.a,null,ee(Ul()))," è detto ",n("i",null,"mediana"),"."),n("p",null,"I quantili di ordine 0.25 ",n(Ji.a,null,ee(Dl()))," e 0.75 ",n(Ji.a,null,ee(Ml()))," sono detti ",n("i",null,"quartili"),"."),n("p",null,"I quantili di ordine ",n(Ji.a,null,ee(Il()))," sono detti ",n("i",null,n(Ji.a,null,"n"),"-esima percentile"),".")),n($i.a,{title:"Varianza"},n("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),n("p",null,n(Ji.a,null,ee(wl()))))),n(ne.a,{title:"Disuguaglianze notevoli"},n($i.a,{title:"Disuguaglianza di Markov"},n("p",null,"Data una variabile aleatoria non-negativa:"),n("p",null,n(Ji.a,null,ee(Yl()))),n("p",null,"Divide in due parti (",n(Ji.a,null,ee(Sl()))," e ",n(Ji.a,null,ee(Cl())),") la funzione X, la cui media risulterà uguale a:"),n("p",null,n(Ji.a,null,ee(Vl())))),n($i.a,{title:"Disuguaglianza di Čebyšëv"},n("blockquote",null,'"disuguaglianza di cebicev"'),n("p",null,"Se la variabile aleatoria ",n(Ji.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",n(Ji.a,null,ee(Nl()))," di distanza dal valore medio è minore o uguale a ",n(Ji.a,null,ee(Fl())),"."),n("p",null,n(Ji.a,null,ee(Ll()))),n("p",null,"E anche:"),n("p",null,n(Ji.a,null,ee(yl()))),n(ae.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),n(ne.a,{title:"Un momento...!"},n($i.a,{title:"Momento"},n("p",null,"Il ",n("i",null,"momento")," ",n(Ji.a,null,"k"),"-esimo di una variabile aleatoria è:"),n("p",null,n(Ji.a,null,ee(kl()))),n(ae.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),n($i.a,{title:"Funzione generatrice dei momenti"},n("p",null,"La ",n("i",null,"funzione generatrice dei momenti")," è:"),n("p",null,n(Ji.a,null,ee(xl()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),n($i.a,{title:"Funzione caratteristica"},n("p",null,"La ",n("i",null,"funzione caratteristica")," è:"),n("p",null,n(Ji.a,null,ee(Pl()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),n(ne.a,{title:"Prove e schemi"},n($i.a,{title:"Variabile con distribuzione"},n("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),n("p",null,n(Ji.a,null,ee(El())))),n($i.a,{title:"Prova di Bernoulli"},n("p",null,"Una prova con solo due possibili esiti: ",n(le.a,null,"successo")," e ",n(ie.a,null,"insuccesso"),".")),n($i.a,{title:"Schema di Bernoulli"},n("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),n(ne.a,{title:"Bernoulliana"},n($i.a,{title:"Distribuzione bernoulliana"},n("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),n("ul",null,n("li",null,"vale ",n(le.a,null,"1")," in caso di ",n(le.a,null,"successo"),"."),n("li",null,"vale ",n(ie.a,null,"0")," in caso di ",n(ie.a,null,"insuccesso"),".")),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(zl())))),n($i.a,{title:"Densità della bernoulliana"},n("p",null,"La distribuzione bernoulliana ha come densità:"),n("p",null,n(Ji.a,null,ee(ql()))))),n(ne.a,{title:"Binomiale"},n($i.a,{title:"Distribuzione binomiale"},n("p",null,"Una variabile aleatoria che conta il numero di successi di ",n(Ji.a,null,"n")," prove di uno schema di Bernoulli."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(gl())),".")),n($i.a,{title:"Densità della binomiale"},n("p",null,"La binomiale ha come densità:"),n("p",null,n(Ji.a,null,ee(Xl())))),n($i.a,{title:"Momenti della binomiale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale è:"),n("p",null,n(Ji.a,null,ee(hl()))),n("p",null,"La ",n("b",null,"media")," di una binomiale è:"),n("p",null,n(Ji.a,null,ee(_l()))),n("p",null,"La ",n("b",null,"varianza")," di una binomiale è:"),n("p",null,n(Ji.a,null,ee(bl()))))),n(ne.a,{title:"Geometrica"},n($i.a,{title:"Distribuzione geometrica"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,"Geo(p)"),".")),n($i.a,{title:"Densità della geometrica"},n("p",null,"La geometrica ha come densità:"),n("p",null,n(Ji.a,null,ee(vl())))),n($i.a,{title:"Momenti della geometrica"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica è:"),n("p",null,n(Ji.a,null,ee(fl()))),n("p",null,"La ",n("b",null,"media")," della geometrica è:"),n("p",null,n(Ji.a,null,ee(ml()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Ji.a,null,ee(dl())))),n($i.a,{title:"Assenza di memoria della geometrica"},n("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Ji.a,null,ee(pl()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Binomiale negativa"},n($i.a,{title:"Distribuzione binomiale negativa"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",n(Ji.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(sl())),".")),n($i.a,{title:"Densità della binomiale negativa"},n("p",null,"La binomiale negativa ha come densità:"),n("p",null,n(Ji.a,null,ee(cl())))),n($i.a,{title:"Momenti della binomiale negativa"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),n("p",null,n(Ji.a,null,ee(ul()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa è:"),n("p",null,n(Ji.a,null,ee(ol()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa è:"),n("p",null,n(Ji.a,null,ee(rl())))))),n(ne.a,{title:"Geometrica traslata"},n($i.a,{title:"Distribuzione geometrica traslata"},n("p",null,"Una variabile aleatoria che conta il numero ",n(Ji.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),n("p",null,"Il suo simbolo rimane ",n(Ji.a,null,ee(tl())),".")),n($i.a,{title:"Densità della geometrica tralsata"},n("p",null,"La geometrica traslata ha come densità:"),n("p",null,n(Ji.a,null,ee(el())))),n($i.a,{title:"Momenti della geometrica traslata"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),n("p",null,n(Ji.a,null,ee(il()))),n("p",null,"La ",n("b",null,"media")," della geometrica traslata è:"),n("p",null,n(Ji.a,null,ee(ll()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(Ji.a,null,ee(al())))),n($i.a,{title:"Assenza di memoria della geometrica traslata"},n("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Ji.a,null,ee(nl()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Binomiale negativa traslata"},n($i.a,{title:"Distribuzione binomiale negativa traslata"},n("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",n(Ji.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo rimane ",n(Ji.a,null,ee($a())),".")),n($i.a,{title:"Densità della binomiale negativa traslata"},n("p",null,"La binomiale negativa traslata ha come densità:"),n("p",null,n(Ji.a,null,ee(Ja())))),n($i.a,{title:"Momenti della binomiale negativa traslata"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),n("p",null,n(Ji.a,null,ee(Ha()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa traslata è:"),n("p",null,n(Ji.a,null,ee(Za()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa traslata è:"),n("p",null,n(Ji.a,null,ee(Wa())))))),n(ne.a,{title:"Ipergeometrica"},n($i.a,{title:"Distribuzione ipergeometrica"},n("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",n(Ji.a,null,"K")," e di insuccessi ",n(Ji.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",n(Ji.a,null,"n")," in blocco."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,"Ipe(N, K, n)"),".")),n($i.a,{title:"Densità della ipergeometrica"},n("p",null,"La ipergeometrica ha come densità:"),n("p",null,n(Ji.a,null,ee(Qa())))),n($i.a,{title:"Momenti della ipergeometrica"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),n("p",null,"La ",n("b",null,"media")," della ipergeometrica è:"),n("p",null,n(Ji.a,null,ee(Ka()))),n("p",null,"La ",n("b",null,"varianza")," della ipergeometrica è:"),n("p",null,n(Ji.a,null,ee(Ra())))))),n(ne.a,{title:"Poissoniana"},n($i.a,{title:"Distribuzione poissoniana"},n("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),n("ul",null,n("li",null,"Binomiale: ",n(Ji.a,null,ee(ja()))),n("li",null,"Il numero di prove tende a infinito: ",n(Ji.a,null,ee(Oa()))),n("li",null,"La probabilità di successo tende a 0: ",n(Ji.a,null,ee(Ga()))),n("li",null,"La media è finita: ",n(Ji.a,null,ee(Ta())))),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(Aa())))),n($i.a,{title:"Densità della poissoniana"},n("p",null,"La poissoniana ha come densità:"),n("p",null,n(Ji.a,null,ee(Ba())))),n($i.a,{title:"Momenti della poissoniana"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),n("p",null,n(Ji.a,null,ee(Ua()))),n("p",null,"La ",n("b",null,"media")," della poissoniana è:"),n("p",null,n(Ji.a,null,ee(Da()))),n("p",null,"La ",n("b",null,"varianza")," della poissoniana è:"),n("p",null,n(Ji.a,null,ee(Ma()))),n("p",null,"Gli altri momenti della poissoniana sono:"),n("ol",{start:2},n("li",null,n(Ji.a,null,ee(Ia()))))))),n(ne.a,{title:"Un altro schema"},n($i.a,{title:"Schema di Poisson"},n("p",null,"Una successione di ",n("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),n("ul",null,n("li",null,"non sono sovrapposti."),n("li",null,"hanno intensità ",n(Ji.a,null,ee(wa()))," costante."),n("li",null,"avvengono indipendentemente gli uni dagli altri."))),n($i.a,{title:"Processo di Poisson"},n("p",null,"Una variabile aleatoria ",n(Ji.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",n(Ji.a,null,ee(Ya()))," in un intervallo di tempo di durata ",n(Ji.a,null,"t"),"."),n("p",null,"E' una distribuzione poissoniana con ",n(Ji.a,null,ee(Sa())),": ",n(Ji.a,null,ee(Ca()))),n(ae.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),n(ne.a,{title:"Esponenziale"},n($i.a,{title:"Distribuzione esponenziale"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",n(Ji.a,null,ee(Va())),"."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(Na())),".")),n($i.a,{title:"Densità dell'esponenziale"},n("p",null,"L'esponenziale ha come ",n("b",null,"densità"),":"),n("p",null,n(Ji.a,null,ee(Fa()))),n("p",null,"L'esponenziale ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Ji.a,null,ee(La())))),n($i.a,{title:"Momenti dell'esponenziale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),n("p",null,n(Ji.a,null,ee(ya()))),n("p",null,"La ",n("b",null,"media")," dell'esponenziale è:"),n("p",null,n(Ji.a,null,ee(ka()))),n("p",null,"La ",n("b",null,"varianza")," dell'esponenziale è:"),n("p",null,n(Ji.a,null,ee(xa())))),n($i.a,{title:"Assenza di memoria della esponenziale"},n("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(Ji.a,null,ee(Pa()))),n(ae.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(ne.a,{title:"Legge gamma"},n($i.a,{title:"Distribuzione gamma"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",n(Ji.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",n(Ji.a,null,ee(Ea())),"."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(za())),".")),n($i.a,{title:"Densità della legge gamma"},n("p",null,"La legge gamma ha come densità:"),n("p",null,n(Ji.a,null,ee(qa())))),n($i.a,{title:"Momenti della legge gamma"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),n("p",null,n(Ji.a,null,ee(ga()))),n("p",null,"La ",n("b",null,"media")," della legge gamma è:"),n("p",null,n(Ji.a,null,ee(Xa()))),n("p",null,"La ",n("b",null,"varianza")," della legge gamma è:"),n("p",null,n(Ji.a,null,ee(ha())))))),n(ne.a,{title:"Uniforme"},n($i.a,{title:"Distribuzione uniforme"},n("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",n(Ji.a,null,ee(_a()))," in modo equiprobabile."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(ba()))),n("p",null,"Su di essa vale la seguente proprietà:"),n("p",null,n(Ji.a,null,ee(va())))),n($i.a,{title:"Densità della distribuzione uniforme"},n("p",null,"La distribuzione uniforme ha come ",n("b",null,"densità"),":"),n("p",null,n(Ji.a,null,ee(fa()))),n("p",null,"La distribuzione uniforme ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(Ji.a,null,ee(ma())))),n($i.a,{title:"Momenti della distribuzione uniforme"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),n("p",null,n(Ji.a,null,ee(da()))),n("p",null,"La ",n("b",null,"media")," della distribuzione uniforme è:"),n("p",null,n(Ji.a,null,ee(pa()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione uniforme è:"),n("p",null,n(Ji.a,null,ee(sa())))))),n(ne.a,{title:"Normale o Gaussiana"},n($i.a,{title:"Distribuzione normale"},n("p",null,"Una variabile aleatoria con una specifica distribuzione."),n("p",null,"Il suo simbolo è ",n(Ji.a,null,ee(ca())),"."),n(ae.a,null,n(Ji.a,null,"\\mu")," e ",n(Ji.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),n($i.a,{title:"Densità della distribuzione normale"},n("p",null,"La distribuzione normale ha come densità:"),n("p",null,n(Ji.a,null,ee(ua())))),n($i.a,{title:"Momenti della distribuzione normale"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),n("p",null,n(Ji.a,null,ee(oa()))),n("p",null,"La ",n("b",null,"media")," della distribuzione normale è:"),n("p",null,n(Ji.a,null,ee(ra()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione normale è:"),n("p",null,n(Ji.a,null,ee(ta())))))),n(ne.a,null,n($i.a,{title:"Trasformazione della normale"},n("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),n("p",null,n(Ji.a,null,ee(ea())))),n($i.a,{title:"Normale standard"},n("p",null,"La distribuzione normale standard ",n(Ji.a,null,"Z")," è:"),n("p",null,n(Ji.a,null,"Z \\sim Nor(0, 1)")),n("p",null,"La sua funzione di ripartizione è detta ",n(Ji.a,null,ee(ia()))," e vale:"),n("p",null,n(Ji.a,null,ee(la())))),n($i.a,{title:"Quantili normali"},n("p",null,"Da un quantile ",n(Ji.a,null,ee(aa()))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),n("p",null,n(Ji.a,null,ee(na()))))),n(ne.a,null,n($i.a,{title:"Gamma e normale"},n("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),n("p",null,n(Ji.a,null,ee($n())))),n($i.a,{title:"La funzione Chi"},n("blockquote",null,'"chi-quadro a un grado di libertà"'),n("p",null,"Esiste una distribuzione Gamma particolare:"),n("p",null,n(Ji.a,null,ee(Jn()))),n("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),n("p",null,n(Ji.a,null,ee(Hn())))),n($i.a,{title:"T di Student"},n("p",null,"Un'altra funzione particolare è la funzione T di Student:"),n("p",null,n(Ji.a,null,ee(Zn()))))),n(ne.a,{title:"Approssimazioni notevoli"},n($i.a,{title:"Ipergeometrica e binomiale"},n("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",n(Ji.a,null,"N")," rispetto a ",n(Ji.a,null,"n"),", si può dire che:"),n("p",null,n(Ji.a,null,ee(Wn())))),n($i.a,{title:"Binomiale e poissoniana"},n("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",n(Ji.a,null,"n")," è grande e ",n(Ji.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),n("p",null,n(Ji.a,null,ee(Qn())))),n($i.a,{title:"Binomiale e normale"},n("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",n(Ji.a,null,"n")," grande e ",n(Ji.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),n("p",null,n(Ji.a,null,ee(Kn())))),n($i.a,{title:"Correzione di Yates"},n("p",null,"Passando da una variabile discreta ",n(Ji.a,null,"X")," a una continua ",n(Ji.a,null,"Y"),", per ogni valore discreto ",n(Ji.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',n(Ji.a,null,ee(Rn())),":"),n("ul",null,n("li",null,n(Ji.a,null,ee(jn()))),n("li",null,n(Ji.a,null,ee(On()))),n("li",null,n(Ji.a,null,ee(Gn()))),n("li",null,n(Ji.a,null,ee(Tn())))))),n(ne.a,{title:"Vettori aleatori"},n($i.a,{title:"Vettore aleatorio"},n("p",null,"Un vettore ",n("b",null,"composto da variabili aleatorie"),"."),n("p",null,"Il suo simbolo generalmente è ",n(Ji.a,null,ee(An()))," oppure ",n(Ji.a,null,ee(Bn())),".")),n($i.a,{title:"Funzioni di ripartizione"},n("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione congiunta"),":"),n("p",null,n(Ji.a,null,ee(Un()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione marginale"),":"),n("p",null,n(Ji.a,null,ee(Dn())))),n($i.a,{title:"Densità discreta"},n("p",null,"I vettori aleatori ",n("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità congiunta"),":"),n("p",null,n(Ji.a,null,ee(Mn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità marginale"),":"),n("p",null,n(Ji.a,null,ee(In()))))),n(ne.a,{title:"Più variabili aleatorie"},n($i.a,{title:"Indipendenza delle variabili aleatorie"},n("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",n(Ji.a,null,"A_i"),":"),n("p",null,n(Ji.a,null,ee(wn())))),n($i.a,{title:"Media dei vettori aleatori"},n("p",null,"E' possibile calcolare la media di qualsiasi funzione ",n(Ji.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),n("p",null,n(Ji.a,null,ee(Yn()))),n(ae.a,null,"Solitamente si calcola la media di ",n(Ji.a,null,"x \\cdot y"),"."),n("p",null,"Le medie di più variabili aleatorie si possono sommare:"),n("p",null,n(Ji.a,null,ee(Sn()))))),n(ne.a,null,n($i.a,{title:"Covarianza"},n("p",null,"Un ",n("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),n("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),n("p",null,n(Ji.a,null,ee(Cn()))),n("p",null,"Ha diverse proprietà:"),n("ul",null,n("li",null,"Il suo ",n("b",null,"valore nullo")," è 0: ",n(Ji.a,null,ee(Vn()))),n("li",null,"E' ",n("b",null,"commutativa"),": ",n(Ji.a,null,ee(Nn()))),n("li",null,"E' ",n("b",null,"semplificabile"),": ",n(Ji.a,null,ee(Fn()))),n("li",null,"E' ",n("b",null,"lineare"),": ",n(Ji.a,null,ee(Ln()))),n("li",null,"E' ",n("b",null,"distributiva"),": ",n(Ji.a,null,ee(yn()))))),n($i.a,{title:"Variabili incorrelate"},n("p",null,"Due variabili sono ",n("i",null,"variabili incorrelate")," se:"),n("p",null,n(Ji.a,null,ee(kn()))),n("p",null,"Variabili indipendenti sono sempre incorrelate.")),n($i.a,{title:"Matrice di covarianza"},n("p",null,"Una matrice ",n(Ji.a,null,ee(xn()))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",n(Ji.a,null,ee(Pn())),":"),n("p",null,n(Ji.a,null,ee(En()))),n("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",n(Ji.a,null,"\\geq 0"),".")),n($i.a,{title:"Coefficiente di correlazione"},n("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),n("p",null,n(Ji.a,null,ee(zn()))),n("p",null,"E' sempre compreso tra -1 e 1:"),n("p",null,n(Ji.a,null,ee(qn()))),n("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),n("p",null,n(Ji.a,null,ee(gn())))),n($i.a,{title:"Varianza di variabili aleatorie sommate"},n("p",null,"La varianza di due variabili aleatorie sommate è:"),n("p",null,n(Ji.a,null,ee(Xn()))),n(ae.a,null,"Si dimostra applicando le proprietà della covarianza!"),n("p",null,"Se più variabili aleatorie ",n(Ji.a,null,"X_i")," sono ",n("b",null,"indipendenti")," (",n(Ji.a,null,ee(hn())),"), allora:"),n("p",null,n(Ji.a,null,ee(_n()))))),n(ne.a,{title:"Campioni"},n($i.a,{title:"Campione casuale"},n("p",null,"Una ",n("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",n(Ji.a,null,"X"),' ("popolazione") ma ',n("b",null,"indipendenti")," tra loro."),n(ae.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",n("b",null,"realizzeranno")," nel loro valore.")),n($i.a,{title:"Momento campionario"},n("p",null,"Il valore dato dalla media aritmetica degli ",n(Ji.a,null,"n")," elementi del campione elevati alla potenza ",n(Ji.a,null,"k"),":"),n("p",null,n(Ji.a,null,ee(bn()))),n("p",null,"Il momento campionario di primo ordine è la ",n("i",null,"media campionaria")," ",n(Ji.a,null,ee(vn())),".")),n($i.a,{title:"Varianza campionaria"},n("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),n("p",null,"Se è noto il valore medio ",n(Ji.a,null,ee(fn()))," di X:"),n("p",null,n(Ji.a,null,ee(mn()))),n("p",null,"Altrimenti:"),n("p",null,n(Ji.a,null,ee(dn()))))),n(ne.a,{title:"Media-ception"},n($i.a,{title:"Media campionaria"},n("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),n("p",null,n(Ji.a,null,ee(pn()))),n(ae.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),n($i.a,{title:"Varianza campionaria"},n("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),n("p",null,n(Ji.a,null,ee(sn()))),n(ae.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),n($i.a,{title:"Correzione campionaria"},n("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),n("p",null,n(Ji.a,null,ee(cn()))),n(ae.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),n(ne.a,{title:"Campionamento di una distribuzione normale"},n($i.a,{title:"Campionamento di una distribuzione normale"},n("p",null,"Se la popolazione ",n(Ji.a,null,"X")," ha una distribuzione normale (",n(Ji.a,null,ee(un())),")...")),n($i.a,{title:"Distribuzione della media campionaria"},n("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),n("p",null,n(Ji.a,null,ee(on())))),n($i.a,{title:"Distribuzione della varianza campionaria"},n("p",null,"...e anche della varianza campionaria!"),n("p",null,n(Ji.a,null,ee(rn()))),n("p",null,n(Ji.a,null,ee(tn())))),n($i.a,{title:"Indipendenza"},n("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),n(ne.a,{title:"Quando i campioni hanno dimensioni infinite"},n($i.a,{title:"Convergenza in distribuzione"},n("p",null,"Se la successione di variabili aleatorie ",n(Ji.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa funzione di ripartizione")," della popolazione ",n(Ji.a,null,"X"),", allora essa ",n("i",null,"converge in distribuzione"),"."),n("p",null,n(Ji.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),n($i.a,{title:"Convergenza in probabilità"},n("p",null,"Se la successione di variabili aleatorie ",n(Ji.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità")," della popolazione ",n(Ji.a,null,"X"),", allora essa ",n("i",null,"converge in probabilità"),"."),n("p",null,n(Ji.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),n($i.a,{title:"Convergenza quasi certa"},n("p",null,"Se la successione di variabili aleatorie ",n(Ji.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità a ")," della popolazione ",n(Ji.a,null,"X"),", allora essa ",n("i",null,"converge quasi certamente"),"."),n("p",null,n(Ji.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),n($i.a,{title:"Convergenza in media quadratica"},n("p",null,"Se la successione di variabili aleatorie ",n(Ji.a,null,"X_n")," all'infinito ha la ",n("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",n(Ji.a,null,"X")," ",n("b",null,"uguale a 0"),", allora essa ",n("i",null,"converge in media quadratica"),"."),n("p",null,n(Ji.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),n($i.a,{title:"Gerarchia delle convergenze"},n("p",null,n(Ji.a,null,"\n \\begin{matrix}\n X_n \\xrightarrow{mq} X\\\\\n X_n \\xrightarrow{qc} X\n \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),n("p",null,"In più:"),n("p",null,n(Ji.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),n(ne.a,{title:"I grandi numeri"},n($i.a,{title:"Legge debole dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Ji.a,null,ee(en()))," ",n("b",null,"converge in probabilità")," alla media della popolazione ",n(Ji.a,null,ee(ln())),", se essa esiste."),n("p",null,n(Ji.a,null,"\\overline{X}_n \\xrightarrow{p} X")),n("p",null,"Ovvero:"),n("p",null,n(Ji.a,null,ee(an()))),n("p",null,n(Ji.a,null,ee(nn())))),n($i.a,{title:"Legge forte dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(Ji.a,null,ee($()))," ",n("b",null,"converge quasi certamente")," alla media della popolazione ",n(Ji.a,null,ee(J())),", se essa esiste."),n("p",null,n(Ji.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),n("p",null,"Ovvero:"),n("p",null,n(Ji.a,null,ee(H()))),n(ae.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),n(ne.a,{title:"Al limite"},n($i.a,{title:"Teorema centrale del limite"},n("p",null,"La successione delle medie campionarie ",n(Ji.a,null,ee(Z()))," ",n("b",null,"converge in distribuzione")," a ",n(Ji.a,null,ee(W())),"."),n("p",null,n(Ji.a,null,ee(Q()))),n("p",null,"Ovvero:"),n("p",null,n(Ji.a,null,ee(K()))))),n(ne.a,{title:"Altre approsimazioni"},n($i.a,{title:"Binomiale e normale"},n("p",null,"E' una somma di ",n("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),n("p",null,n(Ji.a,null,ee(R())))),n($i.a,{title:"Binomiale negativa e normale"},n("p",null,"E' una somma di ",n("b",null,"geometriche"),", e quindi si approssima a una normale:"),n("p",null,n(Ji.a,null,ee(j())))),n($i.a,{title:"Poissoniana e normale"},n("p",null,"E' una somma di altre ",n("b",null,"poissoniane"),", e quindi si approssima a una normale:"),n("p",null,n(Ji.a,null,ee(O())))),n($i.a,{title:"Gamma e normale"},n("p",null,"E' una somma di ",n("b",null,"esponenziali"),", e quindi si approssima a una normale:"),n("p",null,n(Ji.a,null,ee(G())))),n($i.a,{title:"In generale"},n("p",null,"Se ",n(Ji.a,null,"n")," è grande, allora:"),n("p",null,n(Ji.a,null,ee(T()))))),n(ne.a,{title:"Actually statistica"},n($i.a,{title:"Parametri sconosciuti"},n("p",null,"Per indicare parametri sconosciuti di una legge si usa ",n(Ji.a,null,"\\theta"),".")),n($i.a,{title:"Statistica"},n("p",null,"Una variabile aleatoria funzione di un campione:"),n("p",null,n(Ji.a,null,ee(A()))),n(ae.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",n(Ji.a,null,ee(B())),"."))),n(ne.a,{title:"Stimatori"},n($i.a,{title:"Stimatore"},n("p",null,"Una statistica ",n(Ji.a,null,"T_n")," ottenuta da ",n(Ji.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),n($i.a,{title:"Corretto"},n("p",null,"Uno stimatore è ",n("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Ji.a,null,ee(U())))),n($i.a,{title:"Asintoticamente corretto"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(Ji.a,null,ee(D())))),n($i.a,{title:"Consistente in media quadratica"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in media quadratica")," se:"),n("p",null,n(Ji.a,null,ee(M())))),n($i.a,{title:"Consistente in probabilità"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in probabilità")," se:"),n("p",null,n(Ji.a,null,ee(I())))),n($i.a,{title:"Asintoticamente normale"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente normale")," se:"),n("p",null,n(Ji.a,null,ee(w()))))),n(ne.a,{title:"Metodo dei momenti"},n($i.a,{title:"Metodo dei momenti"},n("p",null,"Si può usare il ",n("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",n(Ji.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Ji.a,null,ee(Y()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Ji.a,null,"M")," a ",n(Ji.a,null,"\\theta"),": ",n(Ji.a,null,ee(S()))),n("p",null,"Visto che:"),n("ul",null,n("li",null,n(Ji.a,null,ee(C()))),n("li",null,n(Ji.a,null,ee(V())))),n("p",null,"Allora:"),n("p",null,n(Ji.a,null,ee(N()))),n("p",null,"Se ",n(Ji.a,null,ee(F()))," non è esprimibile in termini di ",n(Ji.a,null,ee(L())),", si possono usare i momenti successivi ",n(Ji.a,null,ee(y())),", ",n(Ji.a,null,ee(k())),", ",n(Ji.a,null,ee(x())),"..."))),n(ne.a,{title:"Metodo della massima verosomiglianza"},n($i.a,{title:"Metodo della massima verosomiglianza"},n("p",null,"Si può usare il ",n("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",n(Ji.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(Ji.a,null,ee(P()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(Ji.a,null,"L")," a ",n(Ji.a,null,"\\theta"),": ",n(Ji.a,null,ee(E()))),n("p",null,"Consiste nel trovare il massimo assoluto ",n(Ji.a,null,ee(z()))," della la funzione di verosomiglianza ",n(Ji.a,null,ee(q())),":"),n("p",null,n(Ji.a,null,ee(g()))),n("p",null,"Gli stimatori di massima verosomiglianza sono ",n("b",null,"asintoticamente corretti"),", ",n("b",null,"consistenti in probabilità")," e ",n("b",null,"asintoticamente normali"),".")),n($i.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},n("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),n("ul",null,n("li",null,"Sono ",n("b",null,"asintoticamente corretti"),"."),n("li",null,"Sono ",n("b",null,"consistenti in probabilità"),"."),n("li",null,"Sono ",n("b",null,"asintoticamente normali"),"."),n("li",null,"Sono ",n("b",null,"invarianti"),": ",n(Ji.a,null,ee(X())))))),n(ne.a,{title:"Nuove stime notevoli"},n($i.a,{title:"Stima di una bernoulliana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Ji.a,null,ee(h())))),n($i.a,{title:"Stima di una poissoniana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Ji.a,null,ee(_())))),n($i.a,{title:"Stima di una esponenziale"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(Ji.a,null,ee(b())))),n($i.a,{title:"Stima di una normale"},n("p",null,"Per il metodo della massima verosomiglianza:"),n("ul",null,n("li",null,n(Ji.a,null,ee(v()))),n("br",null),n("li",null,n(Ji.a,null,ee(f())))))),n(ne.a,{title:"Intervalli di confidenza"},n($i.a,{title:"Confidenza"},n("blockquote",null,'"intervallo di confidenza al 95%"'),n("p",null,"L'intervallo di valori di ",n(Ji.a,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),n("p",null,"L'intervallo di confidenza a N della stima ",n(Ji.a,null,ee(m()))," è l'intervallo ",n(Ji.a,null,"]a, b[")," tale che:"),n("p",null,n(Ji.a,null,ee(d()))),n("p",null,"Può anche essere ",n("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),n(ne.a,{title:"Confidenza nella media di una normale"},n($i.a,{title:"Varianza nota"},n("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Ji.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Ji.a,null,ee(p()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Ji.a,null,ee(s()))),n("li",null,"Intervallo unilatero da destra: ",n(Ji.a,null,ee(c()))))),n($i.a,{title:"Varianza incognita"},n("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(Ji.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(Ji.a,null,ee(u()))),n("li",null,"Intervallo unilatero da sinistra: ",n(Ji.a,null,ee(o()))),n("li",null,"Intervallo unilatero da destra: ",n(Ji.a,null,ee(r())))),n("p",null,n(Ji.a,null,ee(t()))," è un quantile della distribuzione di Student di parametro ",n(Ji.a,null,"v"),"."))),n(ne.a,{title:"Confidenza per la proporzione di una bernoulliana"},n($i.a,{title:"Terzo metodo corretto"},n("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),n("p",null,n(Ji.a,null,ee(e()))))),n(ne.a,{title:"Confidenza per la media di qualsiasi popolazione"},n($i.a,{title:"Approssimando con la normale"},n("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),n("p",null,n(Ji.a,null,ee(i()))))))},l}(Hi.Component)}.call(this,l("hosL").h)}}]); -//# sourceMappingURL=route-statistica.chunk.71281.js.map \ No newline at end of file diff --git a/docs/route-statistica.chunk.71281.js.map b/docs/route-statistica.chunk.71281.js.map deleted file mode 100644 index 1ac4cdd..0000000 --- a/docs/route-statistica.chunk.71281.js.map +++ /dev/null @@ -1 +0,0 @@ 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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__P0_NL\"};","import style from \"./todo.css\";\nimport { Component } from 'preact';\n\nexport default class Todo extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (

{this.props.title}

);\n\t\t}\n\n\t\treturn (\n\t\t\t
\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
\n\t\t);\n\t}\n}\n","import style from \"./minus.css\";\nimport { Component } from 'preact';\n\nexport default class Minus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n render() {\n return (\n
\n {this.props.children}\n
\n )\n }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"hypothesis\":\"hypothesis__3E-73\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"thesis\":\"thesis__13Kp6\"};","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t{this.props.children}\n\t\t\t);\n\t}\n}","import style from \"./plus.css\";\nimport { Component } from 'preact';\n\nexport default class Plus extends Component {\n\trender() {\n\t\treturn {this.props.children};\n\t}\n}\n","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t let title = null;\n\t if(this.props.title !== undefined) {\n title = (

{this.props.title}

)\n }\n\n let children;\n if(Array.isArray(this.props.children)) {\n children = this.props.children.map(element => {\n return (
{element}
);\n });\n }\n else {\n children =
{this.props.children}
;\n }\n\t\treturn (\n\t
\n {title}\n
{children}
\n
\n );\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__2Ld4F\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"theorem\":\"theorem__3Qv59\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1pOoN\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"split\":\"split__3qCWp\",\"splitparent\":\"splitparent__2xagg\",\"splitchild\":\"splitchild__3cEoc\"};","import { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Todo from '../components/todo';\nimport Theorem from \"../components/theorem\";\nimport Hypothesis from \"../components/hypothesis\";\nimport Thesis from \"../components/thesis\";\nimport Proof from \"../components/proof\";\nimport Example from \"../components/example\";\nimport Plus from \"../components/plus\";\nimport Minus from \"../components/minus\";\n\nconst r = String.raw;\n\nexport default class Statistica extends Component {\n\trender() {\n\t /*\n \n \n

\n Gruppo intero di oggetti di cui si cercano informazioni.\n

\n \n \n

\n Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n

\n \n \n

\n Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n

\n \n \n \n \n

\n Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.\n

\n \n Simple random sample}>\n

\n Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.\n

\n \n Sample of convenience}>\n

\n Campione ottenuto in un modo casuale non ben definito.\n

\n \n Sample with replacement}>\n

\n Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n

\n

\n Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n

\n \n \n

\n Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n

\n \n Stratified random sample}>\n

\n Campione ottenuto da un sottoinsieme della popolazione detto strato.\n

\n \n Cluster sample}>\n

\n Campione ottenuto selezionando più cluster di elementi alla volta.\n

\n \n \n \n Sampling variation}>\n

\n Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n

\n \n \n

\n Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.\n

\n \n \n \n \n

\n Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n

\n

\n Serve per verificare delle condizioni.\n

\n \n \n

\n Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.\n

\n

\n Serve per capire quali fattori influenzano il risultato dell'esperimento.\n

\n \n \n \n Numerico o quantitativo}>\n Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n \n Categorico o qualitativo}>\n Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n \n \n\t */\n return (\n
\n

Statistica ed Elementi di Probabilità

\n \n \n

\n {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n

\n \n \n

\n {r`P(E) = \\frac{successi}{prove\\ totali}`}\n

\n \n \n

\n Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n

\n \n \n \n \n
\n \"omegone\"\n
\n

\n L'insieme di tutti gli esiti possibili di un esperimento.\n

\n

\n {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n

\n \n \n
\n \"omeghino\"\n
\n

\n Un elemento dello spazio campionario.\n

\n

\n {r`\\omega = 1`}\n

\n \n \n
\n \"e\"\n
\n

\n Un sottoinsieme dello spazio campionario.\n

\n

\n {r`E = \\left \\{ 1, 2 \\right \\}`}\n

\n

\n Lo spazio campionario stesso è un evento certo.\n

\n \n \n
\n \"not e\"\n
\n

\n Il complementare di un sottoinsieme.\n

\n

\n {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n

\n \n \n
\n \"e intersecato effe\"\n
\n

\n L'intersezione di più sottoinsiemi.\n

\n

\n {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n

\n \n \n
\n \"e unito a effe\"\n
\n

\n L'unione di più sottoinsiemi.\n

\n

\n {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n

\n \n \n
\n \"e meno effe\"\n
\n

\n {r`E \\setminus F = E \\cap \\bar{F}`}\n

\n \n \n
\n \"e contenuto in effe\"\n
\n

\n L'inclusione del primo insieme in un altro.\n

\n

\n {r`E \\subseteq F`}\n

\n

\n Se si verifica E, allora si verifica anche F.\n

\n \n \n
\n \"e è impossibile\"\n
\n

\n Un sottoinsieme vuoto.\n

\n

\n {r`E = \\emptyset`}\n

\n \n \n
\n \"e ed effe si escludono mutualmente\"\n
\n

\n La disgiunzione di due insiemi.\n

\n

\n {r`E \\cap F = \\emptyset`}\n

\n \n \n \n \n
\n \"famiglia effe\"\n
\n

\n I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n

\n

\n {r`\\mathcal{F}`}\n

\n

\n Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n

\n \n {r`\\sigma`}-algebra}>\n
\n \"sigma algebra\"\n
\n

\n Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n

\n
    \n
  1. \n Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n
    2. \n
  2. \n Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n
    3. \n
  3. \n Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n
    4. \n
\n

\n Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n

\n \n \n \n \n
\n \"la partizione e composta da e uno, e due, e tre...\"\n
\n

\n Un insieme di esiti e eventi:\n

\n
    \n
  • Finito.
    • \n
  • In cui tutti gli eventi hanno probabilità diversa da 0.
    • \n
  • In cui tutti gli eventi sono mutualmente esclusivi.
    • \n
  • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
    • \n
\n

\n La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n

\n \n Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n \n \n \n \n \n

\n La probabilità di un evento è un numero tra 0 e 1.\n

\n

\n {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n

\n \n \n

\n La probabilità dello spazio campionario è sempre 1.\n

\n

\n {r`P(\\Omega) = 1`}\n

\n \n \n

\n La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n

\n

\n {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n

\n \n \n \n \n

\n La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n

\n

\n {r`P(\\bar{E}) = 1 - P({E})`}\n

\n \n \n

\n La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n

\n

\n {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n

\n \n \n

\n La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n

\n

\n {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n

\n \n Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n \n \n \n \n \n

\n Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n

\n

\n {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n

\n \n \n

\n Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n

\n \n \n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n

\n

\n Tengo conto dell'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n

\n

\n Tengo conto dell'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n

\n

\n Non mi interessa l'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n

\n \n \n

\n Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n

\n

\n Non mi interessa l'ordine in cui ho estratto i numeri.\n

\n

\n {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n

\n \n \n

\n Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n

\n

\n {r`\\boldsymbol{P}_n = n!`}\n

\n \n \n \n \n
\n \"E dato F\"\n
\n

\n La probabilità che si verifichi E sapendo che si è già verificato F.\n

\n

\n {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n

\n \n Ricorda vagamente le pipe di bash, però al contrario...\n \n \n \n

\n Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n

\n

\n {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n

\n \n \n \n \n

\n Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n

\n

\n {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n

\n \n \n \n \n

\n La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n

\n

\n {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n

\n \n \n

\n La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n

\n

\n {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n

\n \n \n

\n Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n

\n

\n {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n

\n \n In pratica, invertiamo gli eventi.\n \n \n \n \n \n
\n \"eventi indipendenti a due a due\"\n
\n

\n Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n

\n

\n {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n

\n \n \n
\n \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n
\n

\n Si può verificare l'indipendenza di più eventi alla volta:\n

\n

\n {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n

\n

\n Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n

\n \n \n

\n Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n

\n \n Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n \n \n \n \n \n

\n Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n

\n \n Insieme di ripartizione}>\n

\n Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n

\n

\n Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n

\n

\n {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n

\n \n All'aumentare di t, l'insieme conterrà sempre più elementi.\n \n \n \n
\n \"supporto di X\"\n
\n

\n Il codominio della variabile aleatoria è il suo supporto.\n

\n

\n Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n

\n \n \n \n \n

\n La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n

\n

\n {r`p_X (x) = \\begin{cases}\n P([X = x]) \\quad se\\ X \\mapsto x \\\\\n 0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n \\end{cases}`}\n

\n \n \n

\n La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n

\n

\n {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n

\n

\n A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n

\n \n Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n \n \n \n \n \n

\n Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n

\n

\n Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n

\n

\n {r`F_X (t) = P(A_t) = \\begin{cases}\n \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n \\end{cases}`}\n

\n \n \n
    \n
  • È sempre monotona crescente (non strettamente).

    • \n
  • Vale 0 a -\\infty e 1 a +\\infty.

    • \n
  • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
    • \n
\n \n \n

\n Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n

\n

\n {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n

\n \n \n \n \n

\n Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n

\n \n \n

\n Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n

\n

\n {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n

\n \n \n

\n Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n

\n \n \n \n \n

\n Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n

\n

\n {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n

\n

\n Nel discreto, si può calcolare con:\n

\n

\n {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n

\n

\n Nel continuo, si può calcolare con:\n

\n

\n {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n

\n \n \n \n \n

\n Valore per cui la funzione probabilità o funzione densità è massima.\n

\n \n \n

\n Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n

\n

\n \n {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n \n

\n

\n\n

\n

\n Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n

\n

\n I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n

\n

\n I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n

\n \n \n

\n È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n

\n

\n {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n

\n \n \n \n \n

\n Data una variabile aleatoria non-negativa:\n

\n

\n {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n

\n

\n Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n

\n

\n {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n

\n \n \n
\n \"disuguaglianza di cebicev\"\n
\n

\n Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n

\n

\n {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n

\n

\n E anche:\n

\n

\n {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n

\n \n Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n \n \n \n \n \n

\n Il momento k-esimo di una variabile aleatoria è:\n

\n

\n \n {r`\\mu_k = E ( X^k ) = \\begin{cases}\n \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n \\end{cases}`}\n \n

\n \n La media di una variabile aleatoria è anche il suo primo momento.\n \n \n \n

\n La funzione generatrice dei momenti è:\n

\n

\n {r`m_X (t) = E( e^{t \\cdot X} )`}\n

\n

\n Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n

\n

\n E' la trasformata di Laplace della variabile aleatoria di X.\n

\n \n \n

\n La funzione caratteristica è:\n

\n

\n {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n

\n

\n Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n

\n

\n E' la trasformata di Fourier della variabile aleatoria di X.\n

\n \n \n \n \n

\n Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n

\n

\n {r`X \\sim Distribuzione()`}\n

\n \n \n

\n Una prova con solo due possibili esiti: successo e insuccesso.\n

\n \n \n

\n Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n

\n \n \n \n \n

\n Una variabile aleatoria che rappresenta una prova di Bernoulli:\n

\n
    \n
  • vale 1 in caso di successo.
    • \n
  • vale 0 in caso di insuccesso.
    • \n
\n

\n Il suo simbolo è {r`Ber(p)`}\n

\n \n \n

\n La distribuzione bernoulliana ha come densità:\n

\n

\n {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n p \\quad se\\ k = 1\\\\\n q \\quad se\\ k = 0\\\\\n 0 \\quad altrimenti\n \\end{cases} = p^x \\cdot q^{1 - k}`}\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n

\n

\n Il suo simbolo è {r`Bin(n, p)`}.\n

\n \n \n

\n La binomiale ha come densità:\n

\n

\n {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n

\n \n \n

\n La funzione generatrice dei momenti della binomiale è:\n

\n

\n {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n

\n

\n La media di una binomiale è:\n

\n

\n {r`E(X) = n \\cdot p`}\n

\n

\n La varianza di una binomiale è:\n

\n

\n {r`Var(X) = n \\cdot p \\cdot q`}\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n

\n

\n Il suo simbolo è Geo(p).\n

\n \n \n

\n La geometrica ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n

\n \n \n

\n La funzione generatrice dei momenti della geometrica è:\n

\n

\n {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n

\n

\n La media della geometrica è:\n

\n

\n {r`E(X) = \\frac{1}{p}`}\n

\n

\n La varianza della geometrica è:\n

\n

\n {r`Var(X) = \\frac{q}{p^2}`}\n

\n \n \n

\n La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X = i + j | X > i ]) = P([X = j])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n

\n

\n Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n

\n \n \n

\n La binomiale negativa ha come densità:\n

\n

\n {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della binomiale negativa è:\n

\n

\n {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n

\n

\n La media della binomiale negativa è:\n

\n

\n {r`E(X) = \\frac{n}{p}`}\n

\n

\n La varianza della binomiale negativa è:\n

\n

\n {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n

\n

\n Il suo simbolo rimane {r`Geo(p)`}.\n

\n \n \n

\n La geometrica traslata ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n

\n \n \n

\n La funzione generatrice dei momenti della geometrica traslata è:\n

\n

\n {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n

\n

\n La media della geometrica traslata è:\n

\n

\n {r`E(X) = \\frac{q}{p}`}\n

\n

\n La varianza della geometrica è:\n

\n

\n {r`Var(X) = \\frac{q}{p^2}`}\n

\n \n \n

\n La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X = i + j | X > i ]) = P([X = j])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n

\n

\n Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n

\n \n \n

\n La binomiale negativa traslata ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della binomiale negativa traslata è:\n

\n

\n {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n

\n

\n La media della binomiale negativa traslata è:\n

\n

\n {r`E(X) = \\frac{n \\cdot q}{p}`}\n

\n

\n La varianza della binomiale negativa traslata è:\n

\n

\n {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n

\n

\n Il suo simbolo è Ipe(N, K, n).\n

\n \n \n

\n La ipergeometrica ha come densità:\n

\n

\n {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n

\n

\n La media della ipergeometrica è:\n

\n

\n {r`E(X) = n \\cdot \\frac{K}{N}`}\n

\n

\n La varianza della ipergeometrica è:\n

\n

\n {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n

\n
    \n
  • Binomiale: {r`X \\sim Bin(n, p)`}
    • \n
  • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
    • \n
  • La probabilità di successo tende a 0: {r`p \\to 0`}
    • \n
  • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
    • \n
\n

\n Il suo simbolo è {r`Poi(\\mu)`}\n

\n \n \n

\n La poissoniana ha come densità:\n

\n

\n {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della poissoniana è:\n

\n

\n {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n

\n

\n La media della poissoniana è:\n

\n

\n {r`E(X) = \\mu`}\n

\n

\n La varianza della poissoniana è:\n

\n

\n {r`Var(X) = \\mu`}\n

\n

\n Gli altri momenti della poissoniana sono:\n

\n
    \n
  1. {r`E(X^2) = \\mu^2 + \\mu`}
    2. \n
\n

\n \n \n \n \n

\n Una successione di arrivi avvenuti in un certo arco temporale che:\n

\n
    \n
  • non sono sovrapposti.
    • \n
  • hanno intensità {r`\\lambda`} costante.
    • \n
  • avvengono indipendentemente gli uni dagli altri.
    • \n
\n \n \n

\n Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n

\n

\n E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n

\n \n E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n \n \n \n \n \n

\n Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n

\n

\n Il suo simbolo è {r`Esp(\\lambda)`}.\n

\n \n \n

\n L'esponenziale ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad x < 0\\\\\n \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n \\end{cases}`}\n

\n

\n L'esponenziale ha come funzione di ripartizione:\n

\n

\n {r`F_X (t) = \\begin{cases}\n 0 \\qquad \\qquad t < 0\\\\\n 1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n \\end{cases}`}\n

\n \n \n

\n La funzione generatrice dei momenti dell'esponenziale è:\n

\n

\n {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n

\n

\n La media dell'esponenziale è:\n

\n

\n {r`E(X) = \\frac{1}{\\lambda}`}\n

\n

\n La varianza dell'esponenziale è:\n

\n

\n {r`Var(X) = \\frac{1}{\\lambda^2}`}\n

\n \n \n

\n L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n

\n

\n {r`P([X > s + t | X > s]) = P([X > t])`}\n

\n \n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n \n \n \n \n \n

\n Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n

\n

\n Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n

\n \n \n

\n La legge gamma ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n \\end{cases}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della legge gamma è:\n

\n

\n {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n

\n

\n La media della legge gamma è:\n

\n

\n {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n

\n

\n La varianza della legge gamma è:\n

\n

\n {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n

\n

\n Il suo simbolo è {r`Uni(a, b)`}\n

\n

\n Su di essa vale la seguente proprietà:\n

\n

\n {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n

\n \n \n

\n La distribuzione uniforme ha come densità:\n

\n

\n {r`f_X (x) = \\begin{cases}\n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 0 \\qquad \\quad altrimenti \n \\end{cases}`}\n

\n

\n La distribuzione uniforme ha come funzione di ripartizione:\n

\n

\n {r`f_X (x) = \\begin{cases}\n 0 \\qquad \\quad x < a \n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 1 \\qquad \\quad x > b\n \\end{cases}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della distribuzione uniforme è:\n

\n

\n {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n

\n

\n La media della distribuzione uniforme è:\n

\n

\n {r`E(X) = \\frac{a + b}{2}`}\n

\n

\n La varianza della distribuzione uniforme è:\n

\n

\n {r`Var(X) = \\frac{(b - a)^2}{12}`}\n

\n

\n \n \n \n \n

\n Una variabile aleatoria con una specifica distribuzione.\n

\n

\n Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n

\n \n \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n \n \n \n

\n La distribuzione normale ha come densità:\n

\n

\n {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n

\n \n \n

\n

\n La funzione generatrice dei momenti della distribuzione normale è:\n

\n

\n {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n

\n

\n La media della distribuzione normale è:\n

\n

\n {r`E(X) = \\mu`}\n

\n

\n La varianza della distribuzione normale è:\n

\n

\n {r`Var(X) = \\sigma^2`}\n

\n

\n \n \n \n \n

\n Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n

\n

\n {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n

\n \n \n

\n La distribuzione normale standard Z è:\n

\n

\n Z \\sim Nor(0, 1)\n

\n

\n La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n

\n

\n {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n

\n \n \n

\n Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n

\n

\n {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n

\n \n \n \n \n

\n La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n

\n

\n {r`Z^2 \\sim \\chi^2 (v = 1)`}\n

\n \n \n
\n \"chi-quadro a un grado di libertà\"\n
\n

\n Esiste una distribuzione Gamma particolare:\n

\n

\n {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n

\n

\n Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n

\n

\n {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n

\n \n \n

\n Un'altra funzione particolare è la funzione T di Student:\n

\n

\n {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n

\n \n \n \n \n

\n La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n

\n

\n {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n

\n \n \n

\n La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n

\n

\n {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n

\n \n \n

\n Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n

\n

\n {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n

\n \n \n

\n Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n

\n
    \n
  • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
    • \n
  • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
    • \n
  • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
    • \n
  • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
    • \n
\n \n \n \n \n

\n Un vettore composto da variabili aleatorie.\n

\n

\n Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n

\n \n \n

\n I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n

\n

\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n

\n

\n {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n

\n

\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n

\n

\n {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n

\n \n \n

\n I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n

\n

\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n

\n

\n {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n

\n

\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n

\n

\n {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n

\n \n \n \n \n

\n Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n

\n

\n {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n

\n \n \n

\n E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n

\n

\n {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n

\n \n Solitamente si calcola la media di x \\cdot y.\n \n

\n Le medie di più variabili aleatorie si possono sommare:\n

\n

\n {r`E(X + Y) = E(X) + E(Y)`}\n

\n \n \n \n \n

\n Un operatore che misura la correlazione di due variabili aleatorie.\n

\n

\n Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n

\n

\n {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n

\n

\n Ha diverse proprietà:\n

\n
    \n
  • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
    • \n
  • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
    • \n
  • E' semplificabile: {r`Cov(X, X) = Var(X)`}
    • \n
  • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
    • \n
  • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
    • \n
\n \n \n

\n Due variabili sono variabili incorrelate se:\n

\n

\n {r`Cov(X, Y) = 0`}\n

\n

\n Variabili indipendenti sono sempre incorrelate.\n

\n \n \n

\n Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n

\n

\n {r`\n \\boldsymbol{C_X} = \n \\begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n \\end{bmatrix}\n `}\n

\n

\n E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n

\n \n \n

\n Un valore che misura come due variabili aleatorie sono correlate:\n

\n

\n {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n

\n

\n E' sempre compreso tra -1 e 1:\n

\n

\n {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n

\n

\n Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n

\n

\n {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n

\n \n \n

\n La varianza di due variabili aleatorie sommate è:\n

\n

\n {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n

\n \n Si dimostra applicando le proprietà della covarianza!\n \n

\n Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n

\n

\n {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n

\n \n \n \n \n

\n Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n

\n \n Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n \n \n \n

\n Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n

\n

\n {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n

\n

\n Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n

\n \n \n

\n La media aritmetica dello scarto quadratico medio degli elementi del campione.\n

\n

\n Se è noto il valore medio {r`m = E(X)`} di X:\n

\n

\n {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n

\n

\n Altrimenti:\n

\n

\n {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n

\n \n \n \n \n

\n Se calcoliamo la media della media campionaria, risulterà vero che:\n

\n

\n {r`E(\\overline{X}_n) = E(X)`}\n

\n \n Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n \n \n \n

\n Se calcoliamo la varianza della media campionaria, risulterà vero che:\n

\n

\n {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n

\n \n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n \n \n \n

\n Se calcoliamo la media della varianza campionaria, risulterà vero che:\n

\n

\n {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n

\n \n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n \n \n \n \n \n

\n Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n

\n \n \n

\n ...allora sappiamo anche la distribuzione della media campionaria!\n

\n

\n {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n

\n \n \n

\n ...e anche della varianza campionaria!\n

\n

\n {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n

\n

\n {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n

\n \n \n

\n ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n

\n \n \n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n

\n

\n {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n

\n

\n {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a della popolazione X, allora essa converge quasi certamente.\n

\n

\n {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n

\n \n \n

\n Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n

\n

\n {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n

\n \n \n

\n {`\n \\\\begin{matrix}\n X_n \\\\xrightarrow{mq} X\\\\\\\\\n X_n \\\\xrightarrow{qc} X\n \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n }\n

\n

\n In più:\n

\n

\n {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n

\n \n \n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n

\n

\n {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n

\n

\n {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n

\n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n

\n

\n {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n

\n \n Dimostra che l'interpretazione frequentista della probabilità è valida!\n \n \n \n \n \n

\n La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n

\n

\n {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n

\n

\n Ovvero:\n

\n

\n {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n

\n \n \n \n \n

\n E' una somma di bernoulliane, e quindi si approssima a una normale:\n

\n

\n {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n

\n \n \n

\n E' una somma di geometriche, e quindi si approssima a una normale:\n

\n

\n {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n

\n \n \n

\n E' una somma di altre poissoniane, e quindi si approssima a una normale:\n

\n

\n {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n

\n \n \n

\n E' una somma di esponenziali, e quindi si approssima a una normale:\n

\n

\n {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n

\n \n \n

\n Se n è grande, allora:\n

\n

\n {r`Y = \\sum_{i=1}^{n} X_i`}\n

\n \n \n \n \n

\n Per indicare parametri sconosciuti di una legge si usa \\theta.\n

\n \n \n

\n Una variabile aleatoria funzione di un campione:\n

\n

\n {r`T(\\boldsymbol{X})`}\n

\n \n Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n \n \n \n \n \n

\n Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n

\n \n \n

\n Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n

\n

\n {r`E(T_n) = \\theta`}\n

\n \n \n

\n Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n

\n

\n {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n

\n \n \n

\n Uno stimatore è consistente in media quadratica se:\n

\n

\n {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n

\n \n \n

\n Uno stimatore è consistente in probabilità se:\n

\n

\n {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n

\n \n \n

\n Uno stimatore è asintoticamente normale se:\n

\n

\n {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n

\n \n \n \n \n

\n Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n

\n

\n Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n

\n

\n Visto che:\n

\n
    \n
  • {r`\\theta = g(E(X))`}
    • \n
  • {r`\\widehat{E(X)} = \\overline{X}_n`}
    • \n
\n

\n Allora:\n

\n

\n {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n

\n

\n Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n

\n \n \n \n \n

\n Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n

\n

\n Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n

\n

\n Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n

\n

\n {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n

\n

\n Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n

\n \n \n

\n Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n

\n
    \n
  • Sono asintoticamente corretti.
    • \n
  • Sono consistenti in probabilità.
    • \n
  • Sono asintoticamente normali.
    • \n
  • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
    • \n
\n \n \n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n

\n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n

\n \n \n

\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n

\n

\n {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n

\n \n \n

\n Per il metodo della massima verosomiglianza:\n

\n
    \n
  • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

    • \n
  • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
    • \n
\n \n \n \n \n
\n \"intervallo di confidenza al 95%\"\n
\n

\n L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n

\n

\n L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n

\n

\n {r`P( a < W < b ) = N`}\n

\n

\n Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n

\n \n \n \n \n

\n Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n

\n
    \n
  • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
    • \n
\n \n \n

\n Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n

\n
    \n
  • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
    • \n
  • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
    • \n
\n

\n {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n

\n \n \n \n \n

\n L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n

\n

\n {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n

\n \n \n \n \n

\n L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n

\n

\n {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n

\n \n \n
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contenuto in effe"'),l("p",null,"L'",l("b",null,"inclusione")," del primo insieme in un altro."),l("p",null,l(e.a,null,te(z||(z=ee`E \subseteq F`)))),l("p",null,"Se si verifica ",l(e.a,null,"E"),", allora si verifica anche ",l(e.a,null,"F"),".")),l(t.a,{title:"Evento impossibile"},l("blockquote",null,'"e è impossibile"'),l("p",null,"Un sottoinsieme ",l("b",null,"vuoto"),"."),l("p",null,l(e.a,null,te(X||(X=ee`E = \emptyset`))))),l(t.a,{title:"Mutua esclusione"},l("blockquote",null,'"e ed effe si escludono mutualmente"'),l("p",null,"La ",l("b",null,"disgiunzione")," di due insiemi."),l("p",null,l(e.a,null,te(q||(q=ee`E \cap F = \emptyset`)))))),l(o.a,null,l(t.a,{title:"Famiglia degli eventi"},l("blockquote",null,'"famiglia effe"'),l("p",null,"I sottoinsiemi dello spazio campionario formano una ",l("b",null,"famiglia")," di sottoinsiemi detta ",l("i",null,"famiglia degli eventi"),"."),l("p",null,l(e.a,null,te(E||(E=ee`\mathcal{F}`)))),l("p",null,"Qualsiasi sottoinsieme appartenente a ",l(e.a,null,te(P||(P=ee`\mathcal{F}`)))," è considerato un evento.")),l(t.a,{title:l("span",null,l(e.a,null,te(L||(L=ee`\sigma`))),"-algebra")},l("blockquote",null,'"sigma algebra"'),l("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",l("i",null,l(e.a,null,te(x||(x=ee`\sigma`))),"-algebra"),":"),l("ol",null,l("li",null,"Lo spazio campionario è un evento: ",l(e.a,null,te(k||(k=ee`\Omega \in \mathcal{F}`)))),l("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",l(e.a,null,te(F||(F=ee`E \in \mathcal{F} \implies \bar{E} \in \mathcal{F}`)))),l("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",l(e.a,null,te(S||(S=ee`(E, F) \in \mathcal{F} \implies (E \cup F, E \cap F) \in \mathcal{F}`))))),l("p",null,"Un esempio: ",l(e.a,null,te(y||(y=ee`E \in \mathcal{F} \implies \mathcal{F} = \{ \emptyset, E, \bar{E}, \Omega \}`)))))),l(o.a,null,l(t.a,{title:"Partizione"},l("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),l("p",null,"Un insieme di esiti e eventi:"),l("ul",null,l("li",null,l("b",null,"Finito"),"."),l("li",null,"In cui tutti gli eventi hanno ",l("b",null,"probabilità diversa da 0"),"."),l("li",null,"In cui tutti gli eventi sono ",l("b",null,"mutualmente esclusivi"),"."),l("li",null,"In cui l'unione di tutti i suoi elementi ",l("b",null,"copre lo spazio campionario"),".")),l("p",null,"La partizione ",l(e.a,null,te(C||(C=ee`E_i`)))," è composta dagli eventi ",l(e.a,null,te(w||(w=ee`E_1`))),", ",l(e.a,null,te(N||(N=ee`E_2`))),", ",l(e.a,null,te(V||(V=ee`E_3`))),", fino a ",l(e.a,null,te(I||(I=ee`E_n`))),"."),l(u.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),l(o.a,{title:"Assiomi della probabilità"},l(t.a,{title:"Primo assioma della probabilità"},l("p",null,"La probabilità di un evento è un numero tra 0 e 1."),l("p",null,l(e.a,null,te(U||(U=ee`\forall E \in \mathcal{F}, 0 \leq P(E) \leq 1`))))),l(t.a,{title:"Secondo assioma della probabilità"},l("p",null,"La probabilità dello spazio campionario è sempre 1."),l("p",null,l(e.a,null,te(D||(D=ee`P(\Omega) = 1`))))),l(t.a,{title:"Terzo assioma della probabilità"},l("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),l("p",null,l(e.a,null,te(Y||(Y=ee`P \left ( \bigcup_i E_i \right ) = \sum_i P ( E_i )`)))))),l(o.a,{title:"Conseguenze degli assiomi"},l(t.a,{title:"Probabilità di un evento negato"},l("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),l("p",null,l(e.a,null,te(M||(M=ee`P(\bar{E}) = 1 - P({E})`))))),l(t.a,{title:"Probabilità di un evento incluso"},l("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),l("p",null,l(e.a,null,te(A||(A=ee`F \subseteq E \implies P(F) \leq P(E)`))))),l(t.a,{title:"Unione"},l("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),l("p",null,l(e.a,null,te(B||(B=ee`P(E \cup F) = P(E) + P(F) - P(E \cap F)`)))),l(u.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),l(o.a,{title:"Spazi equiprobabili"},l(t.a,{title:"Cosa sono?"},l("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),l("p",null,l(e.a,null,te(T||(T=ee`P(E) = \frac{len(E)}{len(\Omega)}`))))),l(t.a,{title:"Spazi equiprobabili geometrici"},l("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",l("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),l(o.a,{title:"Calcolo combinatorio"},l(t.a,{title:"Disposizioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,te(H||(H=ee`\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}`))))),l(t.a,{title:"Disposizioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,te(O||(O=ee`\boldsymbol{D}^{r}_{n, k} = n^k`))))),l(t.a,{title:"Combinazioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,te(G||(G=ee`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`))))),l(t.a,{title:"Combinazioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(e.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(e.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(e.a,null,te(K||(K=ee`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`))))),l(t.a,{title:"Permutazioni"},l("p",null,"Estraggo ",l(e.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),l("p",null,l(e.a,null,te(R||(R=ee`\boldsymbol{P}_n = n!`)))))),l(o.a,{title:"Probabilità condizionata"},l(t.a,{title:"Eventi condizionati"},l("blockquote",null,'"E dato F"'),l("p",null,"La probabilità che si verifichi ",l(e.a,null,"E")," sapendo che ",l("b",null,"si è già verificato")," ",l(e.a,null,"F"),"."),l("p",null,l(e.a,null,te(j||(j=ee`P(E|F) = \frac{P(E \cap F)}{P(F)}`)))),l(u.a,null,"Ricorda vagamente le pipe di ",l("code",null,"bash"),", però al contrario...")),l(t.a,{title:"Eventi mutualmente esclusivi"},l("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),l("p",null,l(e.a,null,te(Q||(Q=ee`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`)))))),l(o.a,null,l(t.a,{title:"Regola della catena"},l("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),l("p",null,l(e.a,null,te(W||(W=ee`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`)))))),l(o.a,{title:"Le alternative"},l(t.a,{title:"Legge delle alternative"},l("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),l("p",null,l(e.a,null,te(J||(J=ee`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`))))),l(t.a,{title:"Legge condizionata delle alternative"},l("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",l("b",null,"evento"),":"),l("p",null,l(e.a,null,te(Z||(Z=ee`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`))))),l(t.a,{title:"Formula di Bayes"},l("p",null,"Tramite la ",l("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),l("p",null,l(e.a,null,te($||($=ee`P(E_h | F) = \frac{P(F | E_h) \cdot P(E_h)}{P(F)}`)))),l(u.a,null,"In pratica, invertiamo gli eventi."))),l(o.a,{title:"Eventi indipendenti"},l(t.a,{title:"Due eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a due a due"'),l("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),l("p",null,l(e.a,null,te(ll||(ll=ee`P(E \cap F) = P(E) \cdot P(F) \Longleftrightarrow P(E|F) = P(E) \Longleftrightarrow P(F|E) = P(F)`))))),l(t.a,{title:"Più eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),l("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),l("p",null,l(e.a,null,te(al||(al=ee`P(E \cap F \cap G) = P(E) \cdot P(F) \cdot P(G)`)))),l("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),l(t.a,{title:"Famiglia di eventi indipendenti"},l("p",null,"Un insieme di ",l(e.a,null,"n")," eventi è una ",l("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),l(u.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),l(o.a,{title:"Variabili aleatorie"},l(t.a,{title:"Variabile aleatoria"},l("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",l(e.a,null,te(il||(il=ee`X(\omega) : \Omega \to \mathbb{R}`))),".")),l(t.a,{title:l("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},l("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",l(e.a,null,te(nl||(nl=ee`A_t = \{ \omega | X(\omega) \leq t \}`))),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",l(e.a,null,"t"),"."),l("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),l("p",null,l(e.a,null,te(el||(el=ee`\forall t \in \mathbb{R}, A_t \in \mathcal{F}`)))),l(u.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),l(t.a,{title:"Supporto"},l("blockquote",null,'"supporto di X"'),l("p",null,"Il ",l("b",null,"codominio")," della variabile aleatoria è il suo ",l("i",null,"supporto"),"."),l("p",null,"Per indicare che un valore ",l(e.a,null,"x_0")," appartiene al supporto di ",l(e.a,null,"X"),", si usa la notazione ",l(e.a,null,"X \\mapsto x_0"),"."))),l(o.a,{title:"Densità"},l(t.a,{title:"Funzione probabilità"},l("p",null,"La ",l("i",null,"funzione probabilità")," ",l(e.a,null,te(tl||(tl=ee`p_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"discreta")," ",l(e.a,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),l("p",null,l(e.a,null,te(ol||(ol=ee`p_X (x) = \begin{cases} + P([X = x]) \quad se\ X \mapsto x \\ + 0 \qquad \qquad \quad se\ X \not\mapsto x + \end{cases}`))))),l(t.a,{title:"Funzione densità"},l("p",null,"La ",l("i",null,"funzione densità")," ",l(e.a,null,te(ul||(ul=ee`f_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"continua")," ",l(e.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),l("p",null,l(e.a,null,te(rl||(rl=ee`P([a < X \leq b]) = \int_a^b f_X (x) dx`)))),l("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",l("b",null,"non esista")," per una certa variabile aleatoria."),l(u.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),l(o.a,{title:"Funzione di ripartizione"},l(t.a,{title:"Definizione"},l("p",null,"Ogni variabile aleatoria ha una ",l("i",null,"funzione di ripartizione")," ",l(e.a,null,te(sl||(sl=ee`F_X : \mathbb{R} \to [0, 1]`)))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",l(e.a,null,"t"),":"),l("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",l(e.a,null,te(pl||(pl=ee`A_t`))),":"),l("p",null,l(e.a,null,te(dl||(dl=ee`F_X (t) = P(A_t) = \begin{cases} + \sum_{i = 0}^{t} p_X (x_i) \quad nel\ discreto\\ + \\ + \int_{-\infty}^t f_X (x) dx \quad nel\ continuo + \end{cases}`))))),l(t.a,{title:"Proprietà della funzione"},l("ul",null,l("li",null,"È sempre ",l("b",null,"monotona crescente")," (non strettamente)."),l("br",null),l("li",null,"Vale ",l("b",null,"0")," a ",l(e.a,null,"-\\infty")," e ",l("b",null,"1")," a ",l(e.a,null,"+\\infty"),"."),l("br",null),l("li",null,"È ",l("b",null,"continua da destra"),": ",l(e.a,null,te(cl||(cl=ee`\forall x_0 \in \mathbb{R}, F_X (x_0) = \lim_{t \to x^+_0} F_X (t)`)))))),l(t.a,{title:"Probabilità di un valore"},l("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),l("p",null,l(e.a,null,te(ml||(ml=ee`P([X = x_0]) = \lim_{t \to x^+_0} F_X (t) - \lim_{t \to x^-_0} F_X (t)`)))))),l(o.a,{title:"Trasformazioni di variabili aleatorie"},l(t.a,{title:"Nel discreto"},l("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),l(t.a,{title:"Nel continuo (invertibile)"},l("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),l("p",null,l(e.a,null,te(bl||(bl=ee`f_Y (y) = \int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`))))),l(t.a,{title:"Nel... digitale"},l("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",l("a",{href:"https://docs.python.org/3/library/random.html#random.random"},l("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),l(o.a,{title:"Informazioni delle variabili aleatorie"},l(t.a,{title:"Media"},l("p",null,"Ogni variabile aleatoria che ha una ",l("b",null,"funzione di ripartizione")," e un ",l("b",null,"supporto finito")," ha anche una ",l("i",null,"media")," (o ",l("i",null,"valore medio")," o ",l("i",null,"atteso"),"):"),l("p",null,l(e.a,null,te(vl||(vl=ee`E(X) = \int_0^{+infty} (1 - F_X (t)) dt - \int_{-\infty}^{0} F_X (t) dt`)))),l("p",null,"Nel discreto, si può calcolare con:"),l("p",null,l(e.a,null,te(fl||(fl=ee`E(X) = \sum_i P(X = x_i) \cdot x_i`)))),l("p",null,"Nel continuo, si può calcolare con:"),l("p",null,l(e.a,null,te(_l||(_l=ee`E(X) = \int_{-\infty}^{+\infty} f_X (x) \cdot x \cdot dx`)))))),l(o.a,null,l(t.a,{title:"Moda"},l("p",null,"Valore per cui la ",l("b",null,"funzione probabilità")," o ",l("b",null,"funzione densità")," è ",l("b",null,"massima"),".")),l(t.a,{title:"Quantili"},l("p",null,"Il ",l("i",null,"quantile")," ",l(e.a,null,te(hl||(hl=ee`x_{\alpha}`)))," di ordine ",l(e.a,null,te(gl||(gl=ee`0 \leq \alpha \leq 1`)))," della variabile aleatoria ",l(e.a,null,"X")," è il più piccolo numero tale che:"),l("p",null,l(e.a,null,te(zl||(zl=ee`P([X < x_{\alpha}]) \leq \alpha \leq P([X \leq x_{\alpha}])`)))),l("p",null),l("p",null,"Il quantile di ordine 0.5 ",l(e.a,null,te(Xl||(Xl=ee`x_{0.5}`)))," è detto ",l("i",null,"mediana"),"."),l("p",null,"I quantili di ordine 0.25 ",l(e.a,null,te(ql||(ql=ee`x_{0.25}`)))," e 0.75 ",l(e.a,null,te(El||(El=ee`x_{0.75}`)))," sono detti ",l("i",null,"quartili"),"."),l("p",null,"I quantili di ordine ",l(e.a,null,te(Pl||(Pl=ee`\frac{n}{100}`)))," sono detti ",l("i",null,l(e.a,null,"n"),"-esima percentile"),".")),l(t.a,{title:"Varianza"},l("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),l("p",null,l(e.a,null,te(Ll||(Ll=ee`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`)))))),l(o.a,{title:"Disuguaglianze notevoli"},l(t.a,{title:"Disuguaglianza di Markov"},l("p",null,"Data una variabile aleatoria non-negativa:"),l("p",null,l(e.a,null,te(xl||(xl=ee`\forall k > 0, P([X \geq k]) \leq \frac{E(X)}{k}`)))),l("p",null,"Divide in due parti (",l(e.a,null,te(kl||(kl=ee`P(X < k)`)))," e ",l(e.a,null,te(Fl||(Fl=ee`P(X \geq k)`))),") la funzione X, la cui media risulterà uguale a:"),l("p",null,l(e.a,null,te(Sl||(Sl=ee`E(X) = \overline{k} \cdot P(X < k) + k \cdot P(X \geq k)`))))),l(t.a,{title:"Disuguaglianza di Čebyšëv"},l("blockquote",null,'"disuguaglianza di cebicev"'),l("p",null,"Se la variabile aleatoria ",l(e.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",l(e.a,null,te(yl||(yl=ee`\epsilon`)))," di distanza dal valore medio è minore o uguale a ",l(e.a,null,te(Cl||(Cl=ee`\frac{Var(X)}{\epsilon^2}`))),"."),l("p",null,l(e.a,null,te(wl||(wl=ee`\forall \epsilon > 0, P([ \left| X - E(X) \right| \geq \epsilon]) \leq \frac{Var(X)}{\epsilon^2}`)))),l("p",null,"E anche:"),l("p",null,l(e.a,null,te(Nl||(Nl=ee`\forall \epsilon > 0, P([ \left| X - E(X) \right| < \epsilon]) \geq 1 - \frac{Var(X)}{\epsilon^2}`)))),l(u.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),l(o.a,{title:"Un momento...!"},l(t.a,{title:"Momento"},l("p",null,"Il ",l("i",null,"momento")," ",l(e.a,null,"k"),"-esimo di una variabile aleatoria è:"),l("p",null,l(e.a,null,te(Vl||(Vl=ee`\mu_k = E ( X^k ) = \begin{cases} + \sum_i x_i^k p_X (x_i) \qquad nel\ discreto\\ + \\ + \int_{-\infty}^{+\infty} x^k f_X (x) dx \qquad nel\ continuo + \end{cases}`)))),l(u.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),l(t.a,{title:"Funzione generatrice dei momenti"},l("p",null,"La ",l("i",null,"funzione generatrice dei momenti")," è:"),l("p",null,l(e.a,null,te(Il||(Il=ee`m_X (t) = E( e^{t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),l(t.a,{title:"Funzione caratteristica"},l("p",null,"La ",l("i",null,"funzione caratteristica")," è:"),l("p",null,l(e.a,null,te(Ul||(Ul=ee`H_X (t) = E ( e^{i \cdot t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),l(o.a,{title:"Prove e schemi"},l(t.a,{title:"Variabile con distribuzione"},l("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),l("p",null,l(e.a,null,te(Dl||(Dl=ee`X \sim Distribuzione()`))))),l(t.a,{title:"Prova di Bernoulli"},l("p",null,"Una prova con solo due possibili esiti: ",l(r.a,null,"successo")," e ",l(s.a,null,"insuccesso"),".")),l(t.a,{title:"Schema di Bernoulli"},l("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),l(o.a,{title:"Bernoulliana"},l(t.a,{title:"Distribuzione bernoulliana"},l("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),l("ul",null,l("li",null,"vale ",l(r.a,null,"1")," in caso di ",l(r.a,null,"successo"),"."),l("li",null,"vale ",l(s.a,null,"0")," in caso di ",l(s.a,null,"insuccesso"),".")),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Yl||(Yl=ee`Ber(p)`))))),l(t.a,{title:"Densità della bernoulliana"},l("p",null,"La distribuzione bernoulliana ha come densità:"),l("p",null,l(e.a,null,te(Ml||(Ml=ee`f_X (k) : \{0, 1\} = \begin{cases} + p \quad se\ k = 1\\ + q \quad se\ k = 0\\ + 0 \quad altrimenti + \end{cases} = p^x \cdot q^{1 - k}`)))))),l(o.a,{title:"Binomiale"},l(t.a,{title:"Distribuzione binomiale"},l("p",null,"Una variabile aleatoria che conta il numero di successi di ",l(e.a,null,"n")," prove di uno schema di Bernoulli."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Al||(Al=ee`Bin(n, p)`))),".")),l(t.a,{title:"Densità della binomiale"},l("p",null,"La binomiale ha come densità:"),l("p",null,l(e.a,null,te(Bl||(Bl=ee`f_X (k) : \{0..n\} = \binom{n}{k} \cdot p^k \cdot q^{n - k}`))))),l(t.a,{title:"Momenti della binomiale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale è:"),l("p",null,l(e.a,null,te(Tl||(Tl=ee`m_X (t) = (q + p \cdot e^t) ^ n`)))),l("p",null,"La ",l("b",null,"media")," di una binomiale è:"),l("p",null,l(e.a,null,te(Hl||(Hl=ee`E(X) = n \cdot p`)))),l("p",null,"La ",l("b",null,"varianza")," di una binomiale è:"),l("p",null,l(e.a,null,te(Ol||(Ol=ee`Var(X) = n \cdot p \cdot q`)))))),l(o.a,{title:"Geometrica"},l(t.a,{title:"Distribuzione geometrica"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),l("p",null,"Il suo simbolo è ",l(e.a,null,"Geo(p)"),".")),l(t.a,{title:"Densità della geometrica"},l("p",null,"La geometrica ha come densità:"),l("p",null,l(e.a,null,te(Gl||(Gl=ee`f_X (k) : \mathbb{N} = q^{k - 1} p`))))),l(t.a,{title:"Momenti della geometrica"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica è:"),l("p",null,l(e.a,null,te(Kl||(Kl=ee`m_X (t) = \frac{p \cdot e^t}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica è:"),l("p",null,l(e.a,null,te(Rl||(Rl=ee`E(X) = \frac{1}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(e.a,null,te(jl||(jl=ee`Var(X) = \frac{q}{p^2}`))))),l(t.a,{title:"Assenza di memoria della geometrica"},l("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,te(Ql||(Ql=ee`P([X = i + j | X > i ]) = P([X = j])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Binomiale negativa"},l(t.a,{title:"Distribuzione binomiale negativa"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",l(e.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Wl||(Wl=ee`\overline{Bin}(n, p)`))),".")),l(t.a,{title:"Densità della binomiale negativa"},l("p",null,"La binomiale negativa ha come densità:"),l("p",null,l(e.a,null,te(Jl||(Jl=ee`f_X (k) : \{ n .. +\infty \} \in \mathbb{N} = \binom{k - 1}{n - 1} \cdot p^n \cdot q^{k - n} `))))),l(t.a,{title:"Momenti della binomiale negativa"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),l("p",null,l(e.a,null,te(Zl||(Zl=ee`m_X (t) : \{ t < ln(\frac{1}{q}) \} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa è:"),l("p",null,l(e.a,null,te($l||($l=ee`E(X) = \frac{n}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa è:"),l("p",null,l(e.a,null,te(la||(la=ee`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(o.a,{title:"Geometrica traslata"},l(t.a,{title:"Distribuzione geometrica traslata"},l("p",null,"Una variabile aleatoria che conta il numero ",l(e.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),l("p",null,"Il suo simbolo rimane ",l(e.a,null,te(aa||(aa=ee`Geo(p)`))),".")),l(t.a,{title:"Densità della geometrica tralsata"},l("p",null,"La geometrica traslata ha come densità:"),l("p",null,l(e.a,null,te(ia||(ia=ee`f_X (k) : \mathbb{N} = p \cdot q^k `))))),l(t.a,{title:"Momenti della geometrica traslata"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),l("p",null,l(e.a,null,te(na||(na=ee`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \frac{p}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica traslata è:"),l("p",null,l(e.a,null,te(ea||(ea=ee`E(X) = \frac{q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(e.a,null,te(ta||(ta=ee`Var(X) = \frac{q}{p^2}`))))),l(t.a,{title:"Assenza di memoria della geometrica traslata"},l("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,te(oa||(oa=ee`P([X = i + j | X > i ]) = P([X = j])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Binomiale negativa traslata"},l(t.a,{title:"Distribuzione binomiale negativa traslata"},l("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",l(e.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo rimane ",l(e.a,null,te(ua||(ua=ee`\overline{Bin}(n, p)`))),".")),l(t.a,{title:"Densità della binomiale negativa traslata"},l("p",null,"La binomiale negativa traslata ha come densità:"),l("p",null,l(e.a,null,te(ra||(ra=ee`f_X (k) : \mathbb{N} = \binom{k + n - 1}{n - 1} \cdot p^n \cdot q^k `))))),l(t.a,{title:"Momenti della binomiale negativa traslata"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,te(sa||(sa=ee`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,te(pa||(pa=ee`E(X) = \frac{n \cdot q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa traslata è:"),l("p",null,l(e.a,null,te(da||(da=ee`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(o.a,{title:"Ipergeometrica"},l(t.a,{title:"Distribuzione ipergeometrica"},l("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",l(e.a,null,"K")," e di insuccessi ",l(e.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",l(e.a,null,"n")," in blocco."),l("p",null,"Il suo simbolo è ",l(e.a,null,"Ipe(N, K, n)"),".")),l(t.a,{title:"Densità della ipergeometrica"},l("p",null,"La ipergeometrica ha come densità:"),l("p",null,l(e.a,null,te(ca||(ca=ee`f_X (k) : \{0..n\} \in \mathbb{N} = \frac{\binom{K}{k} \cdot \binom{N - K}{n - k}}{\binom{N}{n}}`))))),l(t.a,{title:"Momenti della ipergeometrica"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),l("p",null,"La ",l("b",null,"media")," della ipergeometrica è:"),l("p",null,l(e.a,null,te(ma||(ma=ee`E(X) = n \cdot \frac{K}{N}`)))),l("p",null,"La ",l("b",null,"varianza")," della ipergeometrica è:"),l("p",null,l(e.a,null,te(ba||(ba=ee`Var(X) = n \cdot \frac{K}{N} \cdot \frac{N - K}{N} \cdot \frac{N - n}{N - 1}`))))))),l(o.a,{title:"Poissoniana"},l(t.a,{title:"Distribuzione poissoniana"},l("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),l("ul",null,l("li",null,"Binomiale: ",l(e.a,null,te(va||(va=ee`X \sim Bin(n, p)`)))),l("li",null,"Il numero di prove tende a infinito: ",l(e.a,null,te(fa||(fa=ee`n \to +\infty`)))),l("li",null,"La probabilità di successo tende a 0: ",l(e.a,null,te(_a||(_a=ee`p \to 0`)))),l("li",null,"La media è finita: ",l(e.a,null,te(ha||(ha=ee`E(X) = n \cdot p \to \mu \neq 0`))))),l("p",null,"Il suo simbolo è ",l(e.a,null,te(ga||(ga=ee`Poi(\mu)`))))),l(t.a,{title:"Densità della poissoniana"},l("p",null,"La poissoniana ha come densità:"),l("p",null,l(e.a,null,te(za||(za=ee`f_X (k) : \mathbb{N} = \frac{e^{-\mu} \cdot \mu^k}{k!}`))))),l(t.a,{title:"Momenti della poissoniana"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),l("p",null,l(e.a,null,te(Xa||(Xa=ee`m_X (t) = e^{\mu \cdot (e^t - 1)}`)))),l("p",null,"La ",l("b",null,"media")," della poissoniana è:"),l("p",null,l(e.a,null,te(qa||(qa=ee`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della poissoniana è:"),l("p",null,l(e.a,null,te(Ea||(Ea=ee`Var(X) = \mu`)))),l("p",null,"Gli altri momenti della poissoniana sono:"),l("ol",{start:2},l("li",null,l(e.a,null,te(Pa||(Pa=ee`E(X^2) = \mu^2 + \mu`)))))))),l(o.a,{title:"Un altro schema"},l(t.a,{title:"Schema di Poisson"},l("p",null,"Una successione di ",l("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),l("ul",null,l("li",null,"non sono sovrapposti."),l("li",null,"hanno intensità ",l(e.a,null,te(La||(La=ee`\lambda`)))," costante."),l("li",null,"avvengono indipendentemente gli uni dagli altri."))),l(t.a,{title:"Processo di Poisson"},l("p",null,"Una variabile aleatoria ",l(e.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",l(e.a,null,te(xa||(xa=ee`\lambda`)))," in un intervallo di tempo di durata ",l(e.a,null,"t"),"."),l("p",null,"E' una distribuzione poissoniana con ",l(e.a,null,te(ka||(ka=ee`\mu = t \cdot \lambda`))),": ",l(e.a,null,te(Fa||(Fa=ee`Poi(t \cdot \lambda)`)))),l(u.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),l(o.a,{title:"Esponenziale"},l(t.a,{title:"Distribuzione esponenziale"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",l(e.a,null,te(Sa||(Sa=ee`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(ya||(ya=ee`Esp(\lambda)`))),".")),l(t.a,{title:"Densità dell'esponenziale"},l("p",null,"L'esponenziale ha come ",l("b",null,"densità"),":"),l("p",null,l(e.a,null,te(Ca||(Ca=ee`f_X (x) = \begin{cases} + 0 \qquad \qquad x < 0\\ + \lambda \cdot e^{-\lambda \cdot x} \quad x > 0 + \end{cases}`)))),l("p",null,"L'esponenziale ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(e.a,null,te(wa||(wa=ee`F_X (t) = \begin{cases} + 0 \qquad \qquad t < 0\\ + 1 - e^{-\lambda \cdot t} \quad t \geq 0 + \end{cases}`))))),l(t.a,{title:"Momenti dell'esponenziale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),l("p",null,l(e.a,null,te(Na||(Na=ee`m_X (t) : \{ t | t < \lambda \} \in \mathbb{R} = \frac{\lambda}{\lambda - t}`)))),l("p",null,"La ",l("b",null,"media")," dell'esponenziale è:"),l("p",null,l(e.a,null,te(Va||(Va=ee`E(X) = \frac{1}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," dell'esponenziale è:"),l("p",null,l(e.a,null,te(Ia||(Ia=ee`Var(X) = \frac{1}{\lambda^2}`))))),l(t.a,{title:"Assenza di memoria della esponenziale"},l("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(e.a,null,te(Ua||(Ua=ee`P([X > s + t | X > s]) = P([X > t])`)))),l(u.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(o.a,{title:"Legge gamma"},l(t.a,{title:"Distribuzione gamma"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",l(e.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",l(e.a,null,te(Da||(Da=ee`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Ya||(Ya=ee`\Gamma(n, \lambda)`))),".")),l(t.a,{title:"Densità della legge gamma"},l("p",null,"La legge gamma ha come densità:"),l("p",null,l(e.a,null,te(Ma||(Ma=ee`f_X (x) = \begin{cases} + 0 \qquad \qquad \qquad \qquad \qquad x < 0\\ + \frac{1}{(n-1)!} \cdot \lambda^n \cdot x^{n-1} \cdot e^{-\lambda \cdot x} \quad k > 0 + \end{cases}`))))),l(t.a,{title:"Momenti della legge gamma"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),l("p",null,l(e.a,null,te(Aa||(Aa=ee`m_X (t) : ( t < \lambda ) \in \mathbb{R} = \left( \frac{\lambda}{\lambda - t} \right) ^\alpha`)))),l("p",null,"La ",l("b",null,"media")," della legge gamma è:"),l("p",null,l(e.a,null,te(Ba||(Ba=ee`E(X) = \frac{\alpha}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," della legge gamma è:"),l("p",null,l(e.a,null,te(Ta||(Ta=ee`Var(X) = \frac{\alpha}{\lambda^2}`))))))),l(o.a,{title:"Uniforme"},l(t.a,{title:"Distribuzione uniforme"},l("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",l(e.a,null,te(Ha||(Ha=ee`[a, b]`)))," in modo equiprobabile."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Oa||(Oa=ee`Uni(a, b)`)))),l("p",null,"Su di essa vale la seguente proprietà:"),l("p",null,l(e.a,null,te(Ga||(Ga=ee`P(X \in (c, d)) = \frac{d - c}{b - a}`))))),l(t.a,{title:"Densità della distribuzione uniforme"},l("p",null,"La distribuzione uniforme ha come ",l("b",null,"densità"),":"),l("p",null,l(e.a,null,te(Ka||(Ka=ee`f_X (x) = \begin{cases} + \frac{1}{b - a} \qquad a \leq x \leq b\\ + 0 \qquad \quad altrimenti + \end{cases}`)))),l("p",null,"La distribuzione uniforme ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(e.a,null,te(Ra||(Ra=ee`f_X (x) = \begin{cases} + 0 \qquad \quad x < a + \frac{1}{b - a} \qquad a \leq x \leq b\\ + 1 \qquad \quad x > b + \end{cases}`))))),l(t.a,{title:"Momenti della distribuzione uniforme"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,te(ja||(ja=ee`m_X (t) = \frac{e^{b \cdot t} - e^{a \cdot t}}{(b - a) \cdot t}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,te(Qa||(Qa=ee`E(X) = \frac{a + b}{2}`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione uniforme è:"),l("p",null,l(e.a,null,te(Wa||(Wa=ee`Var(X) = \frac{(b - a)^2}{12}`))))))),l(o.a,{title:"Normale o Gaussiana"},l(t.a,{title:"Distribuzione normale"},l("p",null,"Una variabile aleatoria con una specifica distribuzione."),l("p",null,"Il suo simbolo è ",l(e.a,null,te(Ja||(Ja=ee`Nor(\mu, \sigma^2)`))),"."),l(u.a,null,l(e.a,null,"\\mu")," e ",l(e.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),l(t.a,{title:"Densità della distribuzione normale"},l("p",null,"La distribuzione normale ha come densità:"),l("p",null,l(e.a,null,te(Za||(Za=ee`f_X (x) = \frac{e^{-\frac{(x - \mu)^2}{2 \sigma^2}}}{\sqrt{2 \pi \cdot \sigma^2}}`))))),l(t.a,{title:"Momenti della distribuzione normale"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),l("p",null,l(e.a,null,te($a||($a=ee`m_X (t) = e^{\mu \cdot t + \frac{\sigma^2 \cdot t^2}{2}}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione normale è:"),l("p",null,l(e.a,null,te(li||(li=ee`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione normale è:"),l("p",null,l(e.a,null,te(ai||(ai=ee`Var(X) = \sigma^2`))))))),l(o.a,null,l(t.a,{title:"Trasformazione della normale"},l("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),l("p",null,l(e.a,null,te(ii||(ii=ee`X \sim Nor(m, v^2) \implies \alpha X + \beta \sim Nor(\alpha m + \beta, (\alpha v)^2)`))))),l(t.a,{title:"Normale standard"},l("p",null,"La distribuzione normale standard ",l(e.a,null,"Z")," è:"),l("p",null,l(e.a,null,"Z \\sim Nor(0, 1)")),l("p",null,"La sua funzione di ripartizione è detta ",l(e.a,null,te(ni||(ni=ee`\phi(z)`)))," e vale:"),l("p",null,l(e.a,null,te(ei||(ei=ee`F_Z(z) = \phi(z) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{z} e^{-\frac{x^2}{2}} dx`))))),l(t.a,{title:"Quantili normali"},l("p",null,"Da un quantile ",l(e.a,null,te(ti||(ti=ee`z_\alpha`)))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),l("p",null,l(e.a,null,te(oi||(oi=ee`x_\alpha = \mu + z_\alpha \cdot \sqrt{\sigma^2}`)))))),l(o.a,null,l(t.a,{title:"Gamma e normale"},l("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),l("p",null,l(e.a,null,te(ui||(ui=ee`Z^2 \sim \chi^2 (v = 1)`))))),l(t.a,{title:"La funzione Chi"},l("blockquote",null,'"chi-quadro a un grado di libertà"'),l("p",null,"Esiste una distribuzione Gamma particolare:"),l("p",null,l(e.a,null,te(ri||(ri=ee`\Gamma \left( \frac{1}{2}, \frac{1}{2} \right) = \chi^2 (v = 1)`)))),l("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),l("p",null,l(e.a,null,te(si||(si=ee`\chi^2 (n) + \chi^2 (m) = \chi^2 (n + m)`))))),l(t.a,{title:"T di Student"},l("p",null,"Un'altra funzione particolare è la funzione T di Student:"),l("p",null,l(e.a,null,te(pi||(pi=ee`T(v) = \frac{Nor(0, 1)}{\sqrt{\frac{\chi^2(v)}{v}}}`)))))),l(o.a,{title:"Approssimazioni notevoli"},l(t.a,{title:"Ipergeometrica e binomiale"},l("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",l(e.a,null,"N")," rispetto a ",l(e.a,null,"n"),", si può dire che:"),l("p",null,l(e.a,null,te(di||(di=ee`Ipe(N, K, n) \approx Bin(n, \frac{K}{N})`))))),l(t.a,{title:"Binomiale e poissoniana"},l("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",l(e.a,null,"n")," è grande e ",l(e.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),l("p",null,l(e.a,null,te(ci||(ci=ee`Bin(n, p) \approx Poi(n \cdot p)`))))),l(t.a,{title:"Binomiale e normale"},l("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",l(e.a,null,"n")," grande e ",l(e.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),l("p",null,l(e.a,null,te(mi||(mi=ee`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(t.a,{title:"Correzione di Yates"},l("p",null,"Passando da una variabile discreta ",l(e.a,null,"X")," a una continua ",l(e.a,null,"Y"),", per ogni valore discreto ",l(e.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',l(e.a,null,te(bi||(bi=ee`(k - \frac{1}{2}, k + \frac{1}{2})`))),":"),l("ul",null,l("li",null,l(e.a,null,te(vi||(vi=ee`P(X < k) \simeq P(Y \leq k - \frac{1}{2})`)))),l("li",null,l(e.a,null,te(fi||(fi=ee`P(X \leq k) \simeq P(Y \leq k + \frac{1}{2})`)))),l("li",null,l(e.a,null,te(_i||(_i=ee`P(X \geq k) \simeq P(Y \geq k - \frac{1}{2})`)))),l("li",null,l(e.a,null,te(hi||(hi=ee`P(X > k) \simeq P(Y \geq k + \frac{1}{2})`))))))),l(o.a,{title:"Vettori aleatori"},l(t.a,{title:"Vettore aleatorio"},l("p",null,"Un vettore ",l("b",null,"composto da variabili aleatorie"),"."),l("p",null,"Il suo simbolo generalmente è ",l(e.a,null,te(gi||(gi=ee`\boldsymbol{X}`)))," oppure ",l(e.a,null,te(zi||(zi=ee`X, Y`))),".")),l(t.a,{title:"Funzioni di ripartizione"},l("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione congiunta"),":"),l("p",null,l(e.a,null,te(Xi||(Xi=ee`F_{X, Y} (x, y) = P(X \leq x, Y \leq y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione marginale"),":"),l("p",null,l(e.a,null,te(qi||(qi=ee`F_X (x) = P(X \leq x) = \lim_{y \to +\infty} F_{X, Y} (x, y)`))))),l(t.a,{title:"Densità discreta"},l("p",null,"I vettori aleatori ",l("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità congiunta"),":"),l("p",null,l(e.a,null,te(Ei||(Ei=ee`p_{X, Y} (x, y) = P(X = x, Y = y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità marginale"),":"),l("p",null,l(e.a,null,te(Pi||(Pi=ee`p_X (x) = \sum_j p_{X, Y} (x_i, y_j)`)))))),l(o.a,{title:"Più variabili aleatorie"},l(t.a,{title:"Indipendenza delle variabili aleatorie"},l("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",l(e.a,null,"A_i"),":"),l("p",null,l(e.a,null,te(Li||(Li=ee`P(X_1 \in A_1, \dots, X_n \in A_n) = P(X_1 \in A_1) \times \dots \times P(X_n \in A_n)`))))),l(t.a,{title:"Media dei vettori aleatori"},l("p",null,"E' possibile calcolare la media di qualsiasi funzione ",l(e.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),l("p",null,l(e.a,null,te(xi||(xi=ee`E(g(X, Y)) = \sum_{i, j} g(x_i, y_i) \cdot p_{X, Y} (x_i, y_i)`)))),l(u.a,null,"Solitamente si calcola la media di ",l(e.a,null,"x \\cdot y"),"."),l("p",null,"Le medie di più variabili aleatorie si possono sommare:"),l("p",null,l(e.a,null,te(ki||(ki=ee`E(X + Y) = E(X) + E(Y)`)))))),l(o.a,null,l(t.a,{title:"Covarianza"},l("p",null,"Un ",l("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),l("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),l("p",null,l(e.a,null,te(Fi||(Fi=ee`Cov(X, Y) = E((X - E(X) \cdot (Y - E(Y)) = E(XY) - E(X) \cdot E(Y)`)))),l("p",null,"Ha diverse proprietà:"),l("ul",null,l("li",null,"Il suo ",l("b",null,"valore nullo")," è 0: ",l(e.a,null,te(Si||(Si=ee`Cov(X, \alpha) = 0`)))),l("li",null,"E' ",l("b",null,"commutativa"),": ",l(e.a,null,te(yi||(yi=ee`Cov(X, Y) = Cov(Y, X)`)))),l("li",null,"E' ",l("b",null,"semplificabile"),": ",l(e.a,null,te(Ci||(Ci=ee`Cov(X, X) = Var(X)`)))),l("li",null,"E' ",l("b",null,"lineare"),": ",l(e.a,null,te(wi||(wi=ee`Cov(\alpha X, \beta Y) = \alpha \cdot \beta \cdot Cov(X, Y)`)))),l("li",null,"E' ",l("b",null,"distributiva"),": ",l(e.a,null,te(Ni||(Ni=ee`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`)))))),l(t.a,{title:"Variabili incorrelate"},l("p",null,"Due variabili sono ",l("i",null,"variabili incorrelate")," se:"),l("p",null,l(e.a,null,te(Vi||(Vi=ee`Cov(X, Y) = 0`)))),l("p",null,"Variabili indipendenti sono sempre incorrelate.")),l(t.a,{title:"Matrice di covarianza"},l("p",null,"Una matrice ",l(e.a,null,te(Ii||(Ii=ee`\boldsymbol{C_X}`)))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",l(e.a,null,te(Ui||(Ui=ee`\boldsymbol{X}`))),":"),l("p",null,l(e.a,null,te(Di||(Di=ee` + \boldsymbol{C_X} = + \begin{bmatrix} + Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\ + Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\ + Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3) + \end{bmatrix} + `)))),l("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",l(e.a,null,"\\geq 0"),".")),l(t.a,{title:"Coefficiente di correlazione"},l("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),l("p",null,l(e.a,null,te(Yi||(Yi=ee`\rho_{X, Y} = \frac{Cov(X, Y)}{\sqrt{Var(X)} \cdot \sqrt{Var(Y)}}`)))),l("p",null,"E' sempre compreso tra -1 e 1:"),l("p",null,l(e.a,null,te(Mi||(Mi=ee`-1 \leq \rho_{X, Y} \leq 1`)))),l("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),l("p",null,l(e.a,null,te(Ai||(Ai=ee`Y = a X + b \Longleftrightarrow | \rho_{X, Y} | = 1`))))),l(t.a,{title:"Varianza di variabili aleatorie sommate"},l("p",null,"La varianza di due variabili aleatorie sommate è:"),l("p",null,l(e.a,null,te(Bi||(Bi=ee`Var(X + Y) = Var(X) + Var(Y) + 2 \cdot Cov(X, Y)`)))),l(u.a,null,"Si dimostra applicando le proprietà della covarianza!"),l("p",null,"Se più variabili aleatorie ",l(e.a,null,"X_i")," sono ",l("b",null,"indipendenti")," (",l(e.a,null,te(Ti||(Ti=ee`Cov(X, Y) = 0`))),"), allora:"),l("p",null,l(e.a,null,te(Hi||(Hi=ee`Var \left( \sum_i X_i \right) = \sum_i Var(X_i)`)))))),l(o.a,{title:"Campioni"},l(t.a,{title:"Campione casuale"},l("p",null,"Una ",l("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",l(e.a,null,"X"),' ("popolazione") ma ',l("b",null,"indipendenti")," tra loro."),l(u.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",l("b",null,"realizzeranno")," nel loro valore.")),l(t.a,{title:"Momento campionario"},l("p",null,"Il valore dato dalla media aritmetica degli ",l(e.a,null,"n")," elementi del campione elevati alla potenza ",l(e.a,null,"k"),":"),l("p",null,l(e.a,null,te(Oi||(Oi=ee`M^{(k)}_n = \frac{1}{n} \cdot \sum_{i = 1}^n X_i^k `)))),l("p",null,"Il momento campionario di primo ordine è la ",l("i",null,"media campionaria")," ",l(e.a,null,te(Gi||(Gi=ee`\overline{X}_n`))),".")),l(t.a,{title:"Varianza campionaria"},l("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),l("p",null,"Se è noto il valore medio ",l(e.a,null,te(Ki||(Ki=ee`m = E(X)`)))," di X:"),l("p",null,l(e.a,null,te(Ri||(Ri=ee`S_0^2 = \frac{1}{n} \cdot \sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \cdot m \cdot \overline{X}_n + m^2`)))),l("p",null,"Altrimenti:"),l("p",null,l(e.a,null,te(ji||(ji=ee`S_n^2 = \frac{1}{n - 1} \cdot \sum_{i = 1}^n (X_i - \overline{X}_n)^2 = \frac{1}{n - 1} \cdot ( n \cdot M_2^{(2)} - n \cdot \overline{X}_n^2)`)))))),l(o.a,{title:"Media-ception"},l(t.a,{title:"Media campionaria"},l("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),l("p",null,l(e.a,null,te(Qi||(Qi=ee`E(\overline{X}_n) = E(X)`)))),l(u.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),l(t.a,{title:"Varianza campionaria"},l("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),l("p",null,l(e.a,null,te(Wi||(Wi=ee`Var(\overline{X}_n) = \frac{Var(X)}{n}`)))),l(u.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),l(t.a,{title:"Correzione campionaria"},l("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),l("p",null,l(e.a,null,te(Ji||(Ji=ee`E(S_0^2) = E(S_n^2) = Var(X)`)))),l(u.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),l(o.a,{title:"Campionamento di una distribuzione normale"},l(t.a,{title:"Campionamento di una distribuzione normale"},l("p",null,"Se la popolazione ",l(e.a,null,"X")," ha una distribuzione normale (",l(e.a,null,te(Zi||(Zi=ee`X \sim Nor(\mu, \sigma^2)`))),")...")),l(t.a,{title:"Distribuzione della media campionaria"},l("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),l("p",null,l(e.a,null,te($i||($i=ee`\overline{X}_n \sim Nor \left( \mu, \frac{\sigma^2}{n} \right)`))))),l(t.a,{title:"Distribuzione della varianza campionaria"},l("p",null,"...e anche della varianza campionaria!"),l("p",null,l(e.a,null,te(ln||(ln=ee`S_0^2 \sim \frac{\sigma^2}{n} \cdot \chi^2 (n)`)))),l("p",null,l(e.a,null,te(an||(an=ee`S_n^2 \sim \frac{\sigma^2}{n - 1} \cdot \chi^2 (n-1)`))))),l(t.a,{title:"Indipendenza"},l("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),l(o.a,{title:"Quando i campioni hanno dimensioni infinite"},l(t.a,{title:"Convergenza in distribuzione"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa funzione di ripartizione")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge in distribuzione"),"."),l("p",null,l(e.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),l(t.a,{title:"Convergenza in probabilità"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge in probabilità"),"."),l("p",null,l(e.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),l(t.a,{title:"Convergenza quasi certa"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità a ")," della popolazione ",l(e.a,null,"X"),", allora essa ",l("i",null,"converge quasi certamente"),"."),l("p",null,l(e.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),l(t.a,{title:"Convergenza in media quadratica"},l("p",null,"Se la successione di variabili aleatorie ",l(e.a,null,"X_n")," all'infinito ha la ",l("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",l(e.a,null,"X")," ",l("b",null,"uguale a 0"),", allora essa ",l("i",null,"converge in media quadratica"),"."),l("p",null,l(e.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),l(t.a,{title:"Gerarchia delle convergenze"},l("p",null,l(e.a,null,"\n \\begin{matrix}\n X_n \\xrightarrow{mq} X\\\\\n X_n \\xrightarrow{qc} X\n \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),l("p",null,"In più:"),l("p",null,l(e.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),l(o.a,{title:"I grandi numeri"},l(t.a,{title:"Legge debole dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,te(nn||(nn=ee`\overline{X}_n`)))," ",l("b",null,"converge in probabilità")," alla media della popolazione ",l(e.a,null,te(en||(en=ee`E(X)`))),", se essa esiste."),l("p",null,l(e.a,null,"\\overline{X}_n \\xrightarrow{p} X")),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,te(tn||(tn=ee`\forall \epsilon > 0, \lim_{n \to +\infty} P( | \overline{X}_n - E(X) | < \epsilon) = 1`)))),l("p",null,l(e.a,null,te(on||(on=ee`P( | \overline{X}_n - E(X) | < \epsilon) \to 1`))))),l(t.a,{title:"Legge forte dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,te(un||(un=ee`\overline{X}_n`)))," ",l("b",null,"converge quasi certamente")," alla media della popolazione ",l(e.a,null,te(rn||(rn=ee`E(X)`))),", se essa esiste."),l("p",null,l(e.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,te(sn||(sn=ee`\forall \epsilon > 0, P \left( \lim_{n \to +\infty} | \overline{X}_n - E(X) | < \epsilon \right) = 1`)))),l(u.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),l(o.a,{title:"Al limite"},l(t.a,{title:"Teorema centrale del limite"},l("p",null,"La successione delle medie campionarie ",l(e.a,null,te(pn||(pn=ee`\overline{X}_n`)))," ",l("b",null,"converge in distribuzione")," a ",l(e.a,null,te(dn||(dn=ee`Nor(0, 1) = \Phi()`))),"."),l("p",null,l(e.a,null,te(cn||(cn=ee`\overline{X}_n \approx Nor \left(E(X), \frac{Var(X)}{n} \right)`)))),l("p",null,"Ovvero:"),l("p",null,l(e.a,null,te(mn||(mn=ee`\forall x \in \mathbb{R}, \lim_{n \to +\infty} P \left( \frac{\overline{X}_n - E(X)}{\sqrt{\frac{Var(X)}{n}}} \leq x \right) = \Phi(x)`)))))),l(o.a,{title:"Altre approsimazioni"},l(t.a,{title:"Binomiale e normale"},l("p",null,"E' una somma di ",l("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,te(bn||(bn=ee`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(t.a,{title:"Binomiale negativa e normale"},l("p",null,"E' una somma di ",l("b",null,"geometriche"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,te(vn||(vn=ee`\overline{Bin} (n, p) \approx Nor \left( \frac{n}{p}, \frac{n \cdot (1 - p)}{p^2} \right)`))))),l(t.a,{title:"Poissoniana e normale"},l("p",null,"E' una somma di altre ",l("b",null,"poissoniane"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,te(fn||(fn=ee`Poi(\lambda) \approx Nor(\lambda, \lambda)`))))),l(t.a,{title:"Gamma e normale"},l("p",null,"E' una somma di ",l("b",null,"esponenziali"),", e quindi si approssima a una normale:"),l("p",null,l(e.a,null,te(_n||(_n=ee`\Gamma (\alpha, \lambda) \approx Nor \left( \frac{\alpha}{\lambda}, \frac{\alpha}{\lambda^2} \right)`))))),l(t.a,{title:"In generale"},l("p",null,"Se ",l(e.a,null,"n")," è grande, allora:"),l("p",null,l(e.a,null,te(hn||(hn=ee`Y = \sum_{i=1}^{n} X_i`)))))),l(o.a,{title:"Actually statistica"},l(t.a,{title:"Parametri sconosciuti"},l("p",null,"Per indicare parametri sconosciuti di una legge si usa ",l(e.a,null,"\\theta"),".")),l(t.a,{title:"Statistica"},l("p",null,"Una variabile aleatoria funzione di un campione:"),l("p",null,l(e.a,null,te(gn||(gn=ee`T(\boldsymbol{X})`)))),l(u.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",l(e.a,null,te(zn||(zn=ee`T(\boldsymbol{X}) = \boldsymbol{X}`))),"."))),l(o.a,{title:"Stimatori"},l(t.a,{title:"Stimatore"},l("p",null,"Una statistica ",l(e.a,null,"T_n")," ottenuta da ",l(e.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),l(t.a,{title:"Corretto"},l("p",null,"Uno stimatore è ",l("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(e.a,null,te(Xn||(Xn=ee`E(T_n) = \theta`))))),l(t.a,{title:"Asintoticamente corretto"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(e.a,null,te(qn||(qn=ee`\lim_{n \to +\infty} E(T_n) = \theta`))))),l(t.a,{title:"Consistente in media quadratica"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in media quadratica")," se:"),l("p",null,l(e.a,null,te(En||(En=ee`\lim_{n \to +\infty} E((T_n - \theta)^2) = 0`))))),l(t.a,{title:"Consistente in probabilità"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in probabilità")," se:"),l("p",null,l(e.a,null,te(Pn||(Pn=ee`\forall \epsilon > 0, \lim_{n \to +\infty} P( |T_n - \theta| < \epsilon) = 1`))))),l(t.a,{title:"Asintoticamente normale"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente normale")," se:"),l("p",null,l(e.a,null,te(Ln||(Ln=ee`\lim_{n \to +\infty} \frac{T_n - E(T_n)}{\sqrt{Var(T_n)}} \sim Nor(0, 1)`)))))),l(o.a,{title:"Metodo dei momenti"},l(t.a,{title:"Metodo dei momenti"},l("p",null,"Si può usare il ",l("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",l(e.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(e.a,null,te(xn||(xn=ee`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(e.a,null,"M")," a ",l(e.a,null,"\\theta"),": ",l(e.a,null,te(kn||(kn=ee`\widehat{\theta}_M`)))),l("p",null,"Visto che:"),l("ul",null,l("li",null,l(e.a,null,te(Fn||(Fn=ee`\theta = g(E(X))`)))),l("li",null,l(e.a,null,te(Sn||(Sn=ee`\widehat{E(X)} = \overline{X}_n`))))),l("p",null,"Allora:"),l("p",null,l(e.a,null,te(yn||(yn=ee`\widehat{\theta}_M = g( \overline{X}_n )`)))),l("p",null,"Se ",l(e.a,null,te(Cn||(Cn=ee`\theta`)))," non è esprimibile in termini di ",l(e.a,null,te(wn||(wn=ee`E(X)`))),", si possono usare i momenti successivi ",l(e.a,null,te(Nn||(Nn=ee`M_n^2`))),", ",l(e.a,null,te(Vn||(Vn=ee`M_n^3`))),", ",l(e.a,null,te(In||(In=ee`M_n^3`))),"..."))),l(o.a,{title:"Metodo della massima verosomiglianza"},l(t.a,{title:"Metodo della massima verosomiglianza"},l("p",null,"Si può usare il ",l("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",l(e.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(e.a,null,te(Un||(Un=ee`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(e.a,null,"L")," a ",l(e.a,null,"\\theta"),": ",l(e.a,null,te(Dn||(Dn=ee`\widehat{\theta}_L`)))),l("p",null,"Consiste nel trovare il massimo assoluto ",l(e.a,null,te(Yn||(Yn=ee`\widehat{\theta}_L`)))," della la funzione di verosomiglianza ",l(e.a,null,te(Mn||(Mn=ee`L`))),":"),l("p",null,l(e.a,null,te(An||(An=ee`L(x_1, ..., x_n; \theta) = \prod_{i=1}^n f_X(x_i; \theta)`)))),l("p",null,"Gli stimatori di massima verosomiglianza sono ",l("b",null,"asintoticamente corretti"),", ",l("b",null,"consistenti in probabilità")," e ",l("b",null,"asintoticamente normali"),".")),l(t.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},l("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),l("ul",null,l("li",null,"Sono ",l("b",null,"asintoticamente corretti"),"."),l("li",null,"Sono ",l("b",null,"consistenti in probabilità"),"."),l("li",null,"Sono ",l("b",null,"asintoticamente normali"),"."),l("li",null,"Sono ",l("b",null,"invarianti"),": ",l(e.a,null,te(Bn||(Bn=ee`\widehat{g(\theta)}_L = g(\widehat{\theta}_L)`))))))),l(o.a,{title:"Nuove stime notevoli"},l(t.a,{title:"Stima di una bernoulliana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(e.a,null,te(Tn||(Tn=ee`\widehat{p}_M = \widehat{p}_L = \overline{X}_n`))))),l(t.a,{title:"Stima di una poissoniana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(e.a,null,te(Hn||(Hn=ee`\widehat{\mu}_M = \widehat{\mu}_L = \overline{X}_n`))))),l(t.a,{title:"Stima di una esponenziale"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(e.a,null,te(On||(On=ee`\widehat{\lambda}_M = \widehat{\lambda}_L = \frac{1}{\overline{X}_n}`))))),l(t.a,{title:"Stima di una normale"},l("p",null,"Per il metodo della massima verosomiglianza:"),l("ul",null,l("li",null,l(e.a,null,te(Gn||(Gn=ee`\widehat{\mu}_L = \overline{X}_n`)))),l("br",null),l("li",null,l(e.a,null,te(Kn||(Kn=ee`\widehat{\sigma^2}_L = \frac{\sum (X_i - \overline{X}_n)^2 }{n}`))))))),l(o.a,{title:"Intervalli di confidenza"},l(t.a,{title:"Confidenza"},l("blockquote",null,'"intervallo di confidenza al 95%"'),l("p",null,"L'intervallo di valori di ",l(e.a,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),l("p",null,"L'intervallo di confidenza a N della stima ",l(e.a,null,te(Rn||(Rn=ee`\widehat{W}`)))," è l'intervallo ",l(e.a,null,"]a, b[")," tale che:"),l("p",null,l(e.a,null,te(jn||(jn=ee`P( a < W < b ) = N`)))),l("p",null,"Può anche essere ",l("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),l(o.a,{title:"Confidenza nella media di una normale"},l(t.a,{title:"Varianza nota"},l("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(e.a,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(e.a,null,te(Qn||(Qn=ee`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(e.a,null,te(Wn||(Wn=ee`\mu \in \left( -\infty, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(e.a,null,te(Jn||(Jn=ee`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, +\infty \right)`)))))),l(t.a,{title:"Varianza incognita"},l("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(e.a,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(e.a,null,te(Zn||(Zn=ee`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(e.a,null,te($n||($n=ee`\mu \in \left( -\infty, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(e.a,null,te(le||(le=ee`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, +\infty \right)`))))),l("p",null,l(e.a,null,te(ae||(ae=ee`t_{\alpha, v}`)))," è un quantile della distribuzione di Student di parametro ",l(e.a,null,"v"),"."))),l(o.a,{title:"Confidenza per la proporzione di una bernoulliana"},l(t.a,{title:"Terzo metodo corretto"},l("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),l("p",null,l(e.a,null,te(ie||(ie=ee`p \in \left[ \overline{p} - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}}, \overline{p} + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}} \right]`)))))),l(o.a,{title:"Confidenza per la media di qualsiasi popolazione"},l(t.a,{title:"Approssimando con la normale"},l("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),l("p",null,l(e.a,null,te(ne||(ne=ee`m \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}} \right]`))))))))}}}.call(this,i("hosL").h)},wQ73:function(l,a,i){"use strict";var n=i("hosL");a.a=Object(n.createContext)(!0)}}]); +//# sourceMappingURL=route-statistica.chunk.8a057.esm.js.map \ No newline at end of file diff --git a/docs/route-statistica.chunk.34cdf.esm.js.map b/docs/route-statistica.chunk.8a057.esm.js.map similarity index 57% rename from docs/route-statistica.chunk.34cdf.esm.js.map rename to docs/route-statistica.chunk.8a057.esm.js.map index f9f8b78..0c28532 100644 --- a/docs/route-statistica.chunk.34cdf.esm.js.map +++ b/docs/route-statistica.chunk.8a057.esm.js.map @@ -1 +1 @@ -{"version":3,"sources":[],"names":[],"mappings":"","file":"route-statistica.chunk.34cdf.esm.js","sourceRoot":""} \ No newline at end of file +{"version":3,"sources":[],"names":[],"mappings":"","file":"route-statistica.chunk.8a057.esm.js","sourceRoot":""} \ No newline at end of file diff --git a/docs/route-vldigeometria.chunk.1a7b6.esm.js.map b/docs/route-vldigeometria.chunk.1a7b6.esm.js.map deleted file mode 100644 index 80393b4..0000000 --- a/docs/route-vldigeometria.chunk.1a7b6.esm.js.map +++ /dev/null @@ -1 +0,0 @@ -{"version":3,"sources":[],"names":[],"mappings":"","file":"route-vldigeometria.chunk.1a7b6.esm.js","sourceRoot":""} \ No newline at end of file diff --git a/docs/route-vldigeometria.chunk.4b46b.js b/docs/route-vldigeometria.chunk.4b46b.js deleted file mode 100644 index df6c1fe..0000000 --- a/docs/route-vldigeometria.chunk.4b46b.js +++ /dev/null @@ -1,3 +0,0 @@ -/*! 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",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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\n

Videolezioni di Geometria

\n \n {r`\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n `}\n \n\t\t\t
\n\t\t);\n\t}\n}\n\n","/**\n * Created by Tivie on 13-07-2015.\n */\n\nfunction getDefaultOpts (simple) {\n 'use strict';\n\n var defaultOptions = {\n omitExtraWLInCodeBlocks: {\n defaultValue: false,\n describe: 'Omit the default extra whiteline added to code blocks',\n type: 'boolean'\n },\n noHeaderId: {\n defaultValue: false,\n describe: 'Turn on/off generated header id',\n type: 'boolean'\n },\n prefixHeaderId: {\n defaultValue: false,\n describe: 'Add a prefix to the generated header ids. Passing a string will prefix that string to the header id. Setting to true will add a generic \\'section-\\' prefix',\n type: 'string'\n },\n rawPrefixHeaderId: {\n defaultValue: false,\n describe: 'Setting this option to true will prevent showdown from modifying the prefix. This might result in malformed IDs (if, for instance, the \" char is used in the prefix)',\n type: 'boolean'\n },\n ghCompatibleHeaderId: {\n defaultValue: false,\n describe: 'Generate header ids compatible with github style (spaces are replaced with dashes, a bunch of non alphanumeric chars are removed)',\n type: 'boolean'\n },\n rawHeaderId: {\n defaultValue: false,\n describe: 'Remove only spaces, \\' and \" from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids',\n type: 'boolean'\n },\n headerLevelStart: {\n defaultValue: false,\n describe: 'The header blocks level start',\n type: 'integer'\n },\n parseImgDimensions: {\n defaultValue: false,\n describe: 'Turn on/off image dimension parsing',\n type: 'boolean'\n },\n simplifiedAutoLink: {\n defaultValue: false,\n describe: 'Turn on/off GFM autolink style',\n type: 'boolean'\n },\n excludeTrailingPunctuationFromURLs: {\n defaultValue: false,\n describe: 'Excludes trailing punctuation from links generated with autoLinking',\n type: 'boolean'\n },\n literalMidWordUnderscores: {\n defaultValue: false,\n describe: 'Parse midword underscores as literal underscores',\n type: 'boolean'\n },\n literalMidWordAsterisks: {\n defaultValue: false,\n describe: 'Parse midword asterisks as literal asterisks',\n type: 'boolean'\n },\n strikethrough: {\n defaultValue: false,\n describe: 'Turn on/off strikethrough support',\n type: 'boolean'\n },\n tables: {\n defaultValue: false,\n describe: 'Turn on/off tables support',\n type: 'boolean'\n },\n tablesHeaderId: {\n defaultValue: false,\n describe: 'Add an id to table headers',\n type: 'boolean'\n },\n ghCodeBlocks: {\n defaultValue: true,\n describe: 'Turn on/off GFM fenced code blocks support',\n type: 'boolean'\n },\n tasklists: {\n defaultValue: false,\n describe: 'Turn on/off GFM tasklist support',\n type: 'boolean'\n },\n smoothLivePreview: {\n defaultValue: false,\n describe: 'Prevents weird effects in live previews due to incomplete input',\n type: 'boolean'\n },\n smartIndentationFix: {\n defaultValue: false,\n description: 'Tries to smartly fix indentation in es6 strings',\n type: 'boolean'\n },\n disableForced4SpacesIndentedSublists: {\n defaultValue: false,\n description: 'Disables the requirement of indenting nested sublists by 4 spaces',\n type: 'boolean'\n },\n simpleLineBreaks: {\n defaultValue: false,\n description: 'Parses simple line breaks as
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foo\\
',\n type: 'boolean'\n },\n emoji: {\n defaultValue: false,\n description: 'Enable emoji support. Ex: `this is a :smile: emoji`',\n type: 'boolean'\n },\n underline: {\n defaultValue: false,\n description: 'Enable support for underline. Syntax is double or triple underscores: `__underline word__`. With this option enabled, underscores no longer parses into `` and ``',\n type: 'boolean'\n },\n completeHTMLDocument: {\n defaultValue: false,\n description: 'Outputs a complete html document, including ``, `` and `` tags',\n type: 'boolean'\n },\n metadata: {\n defaultValue: false,\n description: 'Enable support for document metadata (defined at the top of the document between `«««` and `»»»` or between `---` and `---`).',\n type: 'boolean'\n },\n splitAdjacentBlockquotes: {\n defaultValue: false,\n description: 'Split adjacent blockquote blocks',\n type: 'boolean'\n }\n };\n if (simple === false) {\n return JSON.parse(JSON.stringify(defaultOptions));\n }\n var ret = {};\n for (var opt in defaultOptions) {\n if (defaultOptions.hasOwnProperty(opt)) {\n ret[opt] = defaultOptions[opt].defaultValue;\n }\n }\n return ret;\n}\n\nfunction allOptionsOn () {\n 'use strict';\n var options = getDefaultOpts(true),\n ret = {};\n for (var opt in options) {\n if (options.hasOwnProperty(opt)) {\n ret[opt] = true;\n }\n }\n return ret;\n}\n","/**\n * Created by Tivie on 06-01-2015.\n */\n\n// Private properties\nvar showdown = {},\n parsers = {},\n extensions = {},\n globalOptions = getDefaultOpts(true),\n setFlavor = 'vanilla',\n flavor = {\n github: {\n omitExtraWLInCodeBlocks: true,\n simplifiedAutoLink: true,\n excludeTrailingPunctuationFromURLs: true,\n literalMidWordUnderscores: true,\n strikethrough: true,\n tables: true,\n tablesHeaderId: true,\n ghCodeBlocks: true,\n tasklists: true,\n disableForced4SpacesIndentedSublists: true,\n simpleLineBreaks: true,\n requireSpaceBeforeHeadingText: true,\n ghCompatibleHeaderId: true,\n ghMentions: true,\n backslashEscapesHTMLTags: true,\n emoji: true,\n splitAdjacentBlockquotes: true\n },\n original: {\n noHeaderId: true,\n ghCodeBlocks: false\n },\n ghost: {\n omitExtraWLInCodeBlocks: true,\n parseImgDimensions: true,\n simplifiedAutoLink: true,\n excludeTrailingPunctuationFromURLs: true,\n literalMidWordUnderscores: true,\n strikethrough: true,\n tables: true,\n tablesHeaderId: true,\n ghCodeBlocks: true,\n tasklists: true,\n smoothLivePreview: true,\n simpleLineBreaks: true,\n requireSpaceBeforeHeadingText: true,\n ghMentions: false,\n encodeEmails: true\n },\n vanilla: getDefaultOpts(true),\n allOn: allOptionsOn()\n };\n\n/**\n * helper namespace\n * @type {{}}\n */\nshowdown.helper = {};\n\n/**\n * TODO LEGACY SUPPORT CODE\n * @type {{}}\n */\nshowdown.extensions = {};\n\n/**\n * Set a global option\n * @static\n * @param {string} key\n * @param {*} value\n * @returns {showdown}\n */\nshowdown.setOption = function (key, value) {\n 'use strict';\n globalOptions[key] = value;\n return this;\n};\n\n/**\n * Get a global option\n * @static\n * @param {string} key\n * @returns {*}\n */\nshowdown.getOption = function (key) {\n 'use strict';\n return globalOptions[key];\n};\n\n/**\n * Get the global options\n * @static\n * @returns {{}}\n */\nshowdown.getOptions = function () {\n 'use strict';\n return globalOptions;\n};\n\n/**\n * Reset global options to the default values\n * @static\n */\nshowdown.resetOptions = function () {\n 'use strict';\n globalOptions = getDefaultOpts(true);\n};\n\n/**\n * Set the flavor showdown should use as default\n * @param {string} name\n */\nshowdown.setFlavor = function (name) {\n 'use strict';\n if (!flavor.hasOwnProperty(name)) {\n throw Error(name + ' flavor was not found');\n }\n showdown.resetOptions();\n var preset = flavor[name];\n setFlavor = name;\n for (var option in preset) {\n if (preset.hasOwnProperty(option)) {\n globalOptions[option] = preset[option];\n }\n }\n};\n\n/**\n * Get the currently set flavor\n * @returns {string}\n */\nshowdown.getFlavor = function () {\n 'use strict';\n return setFlavor;\n};\n\n/**\n * Get the options of a specified flavor. Returns undefined if the flavor was not found\n * @param {string} name Name of the flavor\n * @returns {{}|undefined}\n */\nshowdown.getFlavorOptions = function (name) {\n 'use strict';\n if (flavor.hasOwnProperty(name)) {\n return flavor[name];\n }\n};\n\n/**\n * Get the default options\n * @static\n * @param {boolean} [simple=true]\n * @returns {{}}\n */\nshowdown.getDefaultOptions = function (simple) {\n 'use strict';\n return getDefaultOpts(simple);\n};\n\n/**\n * Get or set a subParser\n *\n * subParser(name) - Get a registered subParser\n * subParser(name, func) - Register a subParser\n * @static\n * @param {string} name\n * @param {function} [func]\n * @returns {*}\n */\nshowdown.subParser = function (name, func) {\n 'use strict';\n if (showdown.helper.isString(name)) {\n if (typeof func !== 'undefined') {\n parsers[name] = func;\n } else {\n if (parsers.hasOwnProperty(name)) {\n return parsers[name];\n } else {\n throw Error('SubParser named ' + name + ' not registered!');\n }\n }\n }\n};\n\n/**\n * Gets or registers an extension\n * @static\n * @param {string} name\n * @param {object|function=} ext\n * @returns {*}\n */\nshowdown.extension = function (name, ext) {\n 'use strict';\n\n if (!showdown.helper.isString(name)) {\n throw Error('Extension \\'name\\' must be a string');\n }\n\n name = showdown.helper.stdExtName(name);\n\n // Getter\n if (showdown.helper.isUndefined(ext)) {\n if (!extensions.hasOwnProperty(name)) {\n throw Error('Extension named ' + name + ' is not registered!');\n }\n return extensions[name];\n\n // Setter\n } else {\n // Expand extension if it's wrapped in a function\n if (typeof ext === 'function') {\n ext = ext();\n }\n\n // Ensure extension is an array\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n\n var validExtension = validate(ext, name);\n\n if (validExtension.valid) {\n extensions[name] = ext;\n } else {\n throw Error(validExtension.error);\n }\n }\n};\n\n/**\n * Gets all extensions registered\n * @returns {{}}\n */\nshowdown.getAllExtensions = function () {\n 'use strict';\n return extensions;\n};\n\n/**\n * Remove an extension\n * @param {string} name\n */\nshowdown.removeExtension = function (name) {\n 'use strict';\n delete extensions[name];\n};\n\n/**\n * Removes all extensions\n */\nshowdown.resetExtensions = function () {\n 'use strict';\n extensions = {};\n};\n\n/**\n * Validate extension\n * @param {array} extension\n * @param {string} name\n * @returns {{valid: boolean, error: string}}\n */\nfunction validate (extension, name) {\n 'use strict';\n\n var errMsg = (name) ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n ret = {\n valid: true,\n error: ''\n };\n\n if (!showdown.helper.isArray(extension)) {\n extension = [extension];\n }\n\n for (var i = 0; i < extension.length; ++i) {\n var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n ext = extension[i];\n if (typeof ext !== 'object') {\n ret.valid = false;\n ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n return ret;\n }\n\n if (!showdown.helper.isString(ext.type)) {\n ret.valid = false;\n ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n return ret;\n }\n\n var type = ext.type = ext.type.toLowerCase();\n\n // normalize extension type\n if (type === 'language') {\n type = ext.type = 'lang';\n }\n\n if (type === 'html') {\n type = ext.type = 'output';\n }\n\n if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n ret.valid = false;\n ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n return ret;\n }\n\n if (type === 'listener') {\n if (showdown.helper.isUndefined(ext.listeners)) {\n ret.valid = false;\n ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n return ret;\n }\n } else {\n if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n ret.valid = false;\n ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n return ret;\n }\n }\n\n if (ext.listeners) {\n if (typeof ext.listeners !== 'object') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n return ret;\n }\n for (var ln in ext.listeners) {\n if (ext.listeners.hasOwnProperty(ln)) {\n if (typeof ext.listeners[ln] !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n return ret;\n }\n }\n }\n }\n\n if (ext.filter) {\n if (typeof ext.filter !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n return ret;\n }\n } else if (ext.regex) {\n if (showdown.helper.isString(ext.regex)) {\n ext.regex = new RegExp(ext.regex, 'g');\n }\n if (!(ext.regex instanceof RegExp)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n return ret;\n }\n if (showdown.helper.isUndefined(ext.replace)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n return ret;\n }\n }\n }\n return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n 'use strict';\n\n var validateExtension = validate(ext, null);\n if (!validateExtension.valid) {\n console.warn(validateExtension.error);\n return false;\n }\n return true;\n};\n","/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n 'use strict';\n return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n 'use strict';\n var getType = {};\n return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n 'use strict';\n return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n 'use strict';\n return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n 'use strict';\n // check if obj is defined\n if (showdown.helper.isUndefined(obj)) {\n throw new Error('obj param is required');\n }\n\n if (showdown.helper.isUndefined(callback)) {\n throw new Error('callback param is required');\n }\n\n if (!showdown.helper.isFunction(callback)) {\n throw new Error('callback param must be a function/closure');\n }\n\n if (typeof obj.forEach === 'function') {\n obj.forEach(callback);\n } else if (showdown.helper.isArray(obj)) {\n for (var i = 0; i < obj.length; i++) {\n callback(obj[i], i, obj);\n }\n } else if (typeof (obj) === 'object') {\n for (var prop in obj) {\n if (obj.hasOwnProperty(prop)) {\n callback(obj[prop], prop, obj);\n }\n }\n } else {\n throw new Error('obj does not seem to be an array or an iterable object');\n }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n 'use strict';\n return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n 'use strict';\n var charCodeToEscape = m1.charCodeAt(0);\n return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n 'use strict';\n // First we have to escape the escape characters so that\n // we can build a character class out of them\n var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n if (afterBackslash) {\n regexString = '\\\\\\\\' + regexString;\n }\n\n var regex = new RegExp(regexString, 'g');\n text = text.replace(regex, escapeCharactersCallback);\n\n return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n 'use strict';\n\n return txt\n .replace(/"/g, '\"')\n .replace(/</g, '<')\n .replace(/>/g, '>')\n .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n 'use strict';\n var f = flags || '',\n g = f.indexOf('g') > -1,\n x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n l = new RegExp(left, f.replace(/g/g, '')),\n pos = [],\n t, s, m, start, end;\n\n do {\n t = 0;\n while ((m = x.exec(str))) {\n if (l.test(m[0])) {\n if (!(t++)) {\n s = x.lastIndex;\n start = s - m[0].length;\n }\n } else if (t) {\n if (!--t) {\n end = m.index + m[0].length;\n var obj = {\n left: {start: start, end: s},\n match: {start: s, end: m.index},\n right: {start: m.index, end: end},\n wholeMatch: {start: start, end: end}\n };\n pos.push(obj);\n if (!g) {\n return pos;\n }\n }\n }\n }\n } while (t && (x.lastIndex = s));\n\n return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
test
\", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n 'use strict';\n\n var matchPos = rgxFindMatchPos (str, left, right, flags),\n results = [];\n\n for (var i = 0; i < matchPos.length; ++i) {\n results.push([\n str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n str.slice(matchPos[i].match.start, matchPos[i].match.end),\n str.slice(matchPos[i].left.start, matchPos[i].left.end),\n str.slice(matchPos[i].right.start, matchPos[i].right.end)\n ]);\n }\n return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n 'use strict';\n\n if (!showdown.helper.isFunction(replacement)) {\n var repStr = replacement;\n replacement = function () {\n return repStr;\n };\n }\n\n var matchPos = rgxFindMatchPos(str, left, right, flags),\n finalStr = str,\n lng = matchPos.length;\n\n if (lng > 0) {\n var bits = [];\n if (matchPos[0].wholeMatch.start !== 0) {\n bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n }\n for (var i = 0; i < lng; ++i) {\n bits.push(\n replacement(\n str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n str.slice(matchPos[i].match.start, matchPos[i].match.end),\n str.slice(matchPos[i].left.start, matchPos[i].left.end),\n str.slice(matchPos[i].right.start, matchPos[i].right.end)\n )\n );\n if (i < lng - 1) {\n bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n }\n }\n if (matchPos[lng - 1].wholeMatch.end < str.length) {\n bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n }\n finalStr = bits.join('');\n }\n return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n 'use strict';\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n if (regex instanceof RegExp === false) {\n throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n }\n var indexOf = str.substring(fromIndex || 0).search(regex);\n return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n 'use strict';\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n 'use strict';\n var encode = [\n function (ch) {\n return '&#' + ch.charCodeAt(0) + ';';\n },\n function (ch) {\n return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n },\n function (ch) {\n return ch;\n }\n ];\n\n mail = mail.replace(/./g, function (ch) {\n if (ch === '@') {\n // this *must* be encoded. I insist.\n ch = encode[Math.floor(Math.random() * 2)](ch);\n } else {\n var r = Math.random();\n // roughly 10% raw, 45% hex, 45% dec\n ch = (\n r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n );\n }\n return ch;\n });\n\n return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n 'use strict';\n /*jshint bitwise: false*/\n // eslint-disable-next-line space-infix-ops\n targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n /*jshint bitwise: true*/\n padString = String(padString || ' ');\n if (str.length > targetLength) {\n return String(str);\n } else {\n targetLength = targetLength - str.length;\n if (targetLength > padString.length) {\n padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n }\n return String(str) + padString.slice(0,targetLength);\n }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n console = {\n warn: function (msg) {\n 'use strict';\n alert(msg);\n },\n log: function (msg) {\n 'use strict';\n alert(msg);\n },\n error: function (msg) {\n 'use strict';\n throw msg;\n }\n };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n '+1':'\\ud83d\\udc4d',\n '-1':'\\ud83d\\udc4e',\n '100':'\\ud83d\\udcaf',\n '1234':'\\ud83d\\udd22',\n '1st_place_medal':'\\ud83e\\udd47',\n '2nd_place_medal':'\\ud83e\\udd48',\n '3rd_place_medal':'\\ud83e\\udd49',\n '8ball':'\\ud83c\\udfb1',\n 'a':'\\ud83c\\udd70\\ufe0f',\n 'ab':'\\ud83c\\udd8e',\n 'abc':'\\ud83d\\udd24',\n 'abcd':'\\ud83d\\udd21',\n 'accept':'\\ud83c\\ude51',\n 'aerial_tramway':'\\ud83d\\udea1',\n 'airplane':'\\u2708\\ufe0f',\n 'alarm_clock':'\\u23f0',\n 'alembic':'\\u2697\\ufe0f',\n 'alien':'\\ud83d\\udc7d',\n 'ambulance':'\\ud83d\\ude91',\n 'amphora':'\\ud83c\\udffa',\n 'anchor':'\\u2693\\ufe0f',\n 'angel':'\\ud83d\\udc7c',\n 'anger':'\\ud83d\\udca2',\n 'angry':'\\ud83d\\ude20',\n 'anguished':'\\ud83d\\ude27',\n 'ant':'\\ud83d\\udc1c',\n 'apple':'\\ud83c\\udf4e',\n 'aquarius':'\\u2652\\ufe0f',\n 'aries':'\\u2648\\ufe0f',\n 'arrow_backward':'\\u25c0\\ufe0f',\n 'arrow_double_down':'\\u23ec',\n 'arrow_double_up':'\\u23eb',\n 'arrow_down':'\\u2b07\\ufe0f',\n 'arrow_down_small':'\\ud83d\\udd3d',\n 'arrow_forward':'\\u25b6\\ufe0f',\n 'arrow_heading_down':'\\u2935\\ufe0f',\n 'arrow_heading_up':'\\u2934\\ufe0f',\n 'arrow_left':'\\u2b05\\ufe0f',\n 'arrow_lower_left':'\\u2199\\ufe0f',\n 'arrow_lower_right':'\\u2198\\ufe0f',\n 'arrow_right':'\\u27a1\\ufe0f',\n 'arrow_right_hook':'\\u21aa\\ufe0f',\n 'arrow_up':'\\u2b06\\ufe0f',\n 'arrow_up_down':'\\u2195\\ufe0f',\n 'arrow_up_small':'\\ud83d\\udd3c',\n 'arrow_upper_left':'\\u2196\\ufe0f',\n 'arrow_upper_right':'\\u2197\\ufe0f',\n 'arrows_clockwise':'\\ud83d\\udd03',\n 'arrows_counterclockwise':'\\ud83d\\udd04',\n 'art':'\\ud83c\\udfa8',\n 'articulated_lorry':'\\ud83d\\ude9b',\n 'artificial_satellite':'\\ud83d\\udef0',\n 'astonished':'\\ud83d\\ude32',\n 'athletic_shoe':'\\ud83d\\udc5f',\n 'atm':'\\ud83c\\udfe7',\n 'atom_symbol':'\\u269b\\ufe0f',\n 'avocado':'\\ud83e\\udd51',\n 'b':'\\ud83c\\udd71\\ufe0f',\n 'baby':'\\ud83d\\udc76',\n 'baby_bottle':'\\ud83c\\udf7c',\n 'baby_chick':'\\ud83d\\udc24',\n 'baby_symbol':'\\ud83d\\udebc',\n 'back':'\\ud83d\\udd19',\n 'bacon':'\\ud83e\\udd53',\n 'badminton':'\\ud83c\\udff8',\n 'baggage_claim':'\\ud83d\\udec4',\n 'baguette_bread':'\\ud83e\\udd56',\n 'balance_scale':'\\u2696\\ufe0f',\n 'balloon':'\\ud83c\\udf88',\n 'ballot_box':'\\ud83d\\uddf3',\n 'ballot_box_with_check':'\\u2611\\ufe0f',\n 'bamboo':'\\ud83c\\udf8d',\n 'banana':'\\ud83c\\udf4c',\n 'bangbang':'\\u203c\\ufe0f',\n 'bank':'\\ud83c\\udfe6',\n 'bar_chart':'\\ud83d\\udcca',\n 'barber':'\\ud83d\\udc88',\n 'baseball':'\\u26be\\ufe0f',\n 'basketball':'\\ud83c\\udfc0',\n 'basketball_man':'\\u26f9\\ufe0f',\n 'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n 'bat':'\\ud83e\\udd87',\n 'bath':'\\ud83d\\udec0',\n 'bathtub':'\\ud83d\\udec1',\n 'battery':'\\ud83d\\udd0b',\n 'beach_umbrella':'\\ud83c\\udfd6',\n 'bear':'\\ud83d\\udc3b',\n 'bed':'\\ud83d\\udecf',\n 'bee':'\\ud83d\\udc1d',\n 'beer':'\\ud83c\\udf7a',\n 'beers':'\\ud83c\\udf7b',\n 'beetle':'\\ud83d\\udc1e',\n 'beginner':'\\ud83d\\udd30',\n 'bell':'\\ud83d\\udd14',\n 'bellhop_bell':'\\ud83d\\udece',\n 'bento':'\\ud83c\\udf71',\n 'biking_man':'\\ud83d\\udeb4',\n 'bike':'\\ud83d\\udeb2',\n 'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n 'bikini':'\\ud83d\\udc59',\n 'biohazard':'\\u2623\\ufe0f',\n 'bird':'\\ud83d\\udc26',\n 'birthday':'\\ud83c\\udf82',\n 'black_circle':'\\u26ab\\ufe0f',\n 'black_flag':'\\ud83c\\udff4',\n 'black_heart':'\\ud83d\\udda4',\n 'black_joker':'\\ud83c\\udccf',\n 'black_large_square':'\\u2b1b\\ufe0f',\n 'black_medium_small_square':'\\u25fe\\ufe0f',\n 'black_medium_square':'\\u25fc\\ufe0f',\n 'black_nib':'\\u2712\\ufe0f',\n 'black_small_square':'\\u25aa\\ufe0f',\n 'black_square_button':'\\ud83d\\udd32',\n 'blonde_man':'\\ud83d\\udc71',\n 'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n 'blossom':'\\ud83c\\udf3c',\n 'blowfish':'\\ud83d\\udc21',\n 'blue_book':'\\ud83d\\udcd8',\n 'blue_car':'\\ud83d\\ude99',\n 'blue_heart':'\\ud83d\\udc99',\n 'blush':'\\ud83d\\ude0a',\n 'boar':'\\ud83d\\udc17',\n 'boat':'\\u26f5\\ufe0f',\n 'bomb':'\\ud83d\\udca3',\n 'book':'\\ud83d\\udcd6',\n 'bookmark':'\\ud83d\\udd16',\n 'bookmark_tabs':'\\ud83d\\udcd1',\n 'books':'\\ud83d\\udcda',\n 'boom':'\\ud83d\\udca5',\n 'boot':'\\ud83d\\udc62',\n 'bouquet':'\\ud83d\\udc90',\n 'bowing_man':'\\ud83d\\ude47',\n 'bow_and_arrow':'\\ud83c\\udff9',\n 'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n 'bowling':'\\ud83c\\udfb3',\n 'boxing_glove':'\\ud83e\\udd4a',\n 'boy':'\\ud83d\\udc66',\n 'bread':'\\ud83c\\udf5e',\n 'bride_with_veil':'\\ud83d\\udc70',\n 'bridge_at_night':'\\ud83c\\udf09',\n 'briefcase':'\\ud83d\\udcbc',\n 'broken_heart':'\\ud83d\\udc94',\n 'bug':'\\ud83d\\udc1b',\n 'building_construction':'\\ud83c\\udfd7',\n 'bulb':'\\ud83d\\udca1',\n 'bullettrain_front':'\\ud83d\\ude85',\n 'bullettrain_side':'\\ud83d\\ude84',\n 'burrito':'\\ud83c\\udf2f',\n 'bus':'\\ud83d\\ude8c',\n 'business_suit_levitating':'\\ud83d\\udd74',\n 'busstop':'\\ud83d\\ude8f',\n 'bust_in_silhouette':'\\ud83d\\udc64',\n 'busts_in_silhouette':'\\ud83d\\udc65',\n 'butterfly':'\\ud83e\\udd8b',\n 'cactus':'\\ud83c\\udf35',\n 'cake':'\\ud83c\\udf70',\n 'calendar':'\\ud83d\\udcc6',\n 'call_me_hand':'\\ud83e\\udd19',\n 'calling':'\\ud83d\\udcf2',\n 'camel':'\\ud83d\\udc2b',\n 'camera':'\\ud83d\\udcf7',\n 'camera_flash':'\\ud83d\\udcf8',\n 'camping':'\\ud83c\\udfd5',\n 'cancer':'\\u264b\\ufe0f',\n 'candle':'\\ud83d\\udd6f',\n 'candy':'\\ud83c\\udf6c',\n 'canoe':'\\ud83d\\udef6',\n 'capital_abcd':'\\ud83d\\udd20',\n 'capricorn':'\\u2651\\ufe0f',\n 'car':'\\ud83d\\ude97',\n 'card_file_box':'\\ud83d\\uddc3',\n 'card_index':'\\ud83d\\udcc7',\n 'card_index_dividers':'\\ud83d\\uddc2',\n 'carousel_horse':'\\ud83c\\udfa0',\n 'carrot':'\\ud83e\\udd55',\n 'cat':'\\ud83d\\udc31',\n 'cat2':'\\ud83d\\udc08',\n 'cd':'\\ud83d\\udcbf',\n 'chains':'\\u26d3',\n 'champagne':'\\ud83c\\udf7e',\n 'chart':'\\ud83d\\udcb9',\n 'chart_with_downwards_trend':'\\ud83d\\udcc9',\n 'chart_with_upwards_trend':'\\ud83d\\udcc8',\n 'checkered_flag':'\\ud83c\\udfc1',\n 'cheese':'\\ud83e\\uddc0',\n 'cherries':'\\ud83c\\udf52',\n 'cherry_blossom':'\\ud83c\\udf38',\n 'chestnut':'\\ud83c\\udf30',\n 'chicken':'\\ud83d\\udc14',\n 'children_crossing':'\\ud83d\\udeb8',\n 'chipmunk':'\\ud83d\\udc3f',\n 'chocolate_bar':'\\ud83c\\udf6b',\n 'christmas_tree':'\\ud83c\\udf84',\n 'church':'\\u26ea\\ufe0f',\n 'cinema':'\\ud83c\\udfa6',\n 'circus_tent':'\\ud83c\\udfaa',\n 'city_sunrise':'\\ud83c\\udf07',\n 'city_sunset':'\\ud83c\\udf06',\n 'cityscape':'\\ud83c\\udfd9',\n 'cl':'\\ud83c\\udd91',\n 'clamp':'\\ud83d\\udddc',\n 'clap':'\\ud83d\\udc4f',\n 'clapper':'\\ud83c\\udfac',\n 'classical_building':'\\ud83c\\udfdb',\n 'clinking_glasses':'\\ud83e\\udd42',\n 'clipboard':'\\ud83d\\udccb',\n 'clock1':'\\ud83d\\udd50',\n 'clock10':'\\ud83d\\udd59',\n 'clock1030':'\\ud83d\\udd65',\n 'clock11':'\\ud83d\\udd5a',\n 'clock1130':'\\ud83d\\udd66',\n 'clock12':'\\ud83d\\udd5b',\n 'clock1230':'\\ud83d\\udd67',\n 'clock130':'\\ud83d\\udd5c',\n 'clock2':'\\ud83d\\udd51',\n 'clock230':'\\ud83d\\udd5d',\n 'clock3':'\\ud83d\\udd52',\n 'clock330':'\\ud83d\\udd5e',\n 'clock4':'\\ud83d\\udd53',\n 'clock430':'\\ud83d\\udd5f',\n 'clock5':'\\ud83d\\udd54',\n 'clock530':'\\ud83d\\udd60',\n 'clock6':'\\ud83d\\udd55',\n 'clock630':'\\ud83d\\udd61',\n 'clock7':'\\ud83d\\udd56',\n 'clock730':'\\ud83d\\udd62',\n 'clock8':'\\ud83d\\udd57',\n 'clock830':'\\ud83d\\udd63',\n 'clock9':'\\ud83d\\udd58',\n 'clock930':'\\ud83d\\udd64',\n 'closed_book':'\\ud83d\\udcd5',\n 'closed_lock_with_key':'\\ud83d\\udd10',\n 'closed_umbrella':'\\ud83c\\udf02',\n 'cloud':'\\u2601\\ufe0f',\n 'cloud_with_lightning':'\\ud83c\\udf29',\n 'cloud_with_lightning_and_rain':'\\u26c8',\n 'cloud_with_rain':'\\ud83c\\udf27',\n 'cloud_with_snow':'\\ud83c\\udf28',\n 'clown_face':'\\ud83e\\udd21',\n 'clubs':'\\u2663\\ufe0f',\n 'cocktail':'\\ud83c\\udf78',\n 'coffee':'\\u2615\\ufe0f',\n 'coffin':'\\u26b0\\ufe0f',\n 'cold_sweat':'\\ud83d\\ude30',\n 'comet':'\\u2604\\ufe0f',\n 'computer':'\\ud83d\\udcbb',\n 'computer_mouse':'\\ud83d\\uddb1',\n 'confetti_ball':'\\ud83c\\udf8a',\n 'confounded':'\\ud83d\\ude16',\n 'confused':'\\ud83d\\ude15',\n 'congratulations':'\\u3297\\ufe0f',\n 'construction':'\\ud83d\\udea7',\n 'construction_worker_man':'\\ud83d\\udc77',\n 'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n 'control_knobs':'\\ud83c\\udf9b',\n 'convenience_store':'\\ud83c\\udfea',\n 'cookie':'\\ud83c\\udf6a',\n 'cool':'\\ud83c\\udd92',\n 'policeman':'\\ud83d\\udc6e',\n 'copyright':'\\u00a9\\ufe0f',\n 'corn':'\\ud83c\\udf3d',\n 'couch_and_lamp':'\\ud83d\\udecb',\n 'couple':'\\ud83d\\udc6b',\n 'couple_with_heart_woman_man':'\\ud83d\\udc91',\n 'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n 'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n 'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n 'couplekiss_man_woman':'\\ud83d\\udc8f',\n 'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n 'cow':'\\ud83d\\udc2e',\n 'cow2':'\\ud83d\\udc04',\n 'cowboy_hat_face':'\\ud83e\\udd20',\n 'crab':'\\ud83e\\udd80',\n 'crayon':'\\ud83d\\udd8d',\n 'credit_card':'\\ud83d\\udcb3',\n 'crescent_moon':'\\ud83c\\udf19',\n 'cricket':'\\ud83c\\udfcf',\n 'crocodile':'\\ud83d\\udc0a',\n 'croissant':'\\ud83e\\udd50',\n 'crossed_fingers':'\\ud83e\\udd1e',\n 'crossed_flags':'\\ud83c\\udf8c',\n 'crossed_swords':'\\u2694\\ufe0f',\n 'crown':'\\ud83d\\udc51',\n 'cry':'\\ud83d\\ude22',\n 'crying_cat_face':'\\ud83d\\ude3f',\n 'crystal_ball':'\\ud83d\\udd2e',\n 'cucumber':'\\ud83e\\udd52',\n 'cupid':'\\ud83d\\udc98',\n 'curly_loop':'\\u27b0',\n 'currency_exchange':'\\ud83d\\udcb1',\n 'curry':'\\ud83c\\udf5b',\n 'custard':'\\ud83c\\udf6e',\n 'customs':'\\ud83d\\udec3',\n 'cyclone':'\\ud83c\\udf00',\n 'dagger':'\\ud83d\\udde1',\n 'dancer':'\\ud83d\\udc83',\n 'dancing_women':'\\ud83d\\udc6f',\n 'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n 'dango':'\\ud83c\\udf61',\n 'dark_sunglasses':'\\ud83d\\udd76',\n 'dart':'\\ud83c\\udfaf',\n 'dash':'\\ud83d\\udca8',\n 'date':'\\ud83d\\udcc5',\n 'deciduous_tree':'\\ud83c\\udf33',\n 'deer':'\\ud83e\\udd8c',\n 'department_store':'\\ud83c\\udfec',\n 'derelict_house':'\\ud83c\\udfda',\n 'desert':'\\ud83c\\udfdc',\n 'desert_island':'\\ud83c\\udfdd',\n 'desktop_computer':'\\ud83d\\udda5',\n 'male_detective':'\\ud83d\\udd75\\ufe0f',\n 'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n 'diamonds':'\\u2666\\ufe0f',\n 'disappointed':'\\ud83d\\ude1e',\n 'disappointed_relieved':'\\ud83d\\ude25',\n 'dizzy':'\\ud83d\\udcab',\n 'dizzy_face':'\\ud83d\\ude35',\n 'do_not_litter':'\\ud83d\\udeaf',\n 'dog':'\\ud83d\\udc36',\n 'dog2':'\\ud83d\\udc15',\n 'dollar':'\\ud83d\\udcb5',\n 'dolls':'\\ud83c\\udf8e',\n 'dolphin':'\\ud83d\\udc2c',\n 'door':'\\ud83d\\udeaa',\n 'doughnut':'\\ud83c\\udf69',\n 'dove':'\\ud83d\\udd4a',\n 'dragon':'\\ud83d\\udc09',\n 'dragon_face':'\\ud83d\\udc32',\n 'dress':'\\ud83d\\udc57',\n 'dromedary_camel':'\\ud83d\\udc2a',\n 'drooling_face':'\\ud83e\\udd24',\n 'droplet':'\\ud83d\\udca7',\n 'drum':'\\ud83e\\udd41',\n 'duck':'\\ud83e\\udd86',\n 'dvd':'\\ud83d\\udcc0',\n 'e-mail':'\\ud83d\\udce7',\n 'eagle':'\\ud83e\\udd85',\n 'ear':'\\ud83d\\udc42',\n 'ear_of_rice':'\\ud83c\\udf3e',\n 'earth_africa':'\\ud83c\\udf0d',\n 'earth_americas':'\\ud83c\\udf0e',\n 'earth_asia':'\\ud83c\\udf0f',\n 'egg':'\\ud83e\\udd5a',\n 'eggplant':'\\ud83c\\udf46',\n 'eight_pointed_black_star':'\\u2734\\ufe0f',\n 'eight_spoked_asterisk':'\\u2733\\ufe0f',\n 'electric_plug':'\\ud83d\\udd0c',\n 'elephant':'\\ud83d\\udc18',\n 'email':'\\u2709\\ufe0f',\n 'end':'\\ud83d\\udd1a',\n 'envelope_with_arrow':'\\ud83d\\udce9',\n 'euro':'\\ud83d\\udcb6',\n 'european_castle':'\\ud83c\\udff0',\n 'european_post_office':'\\ud83c\\udfe4',\n 'evergreen_tree':'\\ud83c\\udf32',\n 'exclamation':'\\u2757\\ufe0f',\n 'expressionless':'\\ud83d\\ude11',\n 'eye':'\\ud83d\\udc41',\n 'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n 'eyeglasses':'\\ud83d\\udc53',\n 'eyes':'\\ud83d\\udc40',\n 'face_with_head_bandage':'\\ud83e\\udd15',\n 'face_with_thermometer':'\\ud83e\\udd12',\n 'fist_oncoming':'\\ud83d\\udc4a',\n 'factory':'\\ud83c\\udfed',\n 'fallen_leaf':'\\ud83c\\udf42',\n 'family_man_woman_boy':'\\ud83d\\udc6a',\n 'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n 'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n 'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n 'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n 'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n 'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n 'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n 'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n 'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n 'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n 'fast_forward':'\\u23e9',\n 'fax':'\\ud83d\\udce0',\n 'fearful':'\\ud83d\\ude28',\n 'feet':'\\ud83d\\udc3e',\n 'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n 'ferris_wheel':'\\ud83c\\udfa1',\n 'ferry':'\\u26f4',\n 'field_hockey':'\\ud83c\\udfd1',\n 'file_cabinet':'\\ud83d\\uddc4',\n 'file_folder':'\\ud83d\\udcc1',\n 'film_projector':'\\ud83d\\udcfd',\n 'film_strip':'\\ud83c\\udf9e',\n 'fire':'\\ud83d\\udd25',\n 'fire_engine':'\\ud83d\\ude92',\n 'fireworks':'\\ud83c\\udf86',\n 'first_quarter_moon':'\\ud83c\\udf13',\n 'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n 'fish':'\\ud83d\\udc1f',\n 'fish_cake':'\\ud83c\\udf65',\n 'fishing_pole_and_fish':'\\ud83c\\udfa3',\n 'fist_raised':'\\u270a',\n 'fist_left':'\\ud83e\\udd1b',\n 'fist_right':'\\ud83e\\udd1c',\n 'flags':'\\ud83c\\udf8f',\n 'flashlight':'\\ud83d\\udd26',\n 'fleur_de_lis':'\\u269c\\ufe0f',\n 'flight_arrival':'\\ud83d\\udeec',\n 'flight_departure':'\\ud83d\\udeeb',\n 'floppy_disk':'\\ud83d\\udcbe',\n 'flower_playing_cards':'\\ud83c\\udfb4',\n 'flushed':'\\ud83d\\ude33',\n 'fog':'\\ud83c\\udf2b',\n 'foggy':'\\ud83c\\udf01',\n 'football':'\\ud83c\\udfc8',\n 'footprints':'\\ud83d\\udc63',\n 'fork_and_knife':'\\ud83c\\udf74',\n 'fountain':'\\u26f2\\ufe0f',\n 'fountain_pen':'\\ud83d\\udd8b',\n 'four_leaf_clover':'\\ud83c\\udf40',\n 'fox_face':'\\ud83e\\udd8a',\n 'framed_picture':'\\ud83d\\uddbc',\n 'free':'\\ud83c\\udd93',\n 'fried_egg':'\\ud83c\\udf73',\n 'fried_shrimp':'\\ud83c\\udf64',\n 'fries':'\\ud83c\\udf5f',\n 'frog':'\\ud83d\\udc38',\n 'frowning':'\\ud83d\\ude26',\n 'frowning_face':'\\u2639\\ufe0f',\n 'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n 'frowning_woman':'\\ud83d\\ude4d',\n 'middle_finger':'\\ud83d\\udd95',\n 'fuelpump':'\\u26fd\\ufe0f',\n 'full_moon':'\\ud83c\\udf15',\n 'full_moon_with_face':'\\ud83c\\udf1d',\n 'funeral_urn':'\\u26b1\\ufe0f',\n 'game_die':'\\ud83c\\udfb2',\n 'gear':'\\u2699\\ufe0f',\n 'gem':'\\ud83d\\udc8e',\n 'gemini':'\\u264a\\ufe0f',\n 'ghost':'\\ud83d\\udc7b',\n 'gift':'\\ud83c\\udf81',\n 'gift_heart':'\\ud83d\\udc9d',\n 'girl':'\\ud83d\\udc67',\n 'globe_with_meridians':'\\ud83c\\udf10',\n 'goal_net':'\\ud83e\\udd45',\n 'goat':'\\ud83d\\udc10',\n 'golf':'\\u26f3\\ufe0f',\n 'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n 'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n 'gorilla':'\\ud83e\\udd8d',\n 'grapes':'\\ud83c\\udf47',\n 'green_apple':'\\ud83c\\udf4f',\n 'green_book':'\\ud83d\\udcd7',\n 'green_heart':'\\ud83d\\udc9a',\n 'green_salad':'\\ud83e\\udd57',\n 'grey_exclamation':'\\u2755',\n 'grey_question':'\\u2754',\n 'grimacing':'\\ud83d\\ude2c',\n 'grin':'\\ud83d\\ude01',\n 'grinning':'\\ud83d\\ude00',\n 'guardsman':'\\ud83d\\udc82',\n 'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n 'guitar':'\\ud83c\\udfb8',\n 'gun':'\\ud83d\\udd2b',\n 'haircut_woman':'\\ud83d\\udc87',\n 'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n 'hamburger':'\\ud83c\\udf54',\n 'hammer':'\\ud83d\\udd28',\n 'hammer_and_pick':'\\u2692',\n 'hammer_and_wrench':'\\ud83d\\udee0',\n 'hamster':'\\ud83d\\udc39',\n 'hand':'\\u270b',\n 'handbag':'\\ud83d\\udc5c',\n 'handshake':'\\ud83e\\udd1d',\n 'hankey':'\\ud83d\\udca9',\n 'hatched_chick':'\\ud83d\\udc25',\n 'hatching_chick':'\\ud83d\\udc23',\n 'headphones':'\\ud83c\\udfa7',\n 'hear_no_evil':'\\ud83d\\ude49',\n 'heart':'\\u2764\\ufe0f',\n 'heart_decoration':'\\ud83d\\udc9f',\n 'heart_eyes':'\\ud83d\\ude0d',\n 'heart_eyes_cat':'\\ud83d\\ude3b',\n 'heartbeat':'\\ud83d\\udc93',\n 'heartpulse':'\\ud83d\\udc97',\n 'hearts':'\\u2665\\ufe0f',\n 'heavy_check_mark':'\\u2714\\ufe0f',\n 'heavy_division_sign':'\\u2797',\n 'heavy_dollar_sign':'\\ud83d\\udcb2',\n 'heavy_heart_exclamation':'\\u2763\\ufe0f',\n 'heavy_minus_sign':'\\u2796',\n 'heavy_multiplication_x':'\\u2716\\ufe0f',\n 'heavy_plus_sign':'\\u2795',\n 'helicopter':'\\ud83d\\ude81',\n 'herb':'\\ud83c\\udf3f',\n 'hibiscus':'\\ud83c\\udf3a',\n 'high_brightness':'\\ud83d\\udd06',\n 'high_heel':'\\ud83d\\udc60',\n 'hocho':'\\ud83d\\udd2a',\n 'hole':'\\ud83d\\udd73',\n 'honey_pot':'\\ud83c\\udf6f',\n 'horse':'\\ud83d\\udc34',\n 'horse_racing':'\\ud83c\\udfc7',\n 'hospital':'\\ud83c\\udfe5',\n 'hot_pepper':'\\ud83c\\udf36',\n 'hotdog':'\\ud83c\\udf2d',\n 'hotel':'\\ud83c\\udfe8',\n 'hotsprings':'\\u2668\\ufe0f',\n 'hourglass':'\\u231b\\ufe0f',\n 'hourglass_flowing_sand':'\\u23f3',\n 'house':'\\ud83c\\udfe0',\n 'house_with_garden':'\\ud83c\\udfe1',\n 'houses':'\\ud83c\\udfd8',\n 'hugs':'\\ud83e\\udd17',\n 'hushed':'\\ud83d\\ude2f',\n 'ice_cream':'\\ud83c\\udf68',\n 'ice_hockey':'\\ud83c\\udfd2',\n 'ice_skate':'\\u26f8',\n 'icecream':'\\ud83c\\udf66',\n 'id':'\\ud83c\\udd94',\n 'ideograph_advantage':'\\ud83c\\ude50',\n 'imp':'\\ud83d\\udc7f',\n 'inbox_tray':'\\ud83d\\udce5',\n 'incoming_envelope':'\\ud83d\\udce8',\n 'tipping_hand_woman':'\\ud83d\\udc81',\n 'information_source':'\\u2139\\ufe0f',\n 'innocent':'\\ud83d\\ude07',\n 'interrobang':'\\u2049\\ufe0f',\n 'iphone':'\\ud83d\\udcf1',\n 'izakaya_lantern':'\\ud83c\\udfee',\n 'jack_o_lantern':'\\ud83c\\udf83',\n 'japan':'\\ud83d\\uddfe',\n 'japanese_castle':'\\ud83c\\udfef',\n 'japanese_goblin':'\\ud83d\\udc7a',\n 'japanese_ogre':'\\ud83d\\udc79',\n 'jeans':'\\ud83d\\udc56',\n 'joy':'\\ud83d\\ude02',\n 'joy_cat':'\\ud83d\\ude39',\n 'joystick':'\\ud83d\\udd79',\n 'kaaba':'\\ud83d\\udd4b',\n 'key':'\\ud83d\\udd11',\n 'keyboard':'\\u2328\\ufe0f',\n 'keycap_ten':'\\ud83d\\udd1f',\n 'kick_scooter':'\\ud83d\\udef4',\n 'kimono':'\\ud83d\\udc58',\n 'kiss':'\\ud83d\\udc8b',\n 'kissing':'\\ud83d\\ude17',\n 'kissing_cat':'\\ud83d\\ude3d',\n 'kissing_closed_eyes':'\\ud83d\\ude1a',\n 'kissing_heart':'\\ud83d\\ude18',\n 'kissing_smiling_eyes':'\\ud83d\\ude19',\n 'kiwi_fruit':'\\ud83e\\udd5d',\n 'koala':'\\ud83d\\udc28',\n 'koko':'\\ud83c\\ude01',\n 'label':'\\ud83c\\udff7',\n 'large_blue_circle':'\\ud83d\\udd35',\n 'large_blue_diamond':'\\ud83d\\udd37',\n 'large_orange_diamond':'\\ud83d\\udd36',\n 'last_quarter_moon':'\\ud83c\\udf17',\n 'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n 'latin_cross':'\\u271d\\ufe0f',\n 'laughing':'\\ud83d\\ude06',\n 'leaves':'\\ud83c\\udf43',\n 'ledger':'\\ud83d\\udcd2',\n 'left_luggage':'\\ud83d\\udec5',\n 'left_right_arrow':'\\u2194\\ufe0f',\n 'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n 'lemon':'\\ud83c\\udf4b',\n 'leo':'\\u264c\\ufe0f',\n 'leopard':'\\ud83d\\udc06',\n 'level_slider':'\\ud83c\\udf9a',\n 'libra':'\\u264e\\ufe0f',\n 'light_rail':'\\ud83d\\ude88',\n 'link':'\\ud83d\\udd17',\n 'lion':'\\ud83e\\udd81',\n 'lips':'\\ud83d\\udc44',\n 'lipstick':'\\ud83d\\udc84',\n 'lizard':'\\ud83e\\udd8e',\n 'lock':'\\ud83d\\udd12',\n 'lock_with_ink_pen':'\\ud83d\\udd0f',\n 'lollipop':'\\ud83c\\udf6d',\n 'loop':'\\u27bf',\n 'loud_sound':'\\ud83d\\udd0a',\n 'loudspeaker':'\\ud83d\\udce2',\n 'love_hotel':'\\ud83c\\udfe9',\n 'love_letter':'\\ud83d\\udc8c',\n 'low_brightness':'\\ud83d\\udd05',\n 'lying_face':'\\ud83e\\udd25',\n 'm':'\\u24c2\\ufe0f',\n 'mag':'\\ud83d\\udd0d',\n 'mag_right':'\\ud83d\\udd0e',\n 'mahjong':'\\ud83c\\udc04\\ufe0f',\n 'mailbox':'\\ud83d\\udceb',\n 'mailbox_closed':'\\ud83d\\udcea',\n 'mailbox_with_mail':'\\ud83d\\udcec',\n 'mailbox_with_no_mail':'\\ud83d\\udced',\n 'man':'\\ud83d\\udc68',\n 'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n 'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n 'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n 'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n 'man_dancing':'\\ud83d\\udd7a',\n 'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n 'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n 'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n 'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n 'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n 'man_in_tuxedo':'\\ud83e\\udd35',\n 'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n 'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n 'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n 'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n 'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n 'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n 'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n 'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n 'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n 'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n 'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n 'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n 'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n 'man_with_gua_pi_mao':'\\ud83d\\udc72',\n 'man_with_turban':'\\ud83d\\udc73',\n 'tangerine':'\\ud83c\\udf4a',\n 'mans_shoe':'\\ud83d\\udc5e',\n 'mantelpiece_clock':'\\ud83d\\udd70',\n 'maple_leaf':'\\ud83c\\udf41',\n 'martial_arts_uniform':'\\ud83e\\udd4b',\n 'mask':'\\ud83d\\ude37',\n 'massage_woman':'\\ud83d\\udc86',\n 'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n 'meat_on_bone':'\\ud83c\\udf56',\n 'medal_military':'\\ud83c\\udf96',\n 'medal_sports':'\\ud83c\\udfc5',\n 'mega':'\\ud83d\\udce3',\n 'melon':'\\ud83c\\udf48',\n 'memo':'\\ud83d\\udcdd',\n 'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n 'menorah':'\\ud83d\\udd4e',\n 'mens':'\\ud83d\\udeb9',\n 'metal':'\\ud83e\\udd18',\n 'metro':'\\ud83d\\ude87',\n 'microphone':'\\ud83c\\udfa4',\n 'microscope':'\\ud83d\\udd2c',\n 'milk_glass':'\\ud83e\\udd5b',\n 'milky_way':'\\ud83c\\udf0c',\n 'minibus':'\\ud83d\\ude90',\n 'minidisc':'\\ud83d\\udcbd',\n 'mobile_phone_off':'\\ud83d\\udcf4',\n 'money_mouth_face':'\\ud83e\\udd11',\n 'money_with_wings':'\\ud83d\\udcb8',\n 'moneybag':'\\ud83d\\udcb0',\n 'monkey':'\\ud83d\\udc12',\n 'monkey_face':'\\ud83d\\udc35',\n 'monorail':'\\ud83d\\ude9d',\n 'moon':'\\ud83c\\udf14',\n 'mortar_board':'\\ud83c\\udf93',\n 'mosque':'\\ud83d\\udd4c',\n 'motor_boat':'\\ud83d\\udee5',\n 'motor_scooter':'\\ud83d\\udef5',\n 'motorcycle':'\\ud83c\\udfcd',\n 'motorway':'\\ud83d\\udee3',\n 'mount_fuji':'\\ud83d\\uddfb',\n 'mountain':'\\u26f0',\n 'mountain_biking_man':'\\ud83d\\udeb5',\n 'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n 'mountain_cableway':'\\ud83d\\udea0',\n 'mountain_railway':'\\ud83d\\ude9e',\n 'mountain_snow':'\\ud83c\\udfd4',\n 'mouse':'\\ud83d\\udc2d',\n 'mouse2':'\\ud83d\\udc01',\n 'movie_camera':'\\ud83c\\udfa5',\n 'moyai':'\\ud83d\\uddff',\n 'mrs_claus':'\\ud83e\\udd36',\n 'muscle':'\\ud83d\\udcaa',\n 'mushroom':'\\ud83c\\udf44',\n 'musical_keyboard':'\\ud83c\\udfb9',\n 'musical_note':'\\ud83c\\udfb5',\n 'musical_score':'\\ud83c\\udfbc',\n 'mute':'\\ud83d\\udd07',\n 'nail_care':'\\ud83d\\udc85',\n 'name_badge':'\\ud83d\\udcdb',\n 'national_park':'\\ud83c\\udfde',\n 'nauseated_face':'\\ud83e\\udd22',\n 'necktie':'\\ud83d\\udc54',\n 'negative_squared_cross_mark':'\\u274e',\n 'nerd_face':'\\ud83e\\udd13',\n 'neutral_face':'\\ud83d\\ude10',\n 'new':'\\ud83c\\udd95',\n 'new_moon':'\\ud83c\\udf11',\n 'new_moon_with_face':'\\ud83c\\udf1a',\n 'newspaper':'\\ud83d\\udcf0',\n 'newspaper_roll':'\\ud83d\\uddde',\n 'next_track_button':'\\u23ed',\n 'ng':'\\ud83c\\udd96',\n 'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n 'no_good_woman':'\\ud83d\\ude45',\n 'night_with_stars':'\\ud83c\\udf03',\n 'no_bell':'\\ud83d\\udd15',\n 'no_bicycles':'\\ud83d\\udeb3',\n 'no_entry':'\\u26d4\\ufe0f',\n 'no_entry_sign':'\\ud83d\\udeab',\n 'no_mobile_phones':'\\ud83d\\udcf5',\n 'no_mouth':'\\ud83d\\ude36',\n 'no_pedestrians':'\\ud83d\\udeb7',\n 'no_smoking':'\\ud83d\\udead',\n 'non-potable_water':'\\ud83d\\udeb1',\n 'nose':'\\ud83d\\udc43',\n 'notebook':'\\ud83d\\udcd3',\n 'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n 'notes':'\\ud83c\\udfb6',\n 'nut_and_bolt':'\\ud83d\\udd29',\n 'o':'\\u2b55\\ufe0f',\n 'o2':'\\ud83c\\udd7e\\ufe0f',\n 'ocean':'\\ud83c\\udf0a',\n 'octopus':'\\ud83d\\udc19',\n 'oden':'\\ud83c\\udf62',\n 'office':'\\ud83c\\udfe2',\n 'oil_drum':'\\ud83d\\udee2',\n 'ok':'\\ud83c\\udd97',\n 'ok_hand':'\\ud83d\\udc4c',\n 'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n 'ok_woman':'\\ud83d\\ude46',\n 'old_key':'\\ud83d\\udddd',\n 'older_man':'\\ud83d\\udc74',\n 'older_woman':'\\ud83d\\udc75',\n 'om':'\\ud83d\\udd49',\n 'on':'\\ud83d\\udd1b',\n 'oncoming_automobile':'\\ud83d\\ude98',\n 'oncoming_bus':'\\ud83d\\ude8d',\n 'oncoming_police_car':'\\ud83d\\ude94',\n 'oncoming_taxi':'\\ud83d\\ude96',\n 'open_file_folder':'\\ud83d\\udcc2',\n 'open_hands':'\\ud83d\\udc50',\n 'open_mouth':'\\ud83d\\ude2e',\n 'open_umbrella':'\\u2602\\ufe0f',\n 'ophiuchus':'\\u26ce',\n 'orange_book':'\\ud83d\\udcd9',\n 'orthodox_cross':'\\u2626\\ufe0f',\n 'outbox_tray':'\\ud83d\\udce4',\n 'owl':'\\ud83e\\udd89',\n 'ox':'\\ud83d\\udc02',\n 'package':'\\ud83d\\udce6',\n 'page_facing_up':'\\ud83d\\udcc4',\n 'page_with_curl':'\\ud83d\\udcc3',\n 'pager':'\\ud83d\\udcdf',\n 'paintbrush':'\\ud83d\\udd8c',\n 'palm_tree':'\\ud83c\\udf34',\n 'pancakes':'\\ud83e\\udd5e',\n 'panda_face':'\\ud83d\\udc3c',\n 'paperclip':'\\ud83d\\udcce',\n 'paperclips':'\\ud83d\\udd87',\n 'parasol_on_ground':'\\u26f1',\n 'parking':'\\ud83c\\udd7f\\ufe0f',\n 'part_alternation_mark':'\\u303d\\ufe0f',\n 'partly_sunny':'\\u26c5\\ufe0f',\n 'passenger_ship':'\\ud83d\\udef3',\n 'passport_control':'\\ud83d\\udec2',\n 'pause_button':'\\u23f8',\n 'peace_symbol':'\\u262e\\ufe0f',\n 'peach':'\\ud83c\\udf51',\n 'peanuts':'\\ud83e\\udd5c',\n 'pear':'\\ud83c\\udf50',\n 'pen':'\\ud83d\\udd8a',\n 'pencil2':'\\u270f\\ufe0f',\n 'penguin':'\\ud83d\\udc27',\n 'pensive':'\\ud83d\\ude14',\n 'performing_arts':'\\ud83c\\udfad',\n 'persevere':'\\ud83d\\ude23',\n 'person_fencing':'\\ud83e\\udd3a',\n 'pouting_woman':'\\ud83d\\ude4e',\n 'phone':'\\u260e\\ufe0f',\n 'pick':'\\u26cf',\n 'pig':'\\ud83d\\udc37',\n 'pig2':'\\ud83d\\udc16',\n 'pig_nose':'\\ud83d\\udc3d',\n 'pill':'\\ud83d\\udc8a',\n 'pineapple':'\\ud83c\\udf4d',\n 'ping_pong':'\\ud83c\\udfd3',\n 'pisces':'\\u2653\\ufe0f',\n 'pizza':'\\ud83c\\udf55',\n 'place_of_worship':'\\ud83d\\uded0',\n 'plate_with_cutlery':'\\ud83c\\udf7d',\n 'play_or_pause_button':'\\u23ef',\n 'point_down':'\\ud83d\\udc47',\n 'point_left':'\\ud83d\\udc48',\n 'point_right':'\\ud83d\\udc49',\n 'point_up':'\\u261d\\ufe0f',\n 'point_up_2':'\\ud83d\\udc46',\n 'police_car':'\\ud83d\\ude93',\n 'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n 'poodle':'\\ud83d\\udc29',\n 'popcorn':'\\ud83c\\udf7f',\n 'post_office':'\\ud83c\\udfe3',\n 'postal_horn':'\\ud83d\\udcef',\n 'postbox':'\\ud83d\\udcee',\n 'potable_water':'\\ud83d\\udeb0',\n 'potato':'\\ud83e\\udd54',\n 'pouch':'\\ud83d\\udc5d',\n 'poultry_leg':'\\ud83c\\udf57',\n 'pound':'\\ud83d\\udcb7',\n 'rage':'\\ud83d\\ude21',\n 'pouting_cat':'\\ud83d\\ude3e',\n 'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n 'pray':'\\ud83d\\ude4f',\n 'prayer_beads':'\\ud83d\\udcff',\n 'pregnant_woman':'\\ud83e\\udd30',\n 'previous_track_button':'\\u23ee',\n 'prince':'\\ud83e\\udd34',\n 'princess':'\\ud83d\\udc78',\n 'printer':'\\ud83d\\udda8',\n 'purple_heart':'\\ud83d\\udc9c',\n 'purse':'\\ud83d\\udc5b',\n 'pushpin':'\\ud83d\\udccc',\n 'put_litter_in_its_place':'\\ud83d\\udeae',\n 'question':'\\u2753',\n 'rabbit':'\\ud83d\\udc30',\n 'rabbit2':'\\ud83d\\udc07',\n 'racehorse':'\\ud83d\\udc0e',\n 'racing_car':'\\ud83c\\udfce',\n 'radio':'\\ud83d\\udcfb',\n 'radio_button':'\\ud83d\\udd18',\n 'radioactive':'\\u2622\\ufe0f',\n 'railway_car':'\\ud83d\\ude83',\n 'railway_track':'\\ud83d\\udee4',\n 'rainbow':'\\ud83c\\udf08',\n 'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n 'raised_back_of_hand':'\\ud83e\\udd1a',\n 'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n 'raised_hands':'\\ud83d\\ude4c',\n 'raising_hand_woman':'\\ud83d\\ude4b',\n 'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n 'ram':'\\ud83d\\udc0f',\n 'ramen':'\\ud83c\\udf5c',\n 'rat':'\\ud83d\\udc00',\n 'record_button':'\\u23fa',\n 'recycle':'\\u267b\\ufe0f',\n 'red_circle':'\\ud83d\\udd34',\n 'registered':'\\u00ae\\ufe0f',\n 'relaxed':'\\u263a\\ufe0f',\n 'relieved':'\\ud83d\\ude0c',\n 'reminder_ribbon':'\\ud83c\\udf97',\n 'repeat':'\\ud83d\\udd01',\n 'repeat_one':'\\ud83d\\udd02',\n 'rescue_worker_helmet':'\\u26d1',\n 'restroom':'\\ud83d\\udebb',\n 'revolving_hearts':'\\ud83d\\udc9e',\n 'rewind':'\\u23ea',\n 'rhinoceros':'\\ud83e\\udd8f',\n 'ribbon':'\\ud83c\\udf80',\n 'rice':'\\ud83c\\udf5a',\n 'rice_ball':'\\ud83c\\udf59',\n 'rice_cracker':'\\ud83c\\udf58',\n 'rice_scene':'\\ud83c\\udf91',\n 'right_anger_bubble':'\\ud83d\\uddef',\n 'ring':'\\ud83d\\udc8d',\n 'robot':'\\ud83e\\udd16',\n 'rocket':'\\ud83d\\ude80',\n 'rofl':'\\ud83e\\udd23',\n 'roll_eyes':'\\ud83d\\ude44',\n 'roller_coaster':'\\ud83c\\udfa2',\n 'rooster':'\\ud83d\\udc13',\n 'rose':'\\ud83c\\udf39',\n 'rosette':'\\ud83c\\udff5',\n 'rotating_light':'\\ud83d\\udea8',\n 'round_pushpin':'\\ud83d\\udccd',\n 'rowing_man':'\\ud83d\\udea3',\n 'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n 'rugby_football':'\\ud83c\\udfc9',\n 'running_man':'\\ud83c\\udfc3',\n 'running_shirt_with_sash':'\\ud83c\\udfbd',\n 'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n 'sa':'\\ud83c\\ude02\\ufe0f',\n 'sagittarius':'\\u2650\\ufe0f',\n 'sake':'\\ud83c\\udf76',\n 'sandal':'\\ud83d\\udc61',\n 'santa':'\\ud83c\\udf85',\n 'satellite':'\\ud83d\\udce1',\n 'saxophone':'\\ud83c\\udfb7',\n 'school':'\\ud83c\\udfeb',\n 'school_satchel':'\\ud83c\\udf92',\n 'scissors':'\\u2702\\ufe0f',\n 'scorpion':'\\ud83e\\udd82',\n 'scorpius':'\\u264f\\ufe0f',\n 'scream':'\\ud83d\\ude31',\n 'scream_cat':'\\ud83d\\ude40',\n 'scroll':'\\ud83d\\udcdc',\n 'seat':'\\ud83d\\udcba',\n 'secret':'\\u3299\\ufe0f',\n 'see_no_evil':'\\ud83d\\ude48',\n 'seedling':'\\ud83c\\udf31',\n 'selfie':'\\ud83e\\udd33',\n 'shallow_pan_of_food':'\\ud83e\\udd58',\n 'shamrock':'\\u2618\\ufe0f',\n 'shark':'\\ud83e\\udd88',\n 'shaved_ice':'\\ud83c\\udf67',\n 'sheep':'\\ud83d\\udc11',\n 'shell':'\\ud83d\\udc1a',\n 'shield':'\\ud83d\\udee1',\n 'shinto_shrine':'\\u26e9',\n 'ship':'\\ud83d\\udea2',\n 'shirt':'\\ud83d\\udc55',\n 'shopping':'\\ud83d\\udecd',\n 'shopping_cart':'\\ud83d\\uded2',\n 'shower':'\\ud83d\\udebf',\n 'shrimp':'\\ud83e\\udd90',\n 'signal_strength':'\\ud83d\\udcf6',\n 'six_pointed_star':'\\ud83d\\udd2f',\n 'ski':'\\ud83c\\udfbf',\n 'skier':'\\u26f7',\n 'skull':'\\ud83d\\udc80',\n 'skull_and_crossbones':'\\u2620\\ufe0f',\n 'sleeping':'\\ud83d\\ude34',\n 'sleeping_bed':'\\ud83d\\udecc',\n 'sleepy':'\\ud83d\\ude2a',\n 'slightly_frowning_face':'\\ud83d\\ude41',\n 'slightly_smiling_face':'\\ud83d\\ude42',\n 'slot_machine':'\\ud83c\\udfb0',\n 'small_airplane':'\\ud83d\\udee9',\n 'small_blue_diamond':'\\ud83d\\udd39',\n 'small_orange_diamond':'\\ud83d\\udd38',\n 'small_red_triangle':'\\ud83d\\udd3a',\n 'small_red_triangle_down':'\\ud83d\\udd3b',\n 'smile':'\\ud83d\\ude04',\n 'smile_cat':'\\ud83d\\ude38',\n 'smiley':'\\ud83d\\ude03',\n 'smiley_cat':'\\ud83d\\ude3a',\n 'smiling_imp':'\\ud83d\\ude08',\n 'smirk':'\\ud83d\\ude0f',\n 'smirk_cat':'\\ud83d\\ude3c',\n 'smoking':'\\ud83d\\udeac',\n 'snail':'\\ud83d\\udc0c',\n 'snake':'\\ud83d\\udc0d',\n 'sneezing_face':'\\ud83e\\udd27',\n 'snowboarder':'\\ud83c\\udfc2',\n 'snowflake':'\\u2744\\ufe0f',\n 'snowman':'\\u26c4\\ufe0f',\n 'snowman_with_snow':'\\u2603\\ufe0f',\n 'sob':'\\ud83d\\ude2d',\n 'soccer':'\\u26bd\\ufe0f',\n 'soon':'\\ud83d\\udd1c',\n 'sos':'\\ud83c\\udd98',\n 'sound':'\\ud83d\\udd09',\n 'space_invader':'\\ud83d\\udc7e',\n 'spades':'\\u2660\\ufe0f',\n 'spaghetti':'\\ud83c\\udf5d',\n 'sparkle':'\\u2747\\ufe0f',\n 'sparkler':'\\ud83c\\udf87',\n 'sparkles':'\\u2728',\n 'sparkling_heart':'\\ud83d\\udc96',\n 'speak_no_evil':'\\ud83d\\ude4a',\n 'speaker':'\\ud83d\\udd08',\n 'speaking_head':'\\ud83d\\udde3',\n 'speech_balloon':'\\ud83d\\udcac',\n 'speedboat':'\\ud83d\\udea4',\n 'spider':'\\ud83d\\udd77',\n 'spider_web':'\\ud83d\\udd78',\n 'spiral_calendar':'\\ud83d\\uddd3',\n 'spiral_notepad':'\\ud83d\\uddd2',\n 'spoon':'\\ud83e\\udd44',\n 'squid':'\\ud83e\\udd91',\n 'stadium':'\\ud83c\\udfdf',\n 'star':'\\u2b50\\ufe0f',\n 'star2':'\\ud83c\\udf1f',\n 'star_and_crescent':'\\u262a\\ufe0f',\n 'star_of_david':'\\u2721\\ufe0f',\n 'stars':'\\ud83c\\udf20',\n 'station':'\\ud83d\\ude89',\n 'statue_of_liberty':'\\ud83d\\uddfd',\n 'steam_locomotive':'\\ud83d\\ude82',\n 'stew':'\\ud83c\\udf72',\n 'stop_button':'\\u23f9',\n 'stop_sign':'\\ud83d\\uded1',\n 'stopwatch':'\\u23f1',\n 'straight_ruler':'\\ud83d\\udccf',\n 'strawberry':'\\ud83c\\udf53',\n 'stuck_out_tongue':'\\ud83d\\ude1b',\n 'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n 'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n 'studio_microphone':'\\ud83c\\udf99',\n 'stuffed_flatbread':'\\ud83e\\udd59',\n 'sun_behind_large_cloud':'\\ud83c\\udf25',\n 'sun_behind_rain_cloud':'\\ud83c\\udf26',\n 'sun_behind_small_cloud':'\\ud83c\\udf24',\n 'sun_with_face':'\\ud83c\\udf1e',\n 'sunflower':'\\ud83c\\udf3b',\n 'sunglasses':'\\ud83d\\ude0e',\n 'sunny':'\\u2600\\ufe0f',\n 'sunrise':'\\ud83c\\udf05',\n 'sunrise_over_mountains':'\\ud83c\\udf04',\n 'surfing_man':'\\ud83c\\udfc4',\n 'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n 'sushi':'\\ud83c\\udf63',\n 'suspension_railway':'\\ud83d\\ude9f',\n 'sweat':'\\ud83d\\ude13',\n 'sweat_drops':'\\ud83d\\udca6',\n 'sweat_smile':'\\ud83d\\ude05',\n 'sweet_potato':'\\ud83c\\udf60',\n 'swimming_man':'\\ud83c\\udfca',\n 'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n 'symbols':'\\ud83d\\udd23',\n 'synagogue':'\\ud83d\\udd4d',\n 'syringe':'\\ud83d\\udc89',\n 'taco':'\\ud83c\\udf2e',\n 'tada':'\\ud83c\\udf89',\n 'tanabata_tree':'\\ud83c\\udf8b',\n 'taurus':'\\u2649\\ufe0f',\n 'taxi':'\\ud83d\\ude95',\n 'tea':'\\ud83c\\udf75',\n 'telephone_receiver':'\\ud83d\\udcde',\n 'telescope':'\\ud83d\\udd2d',\n 'tennis':'\\ud83c\\udfbe',\n 'tent':'\\u26fa\\ufe0f',\n 'thermometer':'\\ud83c\\udf21',\n 'thinking':'\\ud83e\\udd14',\n 'thought_balloon':'\\ud83d\\udcad',\n 'ticket':'\\ud83c\\udfab',\n 'tickets':'\\ud83c\\udf9f',\n 'tiger':'\\ud83d\\udc2f',\n 'tiger2':'\\ud83d\\udc05',\n 'timer_clock':'\\u23f2',\n 'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n 'tired_face':'\\ud83d\\ude2b',\n 'tm':'\\u2122\\ufe0f',\n 'toilet':'\\ud83d\\udebd',\n 'tokyo_tower':'\\ud83d\\uddfc',\n 'tomato':'\\ud83c\\udf45',\n 'tongue':'\\ud83d\\udc45',\n 'top':'\\ud83d\\udd1d',\n 'tophat':'\\ud83c\\udfa9',\n 'tornado':'\\ud83c\\udf2a',\n 'trackball':'\\ud83d\\uddb2',\n 'tractor':'\\ud83d\\ude9c',\n 'traffic_light':'\\ud83d\\udea5',\n 'train':'\\ud83d\\ude8b',\n 'train2':'\\ud83d\\ude86',\n 'tram':'\\ud83d\\ude8a',\n 'triangular_flag_on_post':'\\ud83d\\udea9',\n 'triangular_ruler':'\\ud83d\\udcd0',\n 'trident':'\\ud83d\\udd31',\n 'triumph':'\\ud83d\\ude24',\n 'trolleybus':'\\ud83d\\ude8e',\n 'trophy':'\\ud83c\\udfc6',\n 'tropical_drink':'\\ud83c\\udf79',\n 'tropical_fish':'\\ud83d\\udc20',\n 'truck':'\\ud83d\\ude9a',\n 'trumpet':'\\ud83c\\udfba',\n 'tulip':'\\ud83c\\udf37',\n 'tumbler_glass':'\\ud83e\\udd43',\n 'turkey':'\\ud83e\\udd83',\n 'turtle':'\\ud83d\\udc22',\n 'tv':'\\ud83d\\udcfa',\n 'twisted_rightwards_arrows':'\\ud83d\\udd00',\n 'two_hearts':'\\ud83d\\udc95',\n 'two_men_holding_hands':'\\ud83d\\udc6c',\n 'two_women_holding_hands':'\\ud83d\\udc6d',\n 'u5272':'\\ud83c\\ude39',\n 'u5408':'\\ud83c\\ude34',\n 'u55b6':'\\ud83c\\ude3a',\n 'u6307':'\\ud83c\\ude2f\\ufe0f',\n 'u6708':'\\ud83c\\ude37\\ufe0f',\n 'u6709':'\\ud83c\\ude36',\n 'u6e80':'\\ud83c\\ude35',\n 'u7121':'\\ud83c\\ude1a\\ufe0f',\n 'u7533':'\\ud83c\\ude38',\n 'u7981':'\\ud83c\\ude32',\n 'u7a7a':'\\ud83c\\ude33',\n 'umbrella':'\\u2614\\ufe0f',\n 'unamused':'\\ud83d\\ude12',\n 'underage':'\\ud83d\\udd1e',\n 'unicorn':'\\ud83e\\udd84',\n 'unlock':'\\ud83d\\udd13',\n 'up':'\\ud83c\\udd99',\n 'upside_down_face':'\\ud83d\\ude43',\n 'v':'\\u270c\\ufe0f',\n 'vertical_traffic_light':'\\ud83d\\udea6',\n 'vhs':'\\ud83d\\udcfc',\n 'vibration_mode':'\\ud83d\\udcf3',\n 'video_camera':'\\ud83d\\udcf9',\n 'video_game':'\\ud83c\\udfae',\n 'violin':'\\ud83c\\udfbb',\n 'virgo':'\\u264d\\ufe0f',\n 'volcano':'\\ud83c\\udf0b',\n 'volleyball':'\\ud83c\\udfd0',\n 'vs':'\\ud83c\\udd9a',\n 'vulcan_salute':'\\ud83d\\udd96',\n 'walking_man':'\\ud83d\\udeb6',\n 'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n 'waning_crescent_moon':'\\ud83c\\udf18',\n 'waning_gibbous_moon':'\\ud83c\\udf16',\n 'warning':'\\u26a0\\ufe0f',\n 'wastebasket':'\\ud83d\\uddd1',\n 'watch':'\\u231a\\ufe0f',\n 'water_buffalo':'\\ud83d\\udc03',\n 'watermelon':'\\ud83c\\udf49',\n 'wave':'\\ud83d\\udc4b',\n 'wavy_dash':'\\u3030\\ufe0f',\n 'waxing_crescent_moon':'\\ud83c\\udf12',\n 'wc':'\\ud83d\\udebe',\n 'weary':'\\ud83d\\ude29',\n 'wedding':'\\ud83d\\udc92',\n 'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n 'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n 'whale':'\\ud83d\\udc33',\n 'whale2':'\\ud83d\\udc0b',\n 'wheel_of_dharma':'\\u2638\\ufe0f',\n 'wheelchair':'\\u267f\\ufe0f',\n 'white_check_mark':'\\u2705',\n 'white_circle':'\\u26aa\\ufe0f',\n 'white_flag':'\\ud83c\\udff3\\ufe0f',\n 'white_flower':'\\ud83d\\udcae',\n 'white_large_square':'\\u2b1c\\ufe0f',\n 'white_medium_small_square':'\\u25fd\\ufe0f',\n 'white_medium_square':'\\u25fb\\ufe0f',\n 'white_small_square':'\\u25ab\\ufe0f',\n 'white_square_button':'\\ud83d\\udd33',\n 'wilted_flower':'\\ud83e\\udd40',\n 'wind_chime':'\\ud83c\\udf90',\n 'wind_face':'\\ud83c\\udf2c',\n 'wine_glass':'\\ud83c\\udf77',\n 'wink':'\\ud83d\\ude09',\n 'wolf':'\\ud83d\\udc3a',\n 'woman':'\\ud83d\\udc69',\n 'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n 'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n 'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n 'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n 'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n 'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n 'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n 'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n 'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n 'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n 'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n 'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n 'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n 'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n 'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n 'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n 'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n 'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n 'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n 'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n 'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n 'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n 'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n 'womans_clothes':'\\ud83d\\udc5a',\n 'womans_hat':'\\ud83d\\udc52',\n 'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n 'womens':'\\ud83d\\udeba',\n 'world_map':'\\ud83d\\uddfa',\n 'worried':'\\ud83d\\ude1f',\n 'wrench':'\\ud83d\\udd27',\n 'writing_hand':'\\u270d\\ufe0f',\n 'x':'\\u274c',\n 'yellow_heart':'\\ud83d\\udc9b',\n 'yen':'\\ud83d\\udcb4',\n 'yin_yang':'\\u262f\\ufe0f',\n 'yum':'\\ud83d\\ude0b',\n 'zap':'\\u26a1\\ufe0f',\n 'zipper_mouth_face':'\\ud83e\\udd10',\n 'zzz':'\\ud83d\\udca4',\n\n /* special emojis :P */\n 'octocat': '\":octocat:\"',\n 'showdown': 'S'\n};\n","/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n 'use strict';\n\n var\n /**\n * Options used by this converter\n * @private\n * @type {{}}\n */\n options = {},\n\n /**\n * Language extensions used by this converter\n * @private\n * @type {Array}\n */\n langExtensions = [],\n\n /**\n * Output modifiers extensions used by this converter\n * @private\n * @type {Array}\n */\n outputModifiers = [],\n\n /**\n * Event listeners\n * @private\n * @type {{}}\n */\n listeners = {},\n\n /**\n * The flavor set in this converter\n */\n setConvFlavor = setFlavor,\n\n /**\n * Metadata of the document\n * @type {{parsed: {}, raw: string, format: string}}\n */\n metadata = {\n parsed: {},\n raw: '',\n format: ''\n };\n\n _constructor();\n\n /**\n * Converter constructor\n * @private\n */\n function _constructor () {\n converterOptions = converterOptions || {};\n\n for (var gOpt in globalOptions) {\n if (globalOptions.hasOwnProperty(gOpt)) {\n options[gOpt] = globalOptions[gOpt];\n }\n }\n\n // Merge options\n if (typeof converterOptions === 'object') {\n for (var opt in converterOptions) {\n if (converterOptions.hasOwnProperty(opt)) {\n options[opt] = converterOptions[opt];\n }\n }\n } else {\n throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n ' was passed instead.');\n }\n\n if (options.extensions) {\n showdown.helper.forEach(options.extensions, _parseExtension);\n }\n }\n\n /**\n * Parse extension\n * @param {*} ext\n * @param {string} [name='']\n * @private\n */\n function _parseExtension (ext, name) {\n\n name = name || null;\n // If it's a string, the extension was previously loaded\n if (showdown.helper.isString(ext)) {\n ext = showdown.helper.stdExtName(ext);\n name = ext;\n\n // LEGACY_SUPPORT CODE\n if (showdown.extensions[ext]) {\n console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n 'Please inform the developer that the extension should be updated!');\n legacyExtensionLoading(showdown.extensions[ext], ext);\n return;\n // END LEGACY SUPPORT CODE\n\n } else if (!showdown.helper.isUndefined(extensions[ext])) {\n ext = extensions[ext];\n\n } else {\n throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n }\n }\n\n if (typeof ext === 'function') {\n ext = ext();\n }\n\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n\n var validExt = validate(ext, name);\n if (!validExt.valid) {\n throw Error(validExt.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n }\n if (ext[i].hasOwnProperty('listeners')) {\n for (var ln in ext[i].listeners) {\n if (ext[i].listeners.hasOwnProperty(ln)) {\n listen(ln, ext[i].listeners[ln]);\n }\n }\n }\n }\n\n }\n\n /**\n * LEGACY_SUPPORT\n * @param {*} ext\n * @param {string} name\n */\n function legacyExtensionLoading (ext, name) {\n if (typeof ext === 'function') {\n ext = ext(new showdown.Converter());\n }\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n var valid = validate(ext, name);\n\n if (!valid.valid) {\n throw Error(valid.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n default:// should never reach here\n throw Error('Extension loader error: Type unrecognized!!!');\n }\n }\n }\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n */\n function listen (name, callback) {\n if (!showdown.helper.isString(name)) {\n throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n }\n\n if (typeof callback !== 'function') {\n throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n }\n\n if (!listeners.hasOwnProperty(name)) {\n listeners[name] = [];\n }\n listeners[name].push(callback);\n }\n\n function rTrimInputText (text) {\n var rsp = text.match(/^\\s*/)[0].length,\n rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n return text.replace(rgx, '');\n }\n\n /**\n * Dispatch an event\n * @private\n * @param {string} evtName Event name\n * @param {string} text Text\n * @param {{}} options Converter Options\n * @param {{}} globals\n * @returns {string}\n */\n this._dispatch = function dispatch (evtName, text, options, globals) {\n if (listeners.hasOwnProperty(evtName)) {\n for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n if (nText && typeof nText !== 'undefined') {\n text = nText;\n }\n }\n }\n return text;\n };\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n * @returns {showdown.Converter}\n */\n this.listen = function (name, callback) {\n listen(name, callback);\n return this;\n };\n\n /**\n * Converts a markdown string into HTML\n * @param {string} text\n * @returns {*}\n */\n this.makeHtml = function (text) {\n //check if text is not falsy\n if (!text) {\n return text;\n }\n\n var globals = {\n gHtmlBlocks: [],\n gHtmlMdBlocks: [],\n gHtmlSpans: [],\n gUrls: {},\n gTitles: {},\n gDimensions: {},\n gListLevel: 0,\n hashLinkCounts: {},\n langExtensions: langExtensions,\n outputModifiers: outputModifiers,\n converter: this,\n ghCodeBlocks: [],\n metadata: {\n parsed: {},\n raw: '',\n format: ''\n }\n };\n\n // This lets us use ¨ trema as an escape char to avoid md5 hashes\n // The choice of character is arbitrary; anything that isn't\n // magic in Markdown will work.\n text = text.replace(/¨/g, '¨T');\n\n // Replace $ with ¨D\n // RegExp interprets $ as a special character\n // when it's in a replacement string\n text = text.replace(/\\$/g, '¨D');\n\n // Standardize line endings\n text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n // Stardardize line spaces\n text = text.replace(/\\u00A0/g, ' ');\n\n if (options.smartIndentationFix) {\n text = rTrimInputText(text);\n }\n\n // Make sure text begins and ends with a couple of newlines:\n text = '\\n\\n' + text + '\\n\\n';\n\n // detab\n text = showdown.subParser('detab')(text, options, globals);\n\n /**\n * Strip any lines consisting only of spaces and tabs.\n * This makes subsequent regexs easier to write, because we can\n * match consecutive blank lines with /\\n+/ instead of something\n * contorted like /[ \\t]*\\n+/\n */\n text = text.replace(/^[ \\t]+$/mg, '');\n\n //run languageExtensions\n showdown.helper.forEach(langExtensions, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // run the sub parsers\n text = showdown.subParser('metadata')(text, options, globals);\n text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('hashCodeTags')(text, options, globals);\n text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n text = showdown.subParser('blockGamut')(text, options, globals);\n text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n // attacklab: Restore dollar signs\n text = text.replace(/¨D/g, '$$');\n\n // attacklab: Restore tremas\n text = text.replace(/¨T/g, '¨');\n\n // render a complete html document instead of a partial if the option is enabled\n text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n // Run output modifiers\n showdown.helper.forEach(outputModifiers, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // update metadata\n metadata = globals.metadata;\n return text;\n };\n\n /**\n * Converts an HTML string into a markdown string\n * @param src\n * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n * @returns {string}\n */\n this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n // replace \\r\\n with \\n\n src = src.replace(/\\r\\n/g, '\\n');\n src = src.replace(/\\r/g, '\\n'); // old macs\n\n // due to an edge case, we need to find this: > <\n // to prevent removing of non silent white spaces\n // ex: this is sparta\n src = src.replace(/>[ \\t]+¨NBSP;<');\n\n if (!HTMLParser) {\n if (window && window.document) {\n HTMLParser = window.document;\n } else {\n throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n }\n }\n\n var doc = HTMLParser.createElement('div');\n doc.innerHTML = src;\n\n var globals = {\n preList: substitutePreCodeTags(doc)\n };\n\n // remove all newlines and collapse spaces\n clean(doc);\n\n // some stuff, like accidental reference links must now be escaped\n // TODO\n // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n var nodes = doc.childNodes,\n mdDoc = '';\n\n for (var i = 0; i < nodes.length; i++) {\n mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n }\n\n function clean (node) {\n for (var n = 0; n < node.childNodes.length; ++n) {\n var child = node.childNodes[n];\n if (child.nodeType === 3) {\n if (!/\\S/.test(child.nodeValue)) {\n node.removeChild(child);\n --n;\n } else {\n child.nodeValue = child.nodeValue.split('\\n').join(' ');\n child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n }\n } else if (child.nodeType === 1) {\n clean(child);\n }\n }\n }\n\n // find all pre tags and replace contents with placeholder\n // we need this so that we can remove all indentation from html\n // to ease up parsing\n function substitutePreCodeTags (doc) {\n\n var pres = doc.querySelectorAll('pre'),\n presPH = [];\n\n for (var i = 0; i < pres.length; ++i) {\n\n if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n var content = pres[i].firstChild.innerHTML.trim(),\n language = pres[i].firstChild.getAttribute('data-language') || '';\n\n // if data-language attribute is not defined, then we look for class language-*\n if (language === '') {\n var classes = pres[i].firstChild.className.split(' ');\n for (var c = 0; c < classes.length; ++c) {\n var matches = classes[c].match(/^language-(.+)$/);\n if (matches !== null) {\n language = matches[1];\n break;\n }\n }\n }\n\n // unescape html entities in content\n content = showdown.helper.unescapeHTMLEntities(content);\n\n presPH.push(content);\n pres[i].outerHTML = '';\n } else {\n presPH.push(pres[i].innerHTML);\n pres[i].innerHTML = '';\n pres[i].setAttribute('prenum', i.toString());\n }\n }\n return presPH;\n }\n\n return mdDoc;\n };\n\n /**\n * Set an option of this Converter instance\n * @param {string} key\n * @param {*} value\n */\n this.setOption = function (key, value) {\n options[key] = value;\n };\n\n /**\n * Get the option of this Converter instance\n * @param {string} key\n * @returns {*}\n */\n this.getOption = function (key) {\n return options[key];\n };\n\n /**\n * Get the options of this Converter instance\n * @returns {{}}\n */\n this.getOptions = function () {\n return options;\n };\n\n /**\n * Add extension to THIS converter\n * @param {{}} extension\n * @param {string} [name=null]\n */\n this.addExtension = function (extension, name) {\n name = name || null;\n _parseExtension(extension, name);\n };\n\n /**\n * Use a global registered extension with THIS converter\n * @param {string} extensionName Name of the previously registered extension\n */\n this.useExtension = function (extensionName) {\n _parseExtension(extensionName);\n };\n\n /**\n * Set the flavor THIS converter should use\n * @param {string} name\n */\n this.setFlavor = function (name) {\n if (!flavor.hasOwnProperty(name)) {\n throw Error(name + ' flavor was not found');\n }\n var preset = flavor[name];\n setConvFlavor = name;\n for (var option in preset) {\n if (preset.hasOwnProperty(option)) {\n options[option] = preset[option];\n }\n }\n };\n\n /**\n * Get the currently set flavor of this converter\n * @returns {string}\n */\n this.getFlavor = function () {\n return setConvFlavor;\n };\n\n /**\n * Remove an extension from THIS converter.\n * Note: This is a costly operation. It's better to initialize a new converter\n * and specify the extensions you wish to use\n * @param {Array} extension\n */\n this.removeExtension = function (extension) {\n if (!showdown.helper.isArray(extension)) {\n extension = [extension];\n }\n for (var a = 0; a < extension.length; ++a) {\n var ext = extension[a];\n for (var i = 0; i < langExtensions.length; ++i) {\n if (langExtensions[i] === ext) {\n langExtensions[i].splice(i, 1);\n }\n }\n for (var ii = 0; ii < outputModifiers.length; ++i) {\n if (outputModifiers[ii] === ext) {\n outputModifiers[ii].splice(i, 1);\n }\n }\n }\n };\n\n /**\n * Get all extension of THIS converter\n * @returns {{language: Array, output: Array}}\n */\n this.getAllExtensions = function () {\n return {\n language: langExtensions,\n output: outputModifiers\n };\n };\n\n /**\n * Get the metadata of the previously parsed document\n * @param raw\n * @returns {string|{}}\n */\n this.getMetadata = function (raw) {\n if (raw) {\n return metadata.raw;\n } else {\n return metadata.parsed;\n }\n };\n\n /**\n * Get the metadata format of the previously parsed document\n * @returns {string}\n */\n this.getMetadataFormat = function () {\n return metadata.format;\n };\n\n /**\n * Private: set a single key, value metadata pair\n * @param {string} key\n * @param {string} value\n */\n this._setMetadataPair = function (key, value) {\n metadata.parsed[key] = value;\n };\n\n /**\n * Private: set metadata format\n * @param {string} format\n */\n this._setMetadataFormat = function (format) {\n metadata.format = format;\n };\n\n /**\n * Private: set metadata raw text\n * @param {string} raw\n */\n this._setMetadataRaw = function (raw) {\n metadata.raw = raw;\n };\n};\n","/**\n * Turn Markdown link shortcuts into XHTML tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n if (showdown.helper.isUndefined(title)) {\n title = '';\n }\n linkId = linkId.toLowerCase();\n\n // Special case for explicit empty url\n if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n url = '';\n } else if (!url) {\n if (!linkId) {\n // lower-case and turn embedded newlines into spaces\n linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n }\n url = '#' + linkId;\n\n if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n url = globals.gUrls[linkId];\n if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n title = globals.gTitles[linkId];\n }\n } else {\n return wholeMatch;\n }\n }\n\n //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n var result = '';\n\n return result;\n };\n\n // First, handle reference-style links: [link text] [id]\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n // Next, inline-style links: [link text](url \"optional title\")\n // cases with crazy urls like ./image/cat1).png\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n writeAnchorTag);\n\n // normal cases\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n writeAnchorTag);\n\n // handle reference-style shortcuts: [link text]\n // These must come last in case you've also got [link test][1]\n // or [link test](/foo)\n text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n // Lastly handle GithubMentions if option is enabled\n if (options.ghMentions) {\n text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n if (escape === '\\\\') {\n return st + mentions;\n }\n\n //check if options.ghMentionsLink is a string\n if (!showdown.helper.isString(options.ghMentionsLink)) {\n throw new Error('ghMentionsLink option must be a string');\n }\n var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n target = '';\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return st + '' + mentions + '';\n });\n }\n\n text = globals.converter._dispatch('anchors.after', text, options, globals);\n return text;\n});\n","// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n delimUrlRegex = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n delimMailRegex = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n replaceLink = function (options) {\n 'use strict';\n return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n var lnkTxt = link,\n append = '',\n target = '',\n lmc = leadingMagicChars || '',\n tmc = trailingMagicChars || '';\n if (/^www\\./i.test(link)) {\n link = link.replace(/^www\\./i, 'http://www.');\n }\n if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n append = trailingPunctuation;\n }\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return lmc + '' + lnkTxt + '' + append + tmc;\n };\n },\n\n replaceMail = function (options, globals) {\n 'use strict';\n return function (wholeMatch, b, mail) {\n var href = 'mailto:';\n b = b || '';\n mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n if (options.encodeEmails) {\n href = showdown.helper.encodeEmailAddress(href + mail);\n mail = showdown.helper.encodeEmailAddress(mail);\n } else {\n href = href + mail;\n }\n return b + '' + mail + '';\n };\n };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n text = text.replace(delimUrlRegex, replaceLink(options));\n text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n 'use strict';\n\n if (!options.simplifiedAutoLink) {\n return text;\n }\n\n text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n if (options.excludeTrailingPunctuationFromURLs) {\n text = text.replace(simpleURLRegex2, replaceLink(options));\n } else {\n text = text.replace(simpleURLRegex, replaceLink(options));\n }\n text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n return text;\n});\n","/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n // we parse blockquotes first so that we can have headings and hrs\n // inside blockquotes\n text = showdown.subParser('blockQuotes')(text, options, globals);\n text = showdown.subParser('headers')(text, options, globals);\n\n // Do Horizontal Rules:\n text = showdown.subParser('horizontalRule')(text, options, globals);\n\n text = showdown.subParser('lists')(text, options, globals);\n text = showdown.subParser('codeBlocks')(text, options, globals);\n text = showdown.subParser('tables')(text, options, globals);\n\n // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n // was to escape raw HTML in the original Markdown source. This time,\n // we're escaping the markup we've just created, so that we don't wrap\n //

tags around block-level tags.\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('paragraphs')(text, options, globals);\n\n text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n return text;\n});\n","showdown.subParser('blockQuotes', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n // add a couple extra lines after the text and endtext mark\n text = text + '\\n\\n';\n\n var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n if (options.splitAdjacentBlockquotes) {\n rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n }\n\n text = text.replace(rgx, function (bq) {\n // attacklab: hack around Konqueror 3.5.4 bug:\n // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n // attacklab: clean up hack\n bq = bq.replace(/¨0/g, '');\n\n bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n bq = bq.replace(/(^|\\n)/g, '$1 ');\n // These leading spaces screw with 

 content, so we need to fix that:\n    bq = bq.replace(/(\\s*
[^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
\\n' + bq + '\\n
', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n","/**\n * Process Markdown `
` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
' + codeblock + end + '
';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
Just type foo `bar` baz at the prompt.
\n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n","/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n","/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n","/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n","/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n","/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
' + codeblock + end + '
';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n","showdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n","showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape 
 elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
\n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n","/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n","/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n","/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n","/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n","/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n","/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n","/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n","showdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n","showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n","showdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n","showdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n","showdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n","showdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n","\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
    ' + globals.preList[num] + '
    ';\n});\n","showdown.subParser('makeMarkdown.strikethrough', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '~~';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '~~';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.strong', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '**';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '**';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.table', function (node, globals) {\n  'use strict';\n\n  var txt = '',\n      tableArray = [[], []],\n      headings   = node.querySelectorAll('thead>tr>th'),\n      rows       = node.querySelectorAll('tbody>tr'),\n      i, ii;\n  for (i = 0; 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diff --git a/docs/route-vldigeometria.chunk.1a7b6.esm.js b/docs/route-vldigeometria.chunk.76957.esm.js
similarity index 98%
rename from docs/route-vldigeometria.chunk.1a7b6.esm.js
rename to docs/route-vldigeometria.chunk.76957.esm.js
index 0b3234b..51ee20e 100644
--- a/docs/route-vldigeometria.chunk.1a7b6.esm.js
+++ b/docs/route-vldigeometria.chunk.76957.esm.js
@@ -1,5 +1,5 @@
-/*! For license information please see route-vldigeometria.chunk.1a7b6.esm.js.LICENSE.txt */
-(window.webpackJsonp=window.webpackJsonp||[]).push([[11],{"1nLj":function(e){e.exports={panel:"panel__1ubJw"}},"9yVG":function(e,r,t){"use strict";(function(e){t.d(r,"a",(function(){return o}));var a=t("1nLj"),n=t.n(a),s=t("hosL");class o extends s.Component{getStyle(){return n.a.panel}render(){let r=null;return void 0!==this.props.title&&(r=e("h3",null,this.props.title)),e("div",{class:this.getStyle(),id:this.props.id},r,this.props.children)}}}).call(this,t("hosL").h)},CoLn:function(e,r,t){"use strict";(function(e){t.d(r,"a",(function(){return l}));var a=t("DUL8"),n=t.n(a),s=t("hosL"),o=t("W7OS"),i=t.n(o);class l extends s.Component{render(){let r=new i.a.Converter;r.setFlavor("github");let t=r.makeHtml(`${this.props.children}`);return e("div",{style:n.a.markdown,dangerouslySetInnerHTML:{__html:t}})}}}).call(this,t("hosL").h)},DUL8:function(e){e.exports={markdown:"markdown__bh-kq"}},QBAg:function(e,r,t){"use strict";t.r(r),function(e){t.d(r,"default",(function(){return c}));var a=t("hosL"),n=t("CoLn"),s=t("9yVG");let o,i=e=>e;const l=String.raw;class c extends a.Component{render(){return e("div",null,e("h1",null,"Videolezioni di Geometria"),e(s.a,null,e(n.a,null,l(o||(o=i`
+/*! For license information please see route-vldigeometria.chunk.76957.esm.js.LICENSE.txt */
+(window.webpackJsonp=window.webpackJsonp||[]).push([[11],{"+Hx3":function(e){e.exports={markdown:"markdown__3Wgu1"}},HKwK:function(e,r,t){"use strict";(function(e){t.d(r,"a",(function(){return o}));var a=t("r4EX"),n=t.n(a),s=t("hosL");class o extends s.Component{getStyle(){return n.a.panel}render(){let r=null;return void 0!==this.props.title&&(r=e("h3",null,this.props.title)),e("div",{class:this.getStyle(),id:this.props.id},r,this.props.children)}}}).call(this,t("hosL").h)},QBAg:function(e,r,t){"use strict";t.r(r),function(e){t.d(r,"default",(function(){return c}));var a=t("hosL"),n=t("wLsy"),s=t("HKwK");let o,i=e=>e;const l=String.raw;class c extends a.Component{render(){return e("div",null,e("h1",null,"Videolezioni di Geometria"),e(s.a,null,e(n.a,null,l(o||(o=i`
 Tutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).
 
 Per comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.
@@ -33,5 +33,5 @@ Per comodità, ho estratto l'url sorgente del video dall'embed presente nella ri
 27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)
 
 Nell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.
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",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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e}}),i.helper.regexes={asteriskDashAndColon:/([*_:~])/g},i.helper.emojis={"+1":"👍","-1":"👎",100:"💯",1234:"🔢","1st_place_medal":"🥇","2nd_place_medal":"🥈","3rd_place_medal":"🥉","8ball":"🎱",a:"🅰️",ab:"🆎",abc:"🔤",abcd:"🔡",accept:"🉑",aerial_tramway:"🚡",airplane:"✈️",alarm_clock:"⏰",alembic:"⚗️",alien:"👽",ambulance:"🚑",amphora:"🏺",anchor:"⚓️",angel:"👼",anger:"💢",angry:"😠",anguished:"😧",ant:"🐜",apple:"🍎",aquarius:"♒️",aries:"♈️",arrow_backward:"◀️",arrow_double_down:"⏬",arrow_double_up:"⏫",arrow_down:"⬇️",arrow_down_small:"🔽",arrow_forward:"▶️",arrow_heading_down:"⤵️",arrow_heading_up:"⤴️",arrow_left:"⬅️",arrow_lower_left:"↙️",arrow_lower_right:"↘️",arrow_right:"➡️",arrow_right_hook:"↪️",arrow_up:"⬆️",arrow_up_down:"↕️",arrow_up_small:"🔼",arrow_upper_left:"↖️",arrow_upper_right:"↗️",arrows_clockwise:"🔃",arrows_counterclockwise:"🔄",art:"🎨",articulated_lorry:"🚛",artificial_satellite:"🛰",astonished:"😲",athletic_shoe:"👟",atm:"🏧",atom_symbol:"⚛️",avocado:"🥑",b:"🅱️",baby:"👶",baby_bottle:"🍼",baby_chick:"🐤",baby_symbol:"🚼",back:"🔙",bacon:"🥓",badminton:"🏸",baggage_claim:"🛄",baguette_bread:"🥖",balance_scale:"⚖️",balloon:"🎈",ballot_box:"🗳",ballot_box_with_check:"☑️",bamboo:"🎍",banana:"🍌",bangbang:"‼️",bank:"🏦",bar_chart:"📊",barber:"💈",baseball:"⚾️",basketball:"🏀",basketball_man:"⛹️",basketball_woman:"⛹️‍♀️",bat:"🦇",bath:"🛀",bathtub:"🛁",battery:"🔋",beach_umbrella:"🏖",bear:"🐻",bed:"🛏",bee:"🐝",beer:"🍺",beers:"🍻",beetle:"🐞",beginner:"🔰",bell:"🔔",bellhop_bell:"🛎",bento:"🍱",biking_man:"🚴",bike:"🚲",biking_woman:"🚴‍♀️",bikini:"👙",biohazard:"☣️",bird:"🐦",birthday:"🎂",black_circle:"⚫️",black_flag:"🏴",black_heart:"🖤",black_joker:"🃏",black_large_square:"⬛️",black_medium_small_square:"◾️",black_medium_square:"◼️",black_nib:"✒️",black_small_square:"▪️",black_square_button:"🔲",blonde_man:"👱",blonde_woman:"👱‍♀️",blossom:"🌼",blowfish:"🐡",blue_book:"📘",blue_car:"🚙",blue_heart:"💙",blush:"😊",boar:"🐗",boat:"⛵️",bomb:"💣",book:"📖",bookmark:"🔖",bookmark_tabs:"📑",books:"📚",boom:"💥",boot:"👢",bouquet:"💐",bowing_man:"🙇",bow_and_arrow:"🏹",bowing_woman:"🙇‍♀️",bowling:"🎳",boxing_glove:"🥊",boy:"👦",bread:"🍞",bride_with_veil:"👰",bridge_at_night:"🌉",briefcase:"💼",broken_heart:"💔",bug:"🐛",building_construction:"🏗",bulb:"💡",bullettrain_front:"🚅",bullettrain_side:"🚄",burrito:"🌯",bus:"🚌",business_suit_levitating:"🕴",busstop:"🚏",bust_in_silhouette:"👤",busts_in_silhouette:"👥",butterfly:"🦋",cactus:"🌵",cake:"🍰",calendar:"📆",call_me_hand:"🤙",calling:"📲",camel:"🐫",camera:"📷",camera_flash:"📸",camping:"🏕",cancer:"♋️",candle:"🕯",candy:"🍬",canoe:"🛶",capital_abcd:"🔠",capricorn:"♑️",car:"🚗",card_file_box:"🗃",card_index:"📇",card_index_dividers:"🗂",carousel_horse:"🎠",carrot:"🥕",cat:"🐱",cat2:"🐈",cd:"💿",chains:"⛓",champagne:"🍾",chart:"💹",chart_with_downwards_trend:"📉",chart_with_upwards_trend:"📈",checkered_flag:"🏁",cheese:"🧀",cherries:"🍒",cherry_blossom:"🌸",chestnut:"🌰",chicken:"🐔",children_crossing:"🚸",chipmunk:"🐿",chocolate_bar:"🍫",christmas_tree:"🎄",church:"⛪️",cinema:"🎦",circus_tent:"🎪",city_sunrise:"🌇",city_sunset:"🌆",cityscape:"🏙",cl:"🆑",clamp:"🗜",clap:"👏",clapper:"🎬",classical_building:"🏛",clinking_glasses:"🥂",clipboard:"📋",clock1:"🕐",clock10:"🕙",clock1030:"🕥",clock11:"🕚",clock1130:"🕦",clock12:"🕛",clock1230:"🕧",clock130:"🕜",clock2:"🕑",clock230:"🕝",clock3:"🕒",clock330:"🕞",clock4:"🕓",clock430:"🕟",clock5:"🕔",clock530:"🕠",clock6:"🕕",clock630:"🕡",clock7:"🕖",clock730:"🕢",clock8:"🕗",clock830:"🕣",clock9:"🕘",clock930:"🕤",closed_book:"📕",closed_lock_with_key:"🔐",closed_umbrella:"🌂",cloud:"☁️",cloud_with_lightning:"🌩",cloud_with_lightning_and_rain:"⛈",cloud_with_rain:"🌧",cloud_with_snow:"🌨",clown_face:"🤡",clubs:"♣️",cocktail:"🍸",coffee:"☕️",coffin:"⚰️",cold_sweat:"😰",comet:"☄️",computer:"💻",computer_mouse:"🖱",confetti_ball:"🎊",confounded:"😖",confused:"😕",congratulations:"㊗️",construction:"🚧",construction_worker_man:"👷",construction_worker_woman:"👷‍♀️",control_knobs:"🎛",convenience_store:"🏪",cookie:"🍪",cool:"🆒",policeman:"👮",copyright:"©️",corn:"🌽",couch_and_lamp:"🛋",couple:"👫",couple_with_heart_woman_man:"💑",couple_with_heart_man_man:"👨‍❤️‍👨",couple_with_heart_woman_woman:"👩‍❤️‍👩",couplekiss_man_man:"👨‍❤️‍💋‍👨",couplekiss_man_woman:"💏",couplekiss_woman_woman:"👩‍❤️‍💋‍👩",cow:"🐮",cow2:"🐄",cowboy_hat_face:"🤠",crab:"🦀",crayon:"🖍",credit_card:"💳",crescent_moon:"🌙",cricket:"🏏",crocodile:"🐊",croissant:"🥐",crossed_fingers:"🤞",crossed_flags:"🎌",crossed_swords:"⚔️",crown:"👑",cry:"😢",crying_cat_face:"😿",crystal_ball:"🔮",cucumber:"🥒",cupid:"💘",curly_loop:"➰",currency_exchange:"💱",curry:"🍛",custard:"🍮",customs:"🛃",cyclone:"🌀",dagger:"🗡",dancer:"💃",dancing_women:"👯",dancing_men:"👯‍♂️",dango:"🍡",dark_sunglasses:"🕶",dart:"🎯",dash:"💨",date:"📅",deciduous_tree:"🌳",deer:"🦌",department_store:"🏬",derelict_house:"🏚",desert:"🏜",desert_island:"🏝",desktop_computer:"🖥",male_detective:"🕵️",diamond_shape_with_a_dot_inside:"💠",diamonds:"♦️",disappointed:"😞",disappointed_relieved:"😥",dizzy:"💫",dizzy_face:"😵",do_not_litter:"🚯",dog:"🐶",dog2:"🐕",dollar:"💵",dolls:"🎎",dolphin:"🐬",door:"🚪",doughnut:"🍩",dove:"🕊",dragon:"🐉",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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extracted by mini-css-extract-plugin\nmodule.exports = {\"markdown\":\"markdown__3Wgu1\"};","import style from \"./panel.less\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n","import { Component } from 'preact';\nimport Markdown from '../components/old/markdown';\nimport Panel from '../components/old/panel';\n\nconst r = String.raw;\n\nexport default class VlDiGeometria extends Component {\n\trender() {\n\t\t//Imported from unimore-info-wiki\n\t\treturn (\n\t\t\t
    \n                
    Videolezioni di Geometria
    \n                \n                    {r`\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n                    `}\n                \n\t\t\t
    \n\t\t);\n\t}\n}\n\n","/**\n * Created by Tivie on 13-07-2015.\n */\n\nfunction getDefaultOpts (simple) {\n  'use strict';\n\n  var defaultOptions = {\n    omitExtraWLInCodeBlocks: {\n      defaultValue: false,\n      describe: 'Omit the default extra whiteline added to code blocks',\n      type: 'boolean'\n    },\n    noHeaderId: {\n      defaultValue: false,\n      describe: 'Turn on/off generated header id',\n      type: 'boolean'\n    },\n    prefixHeaderId: {\n      defaultValue: false,\n      describe: 'Add a prefix to the generated header ids. Passing a string will prefix that string to the header id. Setting to true will add a generic \\'section-\\' prefix',\n      type: 'string'\n    },\n    rawPrefixHeaderId: {\n      defaultValue: false,\n      describe: 'Setting this option to true will prevent showdown from modifying the prefix. This might result in malformed IDs (if, for instance, the \" char is used in the prefix)',\n      type: 'boolean'\n    },\n    ghCompatibleHeaderId: {\n      defaultValue: false,\n      describe: 'Generate header ids compatible with github style (spaces are replaced with dashes, a bunch of non alphanumeric chars are removed)',\n      type: 'boolean'\n    },\n    rawHeaderId: {\n      defaultValue: false,\n      describe: 'Remove only spaces, \\' and \" from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids',\n      type: 'boolean'\n    },\n    headerLevelStart: {\n      defaultValue: false,\n      describe: 'The header blocks level start',\n      type: 'integer'\n    },\n    parseImgDimensions: {\n      defaultValue: false,\n      describe: 'Turn on/off image dimension parsing',\n      type: 'boolean'\n    },\n    simplifiedAutoLink: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM autolink style',\n      type: 'boolean'\n    },\n    excludeTrailingPunctuationFromURLs: {\n      defaultValue: false,\n      describe: 'Excludes trailing punctuation from links generated with autoLinking',\n      type: 'boolean'\n    },\n    literalMidWordUnderscores: {\n      defaultValue: false,\n      describe: 'Parse midword underscores as literal underscores',\n      type: 'boolean'\n    },\n    literalMidWordAsterisks: {\n      defaultValue: false,\n      describe: 'Parse midword asterisks as literal asterisks',\n      type: 'boolean'\n    },\n    strikethrough: {\n      defaultValue: false,\n      describe: 'Turn on/off strikethrough support',\n      type: 'boolean'\n    },\n    tables: {\n      defaultValue: false,\n      describe: 'Turn on/off tables support',\n      type: 'boolean'\n    },\n    tablesHeaderId: {\n      defaultValue: false,\n      describe: 'Add an id to table headers',\n      type: 'boolean'\n    },\n    ghCodeBlocks: {\n      defaultValue: true,\n      describe: 'Turn on/off GFM fenced code blocks support',\n      type: 'boolean'\n    },\n    tasklists: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM tasklist support',\n      type: 'boolean'\n    },\n    smoothLivePreview: {\n      defaultValue: false,\n      describe: 'Prevents weird effects in live previews due to incomplete input',\n      type: 'boolean'\n    },\n    smartIndentationFix: {\n      defaultValue: false,\n      description: 'Tries to smartly fix indentation in es6 strings',\n      type: 'boolean'\n    },\n    disableForced4SpacesIndentedSublists: {\n      defaultValue: false,\n      description: 'Disables the requirement of indenting nested sublists by 4 spaces',\n      type: 'boolean'\n    },\n    simpleLineBreaks: {\n      defaultValue: false,\n      description: 'Parses simple line breaks as 
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    foo\\
    ',\n      type: 'boolean'\n    },\n    emoji: {\n      defaultValue: false,\n      description: 'Enable emoji support. Ex: `this is a :smile: emoji`',\n      type: 'boolean'\n    },\n    underline: {\n      defaultValue: false,\n      description: 'Enable support for underline. Syntax is double or triple underscores: `__underline word__`. With this option enabled, underscores no longer parses into `` and ``',\n      type: 'boolean'\n    },\n    completeHTMLDocument: {\n      defaultValue: false,\n      description: 'Outputs a complete html document, including ``, `` and `` tags',\n      type: 'boolean'\n    },\n    metadata: {\n      defaultValue: false,\n      description: 'Enable support for document metadata (defined at the top of the document between `«««` and `»»»` or between `---` and `---`).',\n      type: 'boolean'\n    },\n    splitAdjacentBlockquotes: {\n      defaultValue: false,\n      description: 'Split adjacent blockquote blocks',\n      type: 'boolean'\n    }\n  };\n  if (simple === false) {\n    return JSON.parse(JSON.stringify(defaultOptions));\n  }\n  var ret = {};\n  for (var opt in defaultOptions) {\n    if (defaultOptions.hasOwnProperty(opt)) {\n      ret[opt] = defaultOptions[opt].defaultValue;\n    }\n  }\n  return ret;\n}\n\nfunction allOptionsOn () {\n  'use strict';\n  var options = getDefaultOpts(true),\n      ret = {};\n  for (var opt in options) {\n    if (options.hasOwnProperty(opt)) {\n      ret[opt] = true;\n    }\n  }\n  return ret;\n}\n","/**\n * Created by Tivie on 06-01-2015.\n */\n\n// Private properties\nvar showdown = {},\n    parsers = {},\n    extensions = {},\n    globalOptions = getDefaultOpts(true),\n    setFlavor = 'vanilla',\n    flavor = {\n      github: {\n        omitExtraWLInCodeBlocks:              true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        disableForced4SpacesIndentedSublists: true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghCompatibleHeaderId:                 true,\n        ghMentions:                           true,\n        backslashEscapesHTMLTags:             true,\n        emoji:                                true,\n        splitAdjacentBlockquotes:             true\n      },\n      original: {\n        noHeaderId:                           true,\n        ghCodeBlocks:                         false\n      },\n      ghost: {\n        omitExtraWLInCodeBlocks:              true,\n        parseImgDimensions:                   true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        smoothLivePreview:                    true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghMentions:                           false,\n        encodeEmails:                         true\n      },\n      vanilla: getDefaultOpts(true),\n      allOn: allOptionsOn()\n    };\n\n/**\n * helper namespace\n * @type {{}}\n */\nshowdown.helper = {};\n\n/**\n * TODO LEGACY SUPPORT CODE\n * @type {{}}\n */\nshowdown.extensions = {};\n\n/**\n * Set a global option\n * @static\n * @param {string} key\n * @param {*} value\n * @returns {showdown}\n */\nshowdown.setOption = function (key, value) {\n  'use strict';\n  globalOptions[key] = value;\n  return this;\n};\n\n/**\n * Get a global option\n * @static\n * @param {string} key\n * @returns {*}\n */\nshowdown.getOption = function (key) {\n  'use strict';\n  return globalOptions[key];\n};\n\n/**\n * Get the global options\n * @static\n * @returns {{}}\n */\nshowdown.getOptions = function () {\n  'use strict';\n  return globalOptions;\n};\n\n/**\n * Reset global options to the default values\n * @static\n */\nshowdown.resetOptions = function () {\n  'use strict';\n  globalOptions = getDefaultOpts(true);\n};\n\n/**\n * Set the flavor showdown should use as default\n * @param {string} name\n */\nshowdown.setFlavor = function (name) {\n  'use strict';\n  if (!flavor.hasOwnProperty(name)) {\n    throw Error(name + ' flavor was not found');\n  }\n  showdown.resetOptions();\n  var preset = flavor[name];\n  setFlavor = name;\n  for (var option in preset) {\n    if (preset.hasOwnProperty(option)) {\n      globalOptions[option] = preset[option];\n    }\n  }\n};\n\n/**\n * Get the currently set flavor\n * @returns {string}\n */\nshowdown.getFlavor = function () {\n  'use strict';\n  return setFlavor;\n};\n\n/**\n * Get the options of a specified flavor. Returns undefined if the flavor was not found\n * @param {string} name Name of the flavor\n * @returns {{}|undefined}\n */\nshowdown.getFlavorOptions = function (name) {\n  'use strict';\n  if (flavor.hasOwnProperty(name)) {\n    return flavor[name];\n  }\n};\n\n/**\n * Get the default options\n * @static\n * @param {boolean} [simple=true]\n * @returns {{}}\n */\nshowdown.getDefaultOptions = function (simple) {\n  'use strict';\n  return getDefaultOpts(simple);\n};\n\n/**\n * Get or set a subParser\n *\n * subParser(name)       - Get a registered subParser\n * subParser(name, func) - Register a subParser\n * @static\n * @param {string} name\n * @param {function} [func]\n * @returns {*}\n */\nshowdown.subParser = function (name, func) {\n  'use strict';\n  if (showdown.helper.isString(name)) {\n    if (typeof func !== 'undefined') {\n      parsers[name] = func;\n    } else {\n      if (parsers.hasOwnProperty(name)) {\n        return parsers[name];\n      } else {\n        throw Error('SubParser named ' + name + ' not registered!');\n      }\n    }\n  }\n};\n\n/**\n * Gets or registers an extension\n * @static\n * @param {string} name\n * @param {object|function=} ext\n * @returns {*}\n */\nshowdown.extension = function (name, ext) {\n  'use strict';\n\n  if (!showdown.helper.isString(name)) {\n    throw Error('Extension \\'name\\' must be a string');\n  }\n\n  name = showdown.helper.stdExtName(name);\n\n  // Getter\n  if (showdown.helper.isUndefined(ext)) {\n    if (!extensions.hasOwnProperty(name)) {\n      throw Error('Extension named ' + name + ' is not registered!');\n    }\n    return extensions[name];\n\n    // Setter\n  } else {\n    // Expand extension if it's wrapped in a function\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    // Ensure extension is an array\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExtension = validate(ext, name);\n\n    if (validExtension.valid) {\n      extensions[name] = ext;\n    } else {\n      throw Error(validExtension.error);\n    }\n  }\n};\n\n/**\n * Gets all extensions registered\n * @returns {{}}\n */\nshowdown.getAllExtensions = function () {\n  'use strict';\n  return extensions;\n};\n\n/**\n * Remove an extension\n * @param {string} name\n */\nshowdown.removeExtension = function (name) {\n  'use strict';\n  delete extensions[name];\n};\n\n/**\n * Removes all extensions\n */\nshowdown.resetExtensions = function () {\n  'use strict';\n  extensions = {};\n};\n\n/**\n * Validate extension\n * @param {array} extension\n * @param {string} name\n * @returns {{valid: boolean, error: string}}\n */\nfunction validate (extension, name) {\n  'use strict';\n\n  var errMsg = (name) ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n      ret = {\n        valid: true,\n        error: ''\n      };\n\n  if (!showdown.helper.isArray(extension)) {\n    extension = [extension];\n  }\n\n  for (var i = 0; i < extension.length; ++i) {\n    var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n        ext = extension[i];\n    if (typeof ext !== 'object') {\n      ret.valid = false;\n      ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n      return ret;\n    }\n\n    if (!showdown.helper.isString(ext.type)) {\n      ret.valid = false;\n      ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n      return ret;\n    }\n\n    var type = ext.type = ext.type.toLowerCase();\n\n    // normalize extension type\n    if (type === 'language') {\n      type = ext.type = 'lang';\n    }\n\n    if (type === 'html') {\n      type = ext.type = 'output';\n    }\n\n    if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n      ret.valid = false;\n      ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n      return ret;\n    }\n\n    if (type === 'listener') {\n      if (showdown.helper.isUndefined(ext.listeners)) {\n        ret.valid = false;\n        ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n        return ret;\n      }\n    } else {\n      if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n        ret.valid = false;\n        ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n        return ret;\n      }\n    }\n\n    if (ext.listeners) {\n      if (typeof ext.listeners !== 'object') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n        return ret;\n      }\n      for (var ln in ext.listeners) {\n        if (ext.listeners.hasOwnProperty(ln)) {\n          if (typeof ext.listeners[ln] !== 'function') {\n            ret.valid = false;\n            ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n              ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n            return ret;\n          }\n        }\n      }\n    }\n\n    if (ext.filter) {\n      if (typeof ext.filter !== 'function') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n        return ret;\n      }\n    } else if (ext.regex) {\n      if (showdown.helper.isString(ext.regex)) {\n        ext.regex = new RegExp(ext.regex, 'g');\n      }\n      if (!(ext.regex instanceof RegExp)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n        return ret;\n      }\n      if (showdown.helper.isUndefined(ext.replace)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n        return ret;\n      }\n    }\n  }\n  return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n  'use strict';\n\n  var validateExtension = validate(ext, null);\n  if (!validateExtension.valid) {\n    console.warn(validateExtension.error);\n    return false;\n  }\n  return true;\n};\n","/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n  showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n  'use strict';\n  return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n  'use strict';\n  var getType = {};\n  return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n  'use strict';\n  return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n  'use strict';\n  return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n  'use strict';\n  // check if obj is defined\n  if (showdown.helper.isUndefined(obj)) {\n    throw new Error('obj param is required');\n  }\n\n  if (showdown.helper.isUndefined(callback)) {\n    throw new Error('callback param is required');\n  }\n\n  if (!showdown.helper.isFunction(callback)) {\n    throw new Error('callback param must be a function/closure');\n  }\n\n  if (typeof obj.forEach === 'function') {\n    obj.forEach(callback);\n  } else if (showdown.helper.isArray(obj)) {\n    for (var i = 0; i < obj.length; i++) {\n      callback(obj[i], i, obj);\n    }\n  } else if (typeof (obj) === 'object') {\n    for (var prop in obj) {\n      if (obj.hasOwnProperty(prop)) {\n        callback(obj[prop], prop, obj);\n      }\n    }\n  } else {\n    throw new Error('obj does not seem to be an array or an iterable object');\n  }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n  'use strict';\n  return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n  'use strict';\n  var charCodeToEscape = m1.charCodeAt(0);\n  return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n  'use strict';\n  // First we have to escape the escape characters so that\n  // we can build a character class out of them\n  var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n  if (afterBackslash) {\n    regexString = '\\\\\\\\' + regexString;\n  }\n\n  var regex = new RegExp(regexString, 'g');\n  text = text.replace(regex, escapeCharactersCallback);\n\n  return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n  'use strict';\n\n  return txt\n    .replace(/"/g, '\"')\n    .replace(/</g, '<')\n    .replace(/>/g, '>')\n    .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n  'use strict';\n  var f = flags || '',\n      g = f.indexOf('g') > -1,\n      x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n      l = new RegExp(left, f.replace(/g/g, '')),\n      pos = [],\n      t, s, m, start, end;\n\n  do {\n    t = 0;\n    while ((m = x.exec(str))) {\n      if (l.test(m[0])) {\n        if (!(t++)) {\n          s = x.lastIndex;\n          start = s - m[0].length;\n        }\n      } else if (t) {\n        if (!--t) {\n          end = m.index + m[0].length;\n          var obj = {\n            left: {start: start, end: s},\n            match: {start: s, end: m.index},\n            right: {start: m.index, end: end},\n            wholeMatch: {start: start, end: end}\n          };\n          pos.push(obj);\n          if (!g) {\n            return pos;\n          }\n        }\n      }\n    }\n  } while (t && (x.lastIndex = s));\n\n  return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
    test
    \", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n  'use strict';\n\n  var matchPos = rgxFindMatchPos (str, left, right, flags),\n      results = [];\n\n  for (var i = 0; i < matchPos.length; ++i) {\n    results.push([\n      str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n      str.slice(matchPos[i].match.start, matchPos[i].match.end),\n      str.slice(matchPos[i].left.start, matchPos[i].left.end),\n      str.slice(matchPos[i].right.start, matchPos[i].right.end)\n    ]);\n  }\n  return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n  'use strict';\n\n  if (!showdown.helper.isFunction(replacement)) {\n    var repStr = replacement;\n    replacement = function () {\n      return repStr;\n    };\n  }\n\n  var matchPos = rgxFindMatchPos(str, left, right, flags),\n      finalStr = str,\n      lng = matchPos.length;\n\n  if (lng > 0) {\n    var bits = [];\n    if (matchPos[0].wholeMatch.start !== 0) {\n      bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n    }\n    for (var i = 0; i < lng; ++i) {\n      bits.push(\n        replacement(\n          str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n          str.slice(matchPos[i].match.start, matchPos[i].match.end),\n          str.slice(matchPos[i].left.start, matchPos[i].left.end),\n          str.slice(matchPos[i].right.start, matchPos[i].right.end)\n        )\n      );\n      if (i < lng - 1) {\n        bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n      }\n    }\n    if (matchPos[lng - 1].wholeMatch.end < str.length) {\n      bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n    }\n    finalStr = bits.join('');\n  }\n  return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  if (regex instanceof RegExp === false) {\n    throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n  }\n  var indexOf = str.substring(fromIndex || 0).search(regex);\n  return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n  'use strict';\n  var encode = [\n    function (ch) {\n      return '&#' + ch.charCodeAt(0) + ';';\n    },\n    function (ch) {\n      return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n    },\n    function (ch) {\n      return ch;\n    }\n  ];\n\n  mail = mail.replace(/./g, function (ch) {\n    if (ch === '@') {\n      // this *must* be encoded. I insist.\n      ch = encode[Math.floor(Math.random() * 2)](ch);\n    } else {\n      var r = Math.random();\n      // roughly 10% raw, 45% hex, 45% dec\n      ch = (\n        r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n      );\n    }\n    return ch;\n  });\n\n  return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n  'use strict';\n  /*jshint bitwise: false*/\n  // eslint-disable-next-line space-infix-ops\n  targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n  /*jshint bitwise: true*/\n  padString = String(padString || ' ');\n  if (str.length > targetLength) {\n    return String(str);\n  } else {\n    targetLength = targetLength - str.length;\n    if (targetLength > padString.length) {\n      padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n    }\n    return String(str) + padString.slice(0,targetLength);\n  }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n  console = {\n    warn: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    log: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    error: function (msg) {\n      'use strict';\n      throw msg;\n    }\n  };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n  asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n  '+1':'\\ud83d\\udc4d',\n  '-1':'\\ud83d\\udc4e',\n  '100':'\\ud83d\\udcaf',\n  '1234':'\\ud83d\\udd22',\n  '1st_place_medal':'\\ud83e\\udd47',\n  '2nd_place_medal':'\\ud83e\\udd48',\n  '3rd_place_medal':'\\ud83e\\udd49',\n  '8ball':'\\ud83c\\udfb1',\n  'a':'\\ud83c\\udd70\\ufe0f',\n  'ab':'\\ud83c\\udd8e',\n  'abc':'\\ud83d\\udd24',\n  'abcd':'\\ud83d\\udd21',\n  'accept':'\\ud83c\\ude51',\n  'aerial_tramway':'\\ud83d\\udea1',\n  'airplane':'\\u2708\\ufe0f',\n  'alarm_clock':'\\u23f0',\n  'alembic':'\\u2697\\ufe0f',\n  'alien':'\\ud83d\\udc7d',\n  'ambulance':'\\ud83d\\ude91',\n  'amphora':'\\ud83c\\udffa',\n  'anchor':'\\u2693\\ufe0f',\n  'angel':'\\ud83d\\udc7c',\n  'anger':'\\ud83d\\udca2',\n  'angry':'\\ud83d\\ude20',\n  'anguished':'\\ud83d\\ude27',\n  'ant':'\\ud83d\\udc1c',\n  'apple':'\\ud83c\\udf4e',\n  'aquarius':'\\u2652\\ufe0f',\n  'aries':'\\u2648\\ufe0f',\n  'arrow_backward':'\\u25c0\\ufe0f',\n  'arrow_double_down':'\\u23ec',\n  'arrow_double_up':'\\u23eb',\n  'arrow_down':'\\u2b07\\ufe0f',\n  'arrow_down_small':'\\ud83d\\udd3d',\n  'arrow_forward':'\\u25b6\\ufe0f',\n  'arrow_heading_down':'\\u2935\\ufe0f',\n  'arrow_heading_up':'\\u2934\\ufe0f',\n  'arrow_left':'\\u2b05\\ufe0f',\n  'arrow_lower_left':'\\u2199\\ufe0f',\n  'arrow_lower_right':'\\u2198\\ufe0f',\n  'arrow_right':'\\u27a1\\ufe0f',\n  'arrow_right_hook':'\\u21aa\\ufe0f',\n  'arrow_up':'\\u2b06\\ufe0f',\n  'arrow_up_down':'\\u2195\\ufe0f',\n  'arrow_up_small':'\\ud83d\\udd3c',\n  'arrow_upper_left':'\\u2196\\ufe0f',\n  'arrow_upper_right':'\\u2197\\ufe0f',\n  'arrows_clockwise':'\\ud83d\\udd03',\n  'arrows_counterclockwise':'\\ud83d\\udd04',\n  'art':'\\ud83c\\udfa8',\n  'articulated_lorry':'\\ud83d\\ude9b',\n  'artificial_satellite':'\\ud83d\\udef0',\n  'astonished':'\\ud83d\\ude32',\n  'athletic_shoe':'\\ud83d\\udc5f',\n  'atm':'\\ud83c\\udfe7',\n  'atom_symbol':'\\u269b\\ufe0f',\n  'avocado':'\\ud83e\\udd51',\n  'b':'\\ud83c\\udd71\\ufe0f',\n  'baby':'\\ud83d\\udc76',\n  'baby_bottle':'\\ud83c\\udf7c',\n  'baby_chick':'\\ud83d\\udc24',\n  'baby_symbol':'\\ud83d\\udebc',\n  'back':'\\ud83d\\udd19',\n  'bacon':'\\ud83e\\udd53',\n  'badminton':'\\ud83c\\udff8',\n  'baggage_claim':'\\ud83d\\udec4',\n  'baguette_bread':'\\ud83e\\udd56',\n  'balance_scale':'\\u2696\\ufe0f',\n  'balloon':'\\ud83c\\udf88',\n  'ballot_box':'\\ud83d\\uddf3',\n  'ballot_box_with_check':'\\u2611\\ufe0f',\n  'bamboo':'\\ud83c\\udf8d',\n  'banana':'\\ud83c\\udf4c',\n  'bangbang':'\\u203c\\ufe0f',\n  'bank':'\\ud83c\\udfe6',\n  'bar_chart':'\\ud83d\\udcca',\n  'barber':'\\ud83d\\udc88',\n  'baseball':'\\u26be\\ufe0f',\n  'basketball':'\\ud83c\\udfc0',\n  'basketball_man':'\\u26f9\\ufe0f',\n  'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n  'bat':'\\ud83e\\udd87',\n  'bath':'\\ud83d\\udec0',\n  'bathtub':'\\ud83d\\udec1',\n  'battery':'\\ud83d\\udd0b',\n  'beach_umbrella':'\\ud83c\\udfd6',\n  'bear':'\\ud83d\\udc3b',\n  'bed':'\\ud83d\\udecf',\n  'bee':'\\ud83d\\udc1d',\n  'beer':'\\ud83c\\udf7a',\n  'beers':'\\ud83c\\udf7b',\n  'beetle':'\\ud83d\\udc1e',\n  'beginner':'\\ud83d\\udd30',\n  'bell':'\\ud83d\\udd14',\n  'bellhop_bell':'\\ud83d\\udece',\n  'bento':'\\ud83c\\udf71',\n  'biking_man':'\\ud83d\\udeb4',\n  'bike':'\\ud83d\\udeb2',\n  'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n  'bikini':'\\ud83d\\udc59',\n  'biohazard':'\\u2623\\ufe0f',\n  'bird':'\\ud83d\\udc26',\n  'birthday':'\\ud83c\\udf82',\n  'black_circle':'\\u26ab\\ufe0f',\n  'black_flag':'\\ud83c\\udff4',\n  'black_heart':'\\ud83d\\udda4',\n  'black_joker':'\\ud83c\\udccf',\n  'black_large_square':'\\u2b1b\\ufe0f',\n  'black_medium_small_square':'\\u25fe\\ufe0f',\n  'black_medium_square':'\\u25fc\\ufe0f',\n  'black_nib':'\\u2712\\ufe0f',\n  'black_small_square':'\\u25aa\\ufe0f',\n  'black_square_button':'\\ud83d\\udd32',\n  'blonde_man':'\\ud83d\\udc71',\n  'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n  'blossom':'\\ud83c\\udf3c',\n  'blowfish':'\\ud83d\\udc21',\n  'blue_book':'\\ud83d\\udcd8',\n  'blue_car':'\\ud83d\\ude99',\n  'blue_heart':'\\ud83d\\udc99',\n  'blush':'\\ud83d\\ude0a',\n  'boar':'\\ud83d\\udc17',\n  'boat':'\\u26f5\\ufe0f',\n  'bomb':'\\ud83d\\udca3',\n  'book':'\\ud83d\\udcd6',\n  'bookmark':'\\ud83d\\udd16',\n  'bookmark_tabs':'\\ud83d\\udcd1',\n  'books':'\\ud83d\\udcda',\n  'boom':'\\ud83d\\udca5',\n  'boot':'\\ud83d\\udc62',\n  'bouquet':'\\ud83d\\udc90',\n  'bowing_man':'\\ud83d\\ude47',\n  'bow_and_arrow':'\\ud83c\\udff9',\n  'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n  'bowling':'\\ud83c\\udfb3',\n  'boxing_glove':'\\ud83e\\udd4a',\n  'boy':'\\ud83d\\udc66',\n  'bread':'\\ud83c\\udf5e',\n  'bride_with_veil':'\\ud83d\\udc70',\n  'bridge_at_night':'\\ud83c\\udf09',\n  'briefcase':'\\ud83d\\udcbc',\n  'broken_heart':'\\ud83d\\udc94',\n  'bug':'\\ud83d\\udc1b',\n  'building_construction':'\\ud83c\\udfd7',\n  'bulb':'\\ud83d\\udca1',\n  'bullettrain_front':'\\ud83d\\ude85',\n  'bullettrain_side':'\\ud83d\\ude84',\n  'burrito':'\\ud83c\\udf2f',\n  'bus':'\\ud83d\\ude8c',\n  'business_suit_levitating':'\\ud83d\\udd74',\n  'busstop':'\\ud83d\\ude8f',\n  'bust_in_silhouette':'\\ud83d\\udc64',\n  'busts_in_silhouette':'\\ud83d\\udc65',\n  'butterfly':'\\ud83e\\udd8b',\n  'cactus':'\\ud83c\\udf35',\n  'cake':'\\ud83c\\udf70',\n  'calendar':'\\ud83d\\udcc6',\n  'call_me_hand':'\\ud83e\\udd19',\n  'calling':'\\ud83d\\udcf2',\n  'camel':'\\ud83d\\udc2b',\n  'camera':'\\ud83d\\udcf7',\n  'camera_flash':'\\ud83d\\udcf8',\n  'camping':'\\ud83c\\udfd5',\n  'cancer':'\\u264b\\ufe0f',\n  'candle':'\\ud83d\\udd6f',\n  'candy':'\\ud83c\\udf6c',\n  'canoe':'\\ud83d\\udef6',\n  'capital_abcd':'\\ud83d\\udd20',\n  'capricorn':'\\u2651\\ufe0f',\n  'car':'\\ud83d\\ude97',\n  'card_file_box':'\\ud83d\\uddc3',\n  'card_index':'\\ud83d\\udcc7',\n  'card_index_dividers':'\\ud83d\\uddc2',\n  'carousel_horse':'\\ud83c\\udfa0',\n  'carrot':'\\ud83e\\udd55',\n  'cat':'\\ud83d\\udc31',\n  'cat2':'\\ud83d\\udc08',\n  'cd':'\\ud83d\\udcbf',\n  'chains':'\\u26d3',\n  'champagne':'\\ud83c\\udf7e',\n  'chart':'\\ud83d\\udcb9',\n  'chart_with_downwards_trend':'\\ud83d\\udcc9',\n  'chart_with_upwards_trend':'\\ud83d\\udcc8',\n  'checkered_flag':'\\ud83c\\udfc1',\n  'cheese':'\\ud83e\\uddc0',\n  'cherries':'\\ud83c\\udf52',\n  'cherry_blossom':'\\ud83c\\udf38',\n  'chestnut':'\\ud83c\\udf30',\n  'chicken':'\\ud83d\\udc14',\n  'children_crossing':'\\ud83d\\udeb8',\n  'chipmunk':'\\ud83d\\udc3f',\n  'chocolate_bar':'\\ud83c\\udf6b',\n  'christmas_tree':'\\ud83c\\udf84',\n  'church':'\\u26ea\\ufe0f',\n  'cinema':'\\ud83c\\udfa6',\n  'circus_tent':'\\ud83c\\udfaa',\n  'city_sunrise':'\\ud83c\\udf07',\n  'city_sunset':'\\ud83c\\udf06',\n  'cityscape':'\\ud83c\\udfd9',\n  'cl':'\\ud83c\\udd91',\n  'clamp':'\\ud83d\\udddc',\n  'clap':'\\ud83d\\udc4f',\n  'clapper':'\\ud83c\\udfac',\n  'classical_building':'\\ud83c\\udfdb',\n  'clinking_glasses':'\\ud83e\\udd42',\n  'clipboard':'\\ud83d\\udccb',\n  'clock1':'\\ud83d\\udd50',\n  'clock10':'\\ud83d\\udd59',\n  'clock1030':'\\ud83d\\udd65',\n  'clock11':'\\ud83d\\udd5a',\n  'clock1130':'\\ud83d\\udd66',\n  'clock12':'\\ud83d\\udd5b',\n  'clock1230':'\\ud83d\\udd67',\n  'clock130':'\\ud83d\\udd5c',\n  'clock2':'\\ud83d\\udd51',\n  'clock230':'\\ud83d\\udd5d',\n  'clock3':'\\ud83d\\udd52',\n  'clock330':'\\ud83d\\udd5e',\n  'clock4':'\\ud83d\\udd53',\n  'clock430':'\\ud83d\\udd5f',\n  'clock5':'\\ud83d\\udd54',\n  'clock530':'\\ud83d\\udd60',\n  'clock6':'\\ud83d\\udd55',\n  'clock630':'\\ud83d\\udd61',\n  'clock7':'\\ud83d\\udd56',\n  'clock730':'\\ud83d\\udd62',\n  'clock8':'\\ud83d\\udd57',\n  'clock830':'\\ud83d\\udd63',\n  'clock9':'\\ud83d\\udd58',\n  'clock930':'\\ud83d\\udd64',\n  'closed_book':'\\ud83d\\udcd5',\n  'closed_lock_with_key':'\\ud83d\\udd10',\n  'closed_umbrella':'\\ud83c\\udf02',\n  'cloud':'\\u2601\\ufe0f',\n  'cloud_with_lightning':'\\ud83c\\udf29',\n  'cloud_with_lightning_and_rain':'\\u26c8',\n  'cloud_with_rain':'\\ud83c\\udf27',\n  'cloud_with_snow':'\\ud83c\\udf28',\n  'clown_face':'\\ud83e\\udd21',\n  'clubs':'\\u2663\\ufe0f',\n  'cocktail':'\\ud83c\\udf78',\n  'coffee':'\\u2615\\ufe0f',\n  'coffin':'\\u26b0\\ufe0f',\n  'cold_sweat':'\\ud83d\\ude30',\n  'comet':'\\u2604\\ufe0f',\n  'computer':'\\ud83d\\udcbb',\n  'computer_mouse':'\\ud83d\\uddb1',\n  'confetti_ball':'\\ud83c\\udf8a',\n  'confounded':'\\ud83d\\ude16',\n  'confused':'\\ud83d\\ude15',\n  'congratulations':'\\u3297\\ufe0f',\n  'construction':'\\ud83d\\udea7',\n  'construction_worker_man':'\\ud83d\\udc77',\n  'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n  'control_knobs':'\\ud83c\\udf9b',\n  'convenience_store':'\\ud83c\\udfea',\n  'cookie':'\\ud83c\\udf6a',\n  'cool':'\\ud83c\\udd92',\n  'policeman':'\\ud83d\\udc6e',\n  'copyright':'\\u00a9\\ufe0f',\n  'corn':'\\ud83c\\udf3d',\n  'couch_and_lamp':'\\ud83d\\udecb',\n  'couple':'\\ud83d\\udc6b',\n  'couple_with_heart_woman_man':'\\ud83d\\udc91',\n  'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n  'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n  'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n  'couplekiss_man_woman':'\\ud83d\\udc8f',\n  'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n  'cow':'\\ud83d\\udc2e',\n  'cow2':'\\ud83d\\udc04',\n  'cowboy_hat_face':'\\ud83e\\udd20',\n  'crab':'\\ud83e\\udd80',\n  'crayon':'\\ud83d\\udd8d',\n  'credit_card':'\\ud83d\\udcb3',\n  'crescent_moon':'\\ud83c\\udf19',\n  'cricket':'\\ud83c\\udfcf',\n  'crocodile':'\\ud83d\\udc0a',\n  'croissant':'\\ud83e\\udd50',\n  'crossed_fingers':'\\ud83e\\udd1e',\n  'crossed_flags':'\\ud83c\\udf8c',\n  'crossed_swords':'\\u2694\\ufe0f',\n  'crown':'\\ud83d\\udc51',\n  'cry':'\\ud83d\\ude22',\n  'crying_cat_face':'\\ud83d\\ude3f',\n  'crystal_ball':'\\ud83d\\udd2e',\n  'cucumber':'\\ud83e\\udd52',\n  'cupid':'\\ud83d\\udc98',\n  'curly_loop':'\\u27b0',\n  'currency_exchange':'\\ud83d\\udcb1',\n  'curry':'\\ud83c\\udf5b',\n  'custard':'\\ud83c\\udf6e',\n  'customs':'\\ud83d\\udec3',\n  'cyclone':'\\ud83c\\udf00',\n  'dagger':'\\ud83d\\udde1',\n  'dancer':'\\ud83d\\udc83',\n  'dancing_women':'\\ud83d\\udc6f',\n  'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n  'dango':'\\ud83c\\udf61',\n  'dark_sunglasses':'\\ud83d\\udd76',\n  'dart':'\\ud83c\\udfaf',\n  'dash':'\\ud83d\\udca8',\n  'date':'\\ud83d\\udcc5',\n  'deciduous_tree':'\\ud83c\\udf33',\n  'deer':'\\ud83e\\udd8c',\n  'department_store':'\\ud83c\\udfec',\n  'derelict_house':'\\ud83c\\udfda',\n  'desert':'\\ud83c\\udfdc',\n  'desert_island':'\\ud83c\\udfdd',\n  'desktop_computer':'\\ud83d\\udda5',\n  'male_detective':'\\ud83d\\udd75\\ufe0f',\n  'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n  'diamonds':'\\u2666\\ufe0f',\n  'disappointed':'\\ud83d\\ude1e',\n  'disappointed_relieved':'\\ud83d\\ude25',\n  'dizzy':'\\ud83d\\udcab',\n  'dizzy_face':'\\ud83d\\ude35',\n  'do_not_litter':'\\ud83d\\udeaf',\n  'dog':'\\ud83d\\udc36',\n  'dog2':'\\ud83d\\udc15',\n  'dollar':'\\ud83d\\udcb5',\n  'dolls':'\\ud83c\\udf8e',\n  'dolphin':'\\ud83d\\udc2c',\n  'door':'\\ud83d\\udeaa',\n  'doughnut':'\\ud83c\\udf69',\n  'dove':'\\ud83d\\udd4a',\n  'dragon':'\\ud83d\\udc09',\n  'dragon_face':'\\ud83d\\udc32',\n  'dress':'\\ud83d\\udc57',\n  'dromedary_camel':'\\ud83d\\udc2a',\n  'drooling_face':'\\ud83e\\udd24',\n  'droplet':'\\ud83d\\udca7',\n  'drum':'\\ud83e\\udd41',\n  'duck':'\\ud83e\\udd86',\n  'dvd':'\\ud83d\\udcc0',\n  'e-mail':'\\ud83d\\udce7',\n  'eagle':'\\ud83e\\udd85',\n  'ear':'\\ud83d\\udc42',\n  'ear_of_rice':'\\ud83c\\udf3e',\n  'earth_africa':'\\ud83c\\udf0d',\n  'earth_americas':'\\ud83c\\udf0e',\n  'earth_asia':'\\ud83c\\udf0f',\n  'egg':'\\ud83e\\udd5a',\n  'eggplant':'\\ud83c\\udf46',\n  'eight_pointed_black_star':'\\u2734\\ufe0f',\n  'eight_spoked_asterisk':'\\u2733\\ufe0f',\n  'electric_plug':'\\ud83d\\udd0c',\n  'elephant':'\\ud83d\\udc18',\n  'email':'\\u2709\\ufe0f',\n  'end':'\\ud83d\\udd1a',\n  'envelope_with_arrow':'\\ud83d\\udce9',\n  'euro':'\\ud83d\\udcb6',\n  'european_castle':'\\ud83c\\udff0',\n  'european_post_office':'\\ud83c\\udfe4',\n  'evergreen_tree':'\\ud83c\\udf32',\n  'exclamation':'\\u2757\\ufe0f',\n  'expressionless':'\\ud83d\\ude11',\n  'eye':'\\ud83d\\udc41',\n  'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n  'eyeglasses':'\\ud83d\\udc53',\n  'eyes':'\\ud83d\\udc40',\n  'face_with_head_bandage':'\\ud83e\\udd15',\n  'face_with_thermometer':'\\ud83e\\udd12',\n  'fist_oncoming':'\\ud83d\\udc4a',\n  'factory':'\\ud83c\\udfed',\n  'fallen_leaf':'\\ud83c\\udf42',\n  'family_man_woman_boy':'\\ud83d\\udc6a',\n  'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'fast_forward':'\\u23e9',\n  'fax':'\\ud83d\\udce0',\n  'fearful':'\\ud83d\\ude28',\n  'feet':'\\ud83d\\udc3e',\n  'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n  'ferris_wheel':'\\ud83c\\udfa1',\n  'ferry':'\\u26f4',\n  'field_hockey':'\\ud83c\\udfd1',\n  'file_cabinet':'\\ud83d\\uddc4',\n  'file_folder':'\\ud83d\\udcc1',\n  'film_projector':'\\ud83d\\udcfd',\n  'film_strip':'\\ud83c\\udf9e',\n  'fire':'\\ud83d\\udd25',\n  'fire_engine':'\\ud83d\\ude92',\n  'fireworks':'\\ud83c\\udf86',\n  'first_quarter_moon':'\\ud83c\\udf13',\n  'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n  'fish':'\\ud83d\\udc1f',\n  'fish_cake':'\\ud83c\\udf65',\n  'fishing_pole_and_fish':'\\ud83c\\udfa3',\n  'fist_raised':'\\u270a',\n  'fist_left':'\\ud83e\\udd1b',\n  'fist_right':'\\ud83e\\udd1c',\n  'flags':'\\ud83c\\udf8f',\n  'flashlight':'\\ud83d\\udd26',\n  'fleur_de_lis':'\\u269c\\ufe0f',\n  'flight_arrival':'\\ud83d\\udeec',\n  'flight_departure':'\\ud83d\\udeeb',\n  'floppy_disk':'\\ud83d\\udcbe',\n  'flower_playing_cards':'\\ud83c\\udfb4',\n  'flushed':'\\ud83d\\ude33',\n  'fog':'\\ud83c\\udf2b',\n  'foggy':'\\ud83c\\udf01',\n  'football':'\\ud83c\\udfc8',\n  'footprints':'\\ud83d\\udc63',\n  'fork_and_knife':'\\ud83c\\udf74',\n  'fountain':'\\u26f2\\ufe0f',\n  'fountain_pen':'\\ud83d\\udd8b',\n  'four_leaf_clover':'\\ud83c\\udf40',\n  'fox_face':'\\ud83e\\udd8a',\n  'framed_picture':'\\ud83d\\uddbc',\n  'free':'\\ud83c\\udd93',\n  'fried_egg':'\\ud83c\\udf73',\n  'fried_shrimp':'\\ud83c\\udf64',\n  'fries':'\\ud83c\\udf5f',\n  'frog':'\\ud83d\\udc38',\n  'frowning':'\\ud83d\\ude26',\n  'frowning_face':'\\u2639\\ufe0f',\n  'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n  'frowning_woman':'\\ud83d\\ude4d',\n  'middle_finger':'\\ud83d\\udd95',\n  'fuelpump':'\\u26fd\\ufe0f',\n  'full_moon':'\\ud83c\\udf15',\n  'full_moon_with_face':'\\ud83c\\udf1d',\n  'funeral_urn':'\\u26b1\\ufe0f',\n  'game_die':'\\ud83c\\udfb2',\n  'gear':'\\u2699\\ufe0f',\n  'gem':'\\ud83d\\udc8e',\n  'gemini':'\\u264a\\ufe0f',\n  'ghost':'\\ud83d\\udc7b',\n  'gift':'\\ud83c\\udf81',\n  'gift_heart':'\\ud83d\\udc9d',\n  'girl':'\\ud83d\\udc67',\n  'globe_with_meridians':'\\ud83c\\udf10',\n  'goal_net':'\\ud83e\\udd45',\n  'goat':'\\ud83d\\udc10',\n  'golf':'\\u26f3\\ufe0f',\n  'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n  'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n  'gorilla':'\\ud83e\\udd8d',\n  'grapes':'\\ud83c\\udf47',\n  'green_apple':'\\ud83c\\udf4f',\n  'green_book':'\\ud83d\\udcd7',\n  'green_heart':'\\ud83d\\udc9a',\n  'green_salad':'\\ud83e\\udd57',\n  'grey_exclamation':'\\u2755',\n  'grey_question':'\\u2754',\n  'grimacing':'\\ud83d\\ude2c',\n  'grin':'\\ud83d\\ude01',\n  'grinning':'\\ud83d\\ude00',\n  'guardsman':'\\ud83d\\udc82',\n  'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n  'guitar':'\\ud83c\\udfb8',\n  'gun':'\\ud83d\\udd2b',\n  'haircut_woman':'\\ud83d\\udc87',\n  'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n  'hamburger':'\\ud83c\\udf54',\n  'hammer':'\\ud83d\\udd28',\n  'hammer_and_pick':'\\u2692',\n  'hammer_and_wrench':'\\ud83d\\udee0',\n  'hamster':'\\ud83d\\udc39',\n  'hand':'\\u270b',\n  'handbag':'\\ud83d\\udc5c',\n  'handshake':'\\ud83e\\udd1d',\n  'hankey':'\\ud83d\\udca9',\n  'hatched_chick':'\\ud83d\\udc25',\n  'hatching_chick':'\\ud83d\\udc23',\n  'headphones':'\\ud83c\\udfa7',\n  'hear_no_evil':'\\ud83d\\ude49',\n  'heart':'\\u2764\\ufe0f',\n  'heart_decoration':'\\ud83d\\udc9f',\n  'heart_eyes':'\\ud83d\\ude0d',\n  'heart_eyes_cat':'\\ud83d\\ude3b',\n  'heartbeat':'\\ud83d\\udc93',\n  'heartpulse':'\\ud83d\\udc97',\n  'hearts':'\\u2665\\ufe0f',\n  'heavy_check_mark':'\\u2714\\ufe0f',\n  'heavy_division_sign':'\\u2797',\n  'heavy_dollar_sign':'\\ud83d\\udcb2',\n  'heavy_heart_exclamation':'\\u2763\\ufe0f',\n  'heavy_minus_sign':'\\u2796',\n  'heavy_multiplication_x':'\\u2716\\ufe0f',\n  'heavy_plus_sign':'\\u2795',\n  'helicopter':'\\ud83d\\ude81',\n  'herb':'\\ud83c\\udf3f',\n  'hibiscus':'\\ud83c\\udf3a',\n  'high_brightness':'\\ud83d\\udd06',\n  'high_heel':'\\ud83d\\udc60',\n  'hocho':'\\ud83d\\udd2a',\n  'hole':'\\ud83d\\udd73',\n  'honey_pot':'\\ud83c\\udf6f',\n  'horse':'\\ud83d\\udc34',\n  'horse_racing':'\\ud83c\\udfc7',\n  'hospital':'\\ud83c\\udfe5',\n  'hot_pepper':'\\ud83c\\udf36',\n  'hotdog':'\\ud83c\\udf2d',\n  'hotel':'\\ud83c\\udfe8',\n  'hotsprings':'\\u2668\\ufe0f',\n  'hourglass':'\\u231b\\ufe0f',\n  'hourglass_flowing_sand':'\\u23f3',\n  'house':'\\ud83c\\udfe0',\n  'house_with_garden':'\\ud83c\\udfe1',\n  'houses':'\\ud83c\\udfd8',\n  'hugs':'\\ud83e\\udd17',\n  'hushed':'\\ud83d\\ude2f',\n  'ice_cream':'\\ud83c\\udf68',\n  'ice_hockey':'\\ud83c\\udfd2',\n  'ice_skate':'\\u26f8',\n  'icecream':'\\ud83c\\udf66',\n  'id':'\\ud83c\\udd94',\n  'ideograph_advantage':'\\ud83c\\ude50',\n  'imp':'\\ud83d\\udc7f',\n  'inbox_tray':'\\ud83d\\udce5',\n  'incoming_envelope':'\\ud83d\\udce8',\n  'tipping_hand_woman':'\\ud83d\\udc81',\n  'information_source':'\\u2139\\ufe0f',\n  'innocent':'\\ud83d\\ude07',\n  'interrobang':'\\u2049\\ufe0f',\n  'iphone':'\\ud83d\\udcf1',\n  'izakaya_lantern':'\\ud83c\\udfee',\n  'jack_o_lantern':'\\ud83c\\udf83',\n  'japan':'\\ud83d\\uddfe',\n  'japanese_castle':'\\ud83c\\udfef',\n  'japanese_goblin':'\\ud83d\\udc7a',\n  'japanese_ogre':'\\ud83d\\udc79',\n  'jeans':'\\ud83d\\udc56',\n  'joy':'\\ud83d\\ude02',\n  'joy_cat':'\\ud83d\\ude39',\n  'joystick':'\\ud83d\\udd79',\n  'kaaba':'\\ud83d\\udd4b',\n  'key':'\\ud83d\\udd11',\n  'keyboard':'\\u2328\\ufe0f',\n  'keycap_ten':'\\ud83d\\udd1f',\n  'kick_scooter':'\\ud83d\\udef4',\n  'kimono':'\\ud83d\\udc58',\n  'kiss':'\\ud83d\\udc8b',\n  'kissing':'\\ud83d\\ude17',\n  'kissing_cat':'\\ud83d\\ude3d',\n  'kissing_closed_eyes':'\\ud83d\\ude1a',\n  'kissing_heart':'\\ud83d\\ude18',\n  'kissing_smiling_eyes':'\\ud83d\\ude19',\n  'kiwi_fruit':'\\ud83e\\udd5d',\n  'koala':'\\ud83d\\udc28',\n  'koko':'\\ud83c\\ude01',\n  'label':'\\ud83c\\udff7',\n  'large_blue_circle':'\\ud83d\\udd35',\n  'large_blue_diamond':'\\ud83d\\udd37',\n  'large_orange_diamond':'\\ud83d\\udd36',\n  'last_quarter_moon':'\\ud83c\\udf17',\n  'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n  'latin_cross':'\\u271d\\ufe0f',\n  'laughing':'\\ud83d\\ude06',\n  'leaves':'\\ud83c\\udf43',\n  'ledger':'\\ud83d\\udcd2',\n  'left_luggage':'\\ud83d\\udec5',\n  'left_right_arrow':'\\u2194\\ufe0f',\n  'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n  'lemon':'\\ud83c\\udf4b',\n  'leo':'\\u264c\\ufe0f',\n  'leopard':'\\ud83d\\udc06',\n  'level_slider':'\\ud83c\\udf9a',\n  'libra':'\\u264e\\ufe0f',\n  'light_rail':'\\ud83d\\ude88',\n  'link':'\\ud83d\\udd17',\n  'lion':'\\ud83e\\udd81',\n  'lips':'\\ud83d\\udc44',\n  'lipstick':'\\ud83d\\udc84',\n  'lizard':'\\ud83e\\udd8e',\n  'lock':'\\ud83d\\udd12',\n  'lock_with_ink_pen':'\\ud83d\\udd0f',\n  'lollipop':'\\ud83c\\udf6d',\n  'loop':'\\u27bf',\n  'loud_sound':'\\ud83d\\udd0a',\n  'loudspeaker':'\\ud83d\\udce2',\n  'love_hotel':'\\ud83c\\udfe9',\n  'love_letter':'\\ud83d\\udc8c',\n  'low_brightness':'\\ud83d\\udd05',\n  'lying_face':'\\ud83e\\udd25',\n  'm':'\\u24c2\\ufe0f',\n  'mag':'\\ud83d\\udd0d',\n  'mag_right':'\\ud83d\\udd0e',\n  'mahjong':'\\ud83c\\udc04\\ufe0f',\n  'mailbox':'\\ud83d\\udceb',\n  'mailbox_closed':'\\ud83d\\udcea',\n  'mailbox_with_mail':'\\ud83d\\udcec',\n  'mailbox_with_no_mail':'\\ud83d\\udced',\n  'man':'\\ud83d\\udc68',\n  'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n  'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n  'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n  'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n  'man_dancing':'\\ud83d\\udd7a',\n  'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n  'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n  'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n  'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n  'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n  'man_in_tuxedo':'\\ud83e\\udd35',\n  'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n  'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n  'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n  'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n  'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n  'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n  'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n  'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n  'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n  'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n  'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n  'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n  'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n  'man_with_gua_pi_mao':'\\ud83d\\udc72',\n  'man_with_turban':'\\ud83d\\udc73',\n  'tangerine':'\\ud83c\\udf4a',\n  'mans_shoe':'\\ud83d\\udc5e',\n  'mantelpiece_clock':'\\ud83d\\udd70',\n  'maple_leaf':'\\ud83c\\udf41',\n  'martial_arts_uniform':'\\ud83e\\udd4b',\n  'mask':'\\ud83d\\ude37',\n  'massage_woman':'\\ud83d\\udc86',\n  'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n  'meat_on_bone':'\\ud83c\\udf56',\n  'medal_military':'\\ud83c\\udf96',\n  'medal_sports':'\\ud83c\\udfc5',\n  'mega':'\\ud83d\\udce3',\n  'melon':'\\ud83c\\udf48',\n  'memo':'\\ud83d\\udcdd',\n  'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n  'menorah':'\\ud83d\\udd4e',\n  'mens':'\\ud83d\\udeb9',\n  'metal':'\\ud83e\\udd18',\n  'metro':'\\ud83d\\ude87',\n  'microphone':'\\ud83c\\udfa4',\n  'microscope':'\\ud83d\\udd2c',\n  'milk_glass':'\\ud83e\\udd5b',\n  'milky_way':'\\ud83c\\udf0c',\n  'minibus':'\\ud83d\\ude90',\n  'minidisc':'\\ud83d\\udcbd',\n  'mobile_phone_off':'\\ud83d\\udcf4',\n  'money_mouth_face':'\\ud83e\\udd11',\n  'money_with_wings':'\\ud83d\\udcb8',\n  'moneybag':'\\ud83d\\udcb0',\n  'monkey':'\\ud83d\\udc12',\n  'monkey_face':'\\ud83d\\udc35',\n  'monorail':'\\ud83d\\ude9d',\n  'moon':'\\ud83c\\udf14',\n  'mortar_board':'\\ud83c\\udf93',\n  'mosque':'\\ud83d\\udd4c',\n  'motor_boat':'\\ud83d\\udee5',\n  'motor_scooter':'\\ud83d\\udef5',\n  'motorcycle':'\\ud83c\\udfcd',\n  'motorway':'\\ud83d\\udee3',\n  'mount_fuji':'\\ud83d\\uddfb',\n  'mountain':'\\u26f0',\n  'mountain_biking_man':'\\ud83d\\udeb5',\n  'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n  'mountain_cableway':'\\ud83d\\udea0',\n  'mountain_railway':'\\ud83d\\ude9e',\n  'mountain_snow':'\\ud83c\\udfd4',\n  'mouse':'\\ud83d\\udc2d',\n  'mouse2':'\\ud83d\\udc01',\n  'movie_camera':'\\ud83c\\udfa5',\n  'moyai':'\\ud83d\\uddff',\n  'mrs_claus':'\\ud83e\\udd36',\n  'muscle':'\\ud83d\\udcaa',\n  'mushroom':'\\ud83c\\udf44',\n  'musical_keyboard':'\\ud83c\\udfb9',\n  'musical_note':'\\ud83c\\udfb5',\n  'musical_score':'\\ud83c\\udfbc',\n  'mute':'\\ud83d\\udd07',\n  'nail_care':'\\ud83d\\udc85',\n  'name_badge':'\\ud83d\\udcdb',\n  'national_park':'\\ud83c\\udfde',\n  'nauseated_face':'\\ud83e\\udd22',\n  'necktie':'\\ud83d\\udc54',\n  'negative_squared_cross_mark':'\\u274e',\n  'nerd_face':'\\ud83e\\udd13',\n  'neutral_face':'\\ud83d\\ude10',\n  'new':'\\ud83c\\udd95',\n  'new_moon':'\\ud83c\\udf11',\n  'new_moon_with_face':'\\ud83c\\udf1a',\n  'newspaper':'\\ud83d\\udcf0',\n  'newspaper_roll':'\\ud83d\\uddde',\n  'next_track_button':'\\u23ed',\n  'ng':'\\ud83c\\udd96',\n  'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n  'no_good_woman':'\\ud83d\\ude45',\n  'night_with_stars':'\\ud83c\\udf03',\n  'no_bell':'\\ud83d\\udd15',\n  'no_bicycles':'\\ud83d\\udeb3',\n  'no_entry':'\\u26d4\\ufe0f',\n  'no_entry_sign':'\\ud83d\\udeab',\n  'no_mobile_phones':'\\ud83d\\udcf5',\n  'no_mouth':'\\ud83d\\ude36',\n  'no_pedestrians':'\\ud83d\\udeb7',\n  'no_smoking':'\\ud83d\\udead',\n  'non-potable_water':'\\ud83d\\udeb1',\n  'nose':'\\ud83d\\udc43',\n  'notebook':'\\ud83d\\udcd3',\n  'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n  'notes':'\\ud83c\\udfb6',\n  'nut_and_bolt':'\\ud83d\\udd29',\n  'o':'\\u2b55\\ufe0f',\n  'o2':'\\ud83c\\udd7e\\ufe0f',\n  'ocean':'\\ud83c\\udf0a',\n  'octopus':'\\ud83d\\udc19',\n  'oden':'\\ud83c\\udf62',\n  'office':'\\ud83c\\udfe2',\n  'oil_drum':'\\ud83d\\udee2',\n  'ok':'\\ud83c\\udd97',\n  'ok_hand':'\\ud83d\\udc4c',\n  'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n  'ok_woman':'\\ud83d\\ude46',\n  'old_key':'\\ud83d\\udddd',\n  'older_man':'\\ud83d\\udc74',\n  'older_woman':'\\ud83d\\udc75',\n  'om':'\\ud83d\\udd49',\n  'on':'\\ud83d\\udd1b',\n  'oncoming_automobile':'\\ud83d\\ude98',\n  'oncoming_bus':'\\ud83d\\ude8d',\n  'oncoming_police_car':'\\ud83d\\ude94',\n  'oncoming_taxi':'\\ud83d\\ude96',\n  'open_file_folder':'\\ud83d\\udcc2',\n  'open_hands':'\\ud83d\\udc50',\n  'open_mouth':'\\ud83d\\ude2e',\n  'open_umbrella':'\\u2602\\ufe0f',\n  'ophiuchus':'\\u26ce',\n  'orange_book':'\\ud83d\\udcd9',\n  'orthodox_cross':'\\u2626\\ufe0f',\n  'outbox_tray':'\\ud83d\\udce4',\n  'owl':'\\ud83e\\udd89',\n  'ox':'\\ud83d\\udc02',\n  'package':'\\ud83d\\udce6',\n  'page_facing_up':'\\ud83d\\udcc4',\n  'page_with_curl':'\\ud83d\\udcc3',\n  'pager':'\\ud83d\\udcdf',\n  'paintbrush':'\\ud83d\\udd8c',\n  'palm_tree':'\\ud83c\\udf34',\n  'pancakes':'\\ud83e\\udd5e',\n  'panda_face':'\\ud83d\\udc3c',\n  'paperclip':'\\ud83d\\udcce',\n  'paperclips':'\\ud83d\\udd87',\n  'parasol_on_ground':'\\u26f1',\n  'parking':'\\ud83c\\udd7f\\ufe0f',\n  'part_alternation_mark':'\\u303d\\ufe0f',\n  'partly_sunny':'\\u26c5\\ufe0f',\n  'passenger_ship':'\\ud83d\\udef3',\n  'passport_control':'\\ud83d\\udec2',\n  'pause_button':'\\u23f8',\n  'peace_symbol':'\\u262e\\ufe0f',\n  'peach':'\\ud83c\\udf51',\n  'peanuts':'\\ud83e\\udd5c',\n  'pear':'\\ud83c\\udf50',\n  'pen':'\\ud83d\\udd8a',\n  'pencil2':'\\u270f\\ufe0f',\n  'penguin':'\\ud83d\\udc27',\n  'pensive':'\\ud83d\\ude14',\n  'performing_arts':'\\ud83c\\udfad',\n  'persevere':'\\ud83d\\ude23',\n  'person_fencing':'\\ud83e\\udd3a',\n  'pouting_woman':'\\ud83d\\ude4e',\n  'phone':'\\u260e\\ufe0f',\n  'pick':'\\u26cf',\n  'pig':'\\ud83d\\udc37',\n  'pig2':'\\ud83d\\udc16',\n  'pig_nose':'\\ud83d\\udc3d',\n  'pill':'\\ud83d\\udc8a',\n  'pineapple':'\\ud83c\\udf4d',\n  'ping_pong':'\\ud83c\\udfd3',\n  'pisces':'\\u2653\\ufe0f',\n  'pizza':'\\ud83c\\udf55',\n  'place_of_worship':'\\ud83d\\uded0',\n  'plate_with_cutlery':'\\ud83c\\udf7d',\n  'play_or_pause_button':'\\u23ef',\n  'point_down':'\\ud83d\\udc47',\n  'point_left':'\\ud83d\\udc48',\n  'point_right':'\\ud83d\\udc49',\n  'point_up':'\\u261d\\ufe0f',\n  'point_up_2':'\\ud83d\\udc46',\n  'police_car':'\\ud83d\\ude93',\n  'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n  'poodle':'\\ud83d\\udc29',\n  'popcorn':'\\ud83c\\udf7f',\n  'post_office':'\\ud83c\\udfe3',\n  'postal_horn':'\\ud83d\\udcef',\n  'postbox':'\\ud83d\\udcee',\n  'potable_water':'\\ud83d\\udeb0',\n  'potato':'\\ud83e\\udd54',\n  'pouch':'\\ud83d\\udc5d',\n  'poultry_leg':'\\ud83c\\udf57',\n  'pound':'\\ud83d\\udcb7',\n  'rage':'\\ud83d\\ude21',\n  'pouting_cat':'\\ud83d\\ude3e',\n  'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n  'pray':'\\ud83d\\ude4f',\n  'prayer_beads':'\\ud83d\\udcff',\n  'pregnant_woman':'\\ud83e\\udd30',\n  'previous_track_button':'\\u23ee',\n  'prince':'\\ud83e\\udd34',\n  'princess':'\\ud83d\\udc78',\n  'printer':'\\ud83d\\udda8',\n  'purple_heart':'\\ud83d\\udc9c',\n  'purse':'\\ud83d\\udc5b',\n  'pushpin':'\\ud83d\\udccc',\n  'put_litter_in_its_place':'\\ud83d\\udeae',\n  'question':'\\u2753',\n  'rabbit':'\\ud83d\\udc30',\n  'rabbit2':'\\ud83d\\udc07',\n  'racehorse':'\\ud83d\\udc0e',\n  'racing_car':'\\ud83c\\udfce',\n  'radio':'\\ud83d\\udcfb',\n  'radio_button':'\\ud83d\\udd18',\n  'radioactive':'\\u2622\\ufe0f',\n  'railway_car':'\\ud83d\\ude83',\n  'railway_track':'\\ud83d\\udee4',\n  'rainbow':'\\ud83c\\udf08',\n  'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n  'raised_back_of_hand':'\\ud83e\\udd1a',\n  'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n  'raised_hands':'\\ud83d\\ude4c',\n  'raising_hand_woman':'\\ud83d\\ude4b',\n  'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n  'ram':'\\ud83d\\udc0f',\n  'ramen':'\\ud83c\\udf5c',\n  'rat':'\\ud83d\\udc00',\n  'record_button':'\\u23fa',\n  'recycle':'\\u267b\\ufe0f',\n  'red_circle':'\\ud83d\\udd34',\n  'registered':'\\u00ae\\ufe0f',\n  'relaxed':'\\u263a\\ufe0f',\n  'relieved':'\\ud83d\\ude0c',\n  'reminder_ribbon':'\\ud83c\\udf97',\n  'repeat':'\\ud83d\\udd01',\n  'repeat_one':'\\ud83d\\udd02',\n  'rescue_worker_helmet':'\\u26d1',\n  'restroom':'\\ud83d\\udebb',\n  'revolving_hearts':'\\ud83d\\udc9e',\n  'rewind':'\\u23ea',\n  'rhinoceros':'\\ud83e\\udd8f',\n  'ribbon':'\\ud83c\\udf80',\n  'rice':'\\ud83c\\udf5a',\n  'rice_ball':'\\ud83c\\udf59',\n  'rice_cracker':'\\ud83c\\udf58',\n  'rice_scene':'\\ud83c\\udf91',\n  'right_anger_bubble':'\\ud83d\\uddef',\n  'ring':'\\ud83d\\udc8d',\n  'robot':'\\ud83e\\udd16',\n  'rocket':'\\ud83d\\ude80',\n  'rofl':'\\ud83e\\udd23',\n  'roll_eyes':'\\ud83d\\ude44',\n  'roller_coaster':'\\ud83c\\udfa2',\n  'rooster':'\\ud83d\\udc13',\n  'rose':'\\ud83c\\udf39',\n  'rosette':'\\ud83c\\udff5',\n  'rotating_light':'\\ud83d\\udea8',\n  'round_pushpin':'\\ud83d\\udccd',\n  'rowing_man':'\\ud83d\\udea3',\n  'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n  'rugby_football':'\\ud83c\\udfc9',\n  'running_man':'\\ud83c\\udfc3',\n  'running_shirt_with_sash':'\\ud83c\\udfbd',\n  'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n  'sa':'\\ud83c\\ude02\\ufe0f',\n  'sagittarius':'\\u2650\\ufe0f',\n  'sake':'\\ud83c\\udf76',\n  'sandal':'\\ud83d\\udc61',\n  'santa':'\\ud83c\\udf85',\n  'satellite':'\\ud83d\\udce1',\n  'saxophone':'\\ud83c\\udfb7',\n  'school':'\\ud83c\\udfeb',\n  'school_satchel':'\\ud83c\\udf92',\n  'scissors':'\\u2702\\ufe0f',\n  'scorpion':'\\ud83e\\udd82',\n  'scorpius':'\\u264f\\ufe0f',\n  'scream':'\\ud83d\\ude31',\n  'scream_cat':'\\ud83d\\ude40',\n  'scroll':'\\ud83d\\udcdc',\n  'seat':'\\ud83d\\udcba',\n  'secret':'\\u3299\\ufe0f',\n  'see_no_evil':'\\ud83d\\ude48',\n  'seedling':'\\ud83c\\udf31',\n  'selfie':'\\ud83e\\udd33',\n  'shallow_pan_of_food':'\\ud83e\\udd58',\n  'shamrock':'\\u2618\\ufe0f',\n  'shark':'\\ud83e\\udd88',\n  'shaved_ice':'\\ud83c\\udf67',\n  'sheep':'\\ud83d\\udc11',\n  'shell':'\\ud83d\\udc1a',\n  'shield':'\\ud83d\\udee1',\n  'shinto_shrine':'\\u26e9',\n  'ship':'\\ud83d\\udea2',\n  'shirt':'\\ud83d\\udc55',\n  'shopping':'\\ud83d\\udecd',\n  'shopping_cart':'\\ud83d\\uded2',\n  'shower':'\\ud83d\\udebf',\n  'shrimp':'\\ud83e\\udd90',\n  'signal_strength':'\\ud83d\\udcf6',\n  'six_pointed_star':'\\ud83d\\udd2f',\n  'ski':'\\ud83c\\udfbf',\n  'skier':'\\u26f7',\n  'skull':'\\ud83d\\udc80',\n  'skull_and_crossbones':'\\u2620\\ufe0f',\n  'sleeping':'\\ud83d\\ude34',\n  'sleeping_bed':'\\ud83d\\udecc',\n  'sleepy':'\\ud83d\\ude2a',\n  'slightly_frowning_face':'\\ud83d\\ude41',\n  'slightly_smiling_face':'\\ud83d\\ude42',\n  'slot_machine':'\\ud83c\\udfb0',\n  'small_airplane':'\\ud83d\\udee9',\n  'small_blue_diamond':'\\ud83d\\udd39',\n  'small_orange_diamond':'\\ud83d\\udd38',\n  'small_red_triangle':'\\ud83d\\udd3a',\n  'small_red_triangle_down':'\\ud83d\\udd3b',\n  'smile':'\\ud83d\\ude04',\n  'smile_cat':'\\ud83d\\ude38',\n  'smiley':'\\ud83d\\ude03',\n  'smiley_cat':'\\ud83d\\ude3a',\n  'smiling_imp':'\\ud83d\\ude08',\n  'smirk':'\\ud83d\\ude0f',\n  'smirk_cat':'\\ud83d\\ude3c',\n  'smoking':'\\ud83d\\udeac',\n  'snail':'\\ud83d\\udc0c',\n  'snake':'\\ud83d\\udc0d',\n  'sneezing_face':'\\ud83e\\udd27',\n  'snowboarder':'\\ud83c\\udfc2',\n  'snowflake':'\\u2744\\ufe0f',\n  'snowman':'\\u26c4\\ufe0f',\n  'snowman_with_snow':'\\u2603\\ufe0f',\n  'sob':'\\ud83d\\ude2d',\n  'soccer':'\\u26bd\\ufe0f',\n  'soon':'\\ud83d\\udd1c',\n  'sos':'\\ud83c\\udd98',\n  'sound':'\\ud83d\\udd09',\n  'space_invader':'\\ud83d\\udc7e',\n  'spades':'\\u2660\\ufe0f',\n  'spaghetti':'\\ud83c\\udf5d',\n  'sparkle':'\\u2747\\ufe0f',\n  'sparkler':'\\ud83c\\udf87',\n  'sparkles':'\\u2728',\n  'sparkling_heart':'\\ud83d\\udc96',\n  'speak_no_evil':'\\ud83d\\ude4a',\n  'speaker':'\\ud83d\\udd08',\n  'speaking_head':'\\ud83d\\udde3',\n  'speech_balloon':'\\ud83d\\udcac',\n  'speedboat':'\\ud83d\\udea4',\n  'spider':'\\ud83d\\udd77',\n  'spider_web':'\\ud83d\\udd78',\n  'spiral_calendar':'\\ud83d\\uddd3',\n  'spiral_notepad':'\\ud83d\\uddd2',\n  'spoon':'\\ud83e\\udd44',\n  'squid':'\\ud83e\\udd91',\n  'stadium':'\\ud83c\\udfdf',\n  'star':'\\u2b50\\ufe0f',\n  'star2':'\\ud83c\\udf1f',\n  'star_and_crescent':'\\u262a\\ufe0f',\n  'star_of_david':'\\u2721\\ufe0f',\n  'stars':'\\ud83c\\udf20',\n  'station':'\\ud83d\\ude89',\n  'statue_of_liberty':'\\ud83d\\uddfd',\n  'steam_locomotive':'\\ud83d\\ude82',\n  'stew':'\\ud83c\\udf72',\n  'stop_button':'\\u23f9',\n  'stop_sign':'\\ud83d\\uded1',\n  'stopwatch':'\\u23f1',\n  'straight_ruler':'\\ud83d\\udccf',\n  'strawberry':'\\ud83c\\udf53',\n  'stuck_out_tongue':'\\ud83d\\ude1b',\n  'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n  'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n  'studio_microphone':'\\ud83c\\udf99',\n  'stuffed_flatbread':'\\ud83e\\udd59',\n  'sun_behind_large_cloud':'\\ud83c\\udf25',\n  'sun_behind_rain_cloud':'\\ud83c\\udf26',\n  'sun_behind_small_cloud':'\\ud83c\\udf24',\n  'sun_with_face':'\\ud83c\\udf1e',\n  'sunflower':'\\ud83c\\udf3b',\n  'sunglasses':'\\ud83d\\ude0e',\n  'sunny':'\\u2600\\ufe0f',\n  'sunrise':'\\ud83c\\udf05',\n  'sunrise_over_mountains':'\\ud83c\\udf04',\n  'surfing_man':'\\ud83c\\udfc4',\n  'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n  'sushi':'\\ud83c\\udf63',\n  'suspension_railway':'\\ud83d\\ude9f',\n  'sweat':'\\ud83d\\ude13',\n  'sweat_drops':'\\ud83d\\udca6',\n  'sweat_smile':'\\ud83d\\ude05',\n  'sweet_potato':'\\ud83c\\udf60',\n  'swimming_man':'\\ud83c\\udfca',\n  'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n  'symbols':'\\ud83d\\udd23',\n  'synagogue':'\\ud83d\\udd4d',\n  'syringe':'\\ud83d\\udc89',\n  'taco':'\\ud83c\\udf2e',\n  'tada':'\\ud83c\\udf89',\n  'tanabata_tree':'\\ud83c\\udf8b',\n  'taurus':'\\u2649\\ufe0f',\n  'taxi':'\\ud83d\\ude95',\n  'tea':'\\ud83c\\udf75',\n  'telephone_receiver':'\\ud83d\\udcde',\n  'telescope':'\\ud83d\\udd2d',\n  'tennis':'\\ud83c\\udfbe',\n  'tent':'\\u26fa\\ufe0f',\n  'thermometer':'\\ud83c\\udf21',\n  'thinking':'\\ud83e\\udd14',\n  'thought_balloon':'\\ud83d\\udcad',\n  'ticket':'\\ud83c\\udfab',\n  'tickets':'\\ud83c\\udf9f',\n  'tiger':'\\ud83d\\udc2f',\n  'tiger2':'\\ud83d\\udc05',\n  'timer_clock':'\\u23f2',\n  'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n  'tired_face':'\\ud83d\\ude2b',\n  'tm':'\\u2122\\ufe0f',\n  'toilet':'\\ud83d\\udebd',\n  'tokyo_tower':'\\ud83d\\uddfc',\n  'tomato':'\\ud83c\\udf45',\n  'tongue':'\\ud83d\\udc45',\n  'top':'\\ud83d\\udd1d',\n  'tophat':'\\ud83c\\udfa9',\n  'tornado':'\\ud83c\\udf2a',\n  'trackball':'\\ud83d\\uddb2',\n  'tractor':'\\ud83d\\ude9c',\n  'traffic_light':'\\ud83d\\udea5',\n  'train':'\\ud83d\\ude8b',\n  'train2':'\\ud83d\\ude86',\n  'tram':'\\ud83d\\ude8a',\n  'triangular_flag_on_post':'\\ud83d\\udea9',\n  'triangular_ruler':'\\ud83d\\udcd0',\n  'trident':'\\ud83d\\udd31',\n  'triumph':'\\ud83d\\ude24',\n  'trolleybus':'\\ud83d\\ude8e',\n  'trophy':'\\ud83c\\udfc6',\n  'tropical_drink':'\\ud83c\\udf79',\n  'tropical_fish':'\\ud83d\\udc20',\n  'truck':'\\ud83d\\ude9a',\n  'trumpet':'\\ud83c\\udfba',\n  'tulip':'\\ud83c\\udf37',\n  'tumbler_glass':'\\ud83e\\udd43',\n  'turkey':'\\ud83e\\udd83',\n  'turtle':'\\ud83d\\udc22',\n  'tv':'\\ud83d\\udcfa',\n  'twisted_rightwards_arrows':'\\ud83d\\udd00',\n  'two_hearts':'\\ud83d\\udc95',\n  'two_men_holding_hands':'\\ud83d\\udc6c',\n  'two_women_holding_hands':'\\ud83d\\udc6d',\n  'u5272':'\\ud83c\\ude39',\n  'u5408':'\\ud83c\\ude34',\n  'u55b6':'\\ud83c\\ude3a',\n  'u6307':'\\ud83c\\ude2f\\ufe0f',\n  'u6708':'\\ud83c\\ude37\\ufe0f',\n  'u6709':'\\ud83c\\ude36',\n  'u6e80':'\\ud83c\\ude35',\n  'u7121':'\\ud83c\\ude1a\\ufe0f',\n  'u7533':'\\ud83c\\ude38',\n  'u7981':'\\ud83c\\ude32',\n  'u7a7a':'\\ud83c\\ude33',\n  'umbrella':'\\u2614\\ufe0f',\n  'unamused':'\\ud83d\\ude12',\n  'underage':'\\ud83d\\udd1e',\n  'unicorn':'\\ud83e\\udd84',\n  'unlock':'\\ud83d\\udd13',\n  'up':'\\ud83c\\udd99',\n  'upside_down_face':'\\ud83d\\ude43',\n  'v':'\\u270c\\ufe0f',\n  'vertical_traffic_light':'\\ud83d\\udea6',\n  'vhs':'\\ud83d\\udcfc',\n  'vibration_mode':'\\ud83d\\udcf3',\n  'video_camera':'\\ud83d\\udcf9',\n  'video_game':'\\ud83c\\udfae',\n  'violin':'\\ud83c\\udfbb',\n  'virgo':'\\u264d\\ufe0f',\n  'volcano':'\\ud83c\\udf0b',\n  'volleyball':'\\ud83c\\udfd0',\n  'vs':'\\ud83c\\udd9a',\n  'vulcan_salute':'\\ud83d\\udd96',\n  'walking_man':'\\ud83d\\udeb6',\n  'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n  'waning_crescent_moon':'\\ud83c\\udf18',\n  'waning_gibbous_moon':'\\ud83c\\udf16',\n  'warning':'\\u26a0\\ufe0f',\n  'wastebasket':'\\ud83d\\uddd1',\n  'watch':'\\u231a\\ufe0f',\n  'water_buffalo':'\\ud83d\\udc03',\n  'watermelon':'\\ud83c\\udf49',\n  'wave':'\\ud83d\\udc4b',\n  'wavy_dash':'\\u3030\\ufe0f',\n  'waxing_crescent_moon':'\\ud83c\\udf12',\n  'wc':'\\ud83d\\udebe',\n  'weary':'\\ud83d\\ude29',\n  'wedding':'\\ud83d\\udc92',\n  'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n  'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n  'whale':'\\ud83d\\udc33',\n  'whale2':'\\ud83d\\udc0b',\n  'wheel_of_dharma':'\\u2638\\ufe0f',\n  'wheelchair':'\\u267f\\ufe0f',\n  'white_check_mark':'\\u2705',\n  'white_circle':'\\u26aa\\ufe0f',\n  'white_flag':'\\ud83c\\udff3\\ufe0f',\n  'white_flower':'\\ud83d\\udcae',\n  'white_large_square':'\\u2b1c\\ufe0f',\n  'white_medium_small_square':'\\u25fd\\ufe0f',\n  'white_medium_square':'\\u25fb\\ufe0f',\n  'white_small_square':'\\u25ab\\ufe0f',\n  'white_square_button':'\\ud83d\\udd33',\n  'wilted_flower':'\\ud83e\\udd40',\n  'wind_chime':'\\ud83c\\udf90',\n  'wind_face':'\\ud83c\\udf2c',\n  'wine_glass':'\\ud83c\\udf77',\n  'wink':'\\ud83d\\ude09',\n  'wolf':'\\ud83d\\udc3a',\n  'woman':'\\ud83d\\udc69',\n  'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n  'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n  'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n  'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n  'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n  'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n  'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n  'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n  'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n  'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n  'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n  'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n  'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n  'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n  'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n  'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n  'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n  'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n  'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n  'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n  'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n  'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n  'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n  'womans_clothes':'\\ud83d\\udc5a',\n  'womans_hat':'\\ud83d\\udc52',\n  'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n  'womens':'\\ud83d\\udeba',\n  'world_map':'\\ud83d\\uddfa',\n  'worried':'\\ud83d\\ude1f',\n  'wrench':'\\ud83d\\udd27',\n  'writing_hand':'\\u270d\\ufe0f',\n  'x':'\\u274c',\n  'yellow_heart':'\\ud83d\\udc9b',\n  'yen':'\\ud83d\\udcb4',\n  'yin_yang':'\\u262f\\ufe0f',\n  'yum':'\\ud83d\\ude0b',\n  'zap':'\\u26a1\\ufe0f',\n  'zipper_mouth_face':'\\ud83e\\udd10',\n  'zzz':'\\ud83d\\udca4',\n\n  /* special emojis :P */\n  'octocat':  '\":octocat:\"',\n  'showdown': 'S'\n};\n","/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n  'use strict';\n\n  var\n      /**\n       * Options used by this converter\n       * @private\n       * @type {{}}\n       */\n      options = {},\n\n      /**\n       * Language extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      langExtensions = [],\n\n      /**\n       * Output modifiers extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      outputModifiers = [],\n\n      /**\n       * Event listeners\n       * @private\n       * @type {{}}\n       */\n      listeners = {},\n\n      /**\n       * The flavor set in this converter\n       */\n      setConvFlavor = setFlavor,\n\n      /**\n       * Metadata of the document\n       * @type {{parsed: {}, raw: string, format: string}}\n       */\n      metadata = {\n        parsed: {},\n        raw: '',\n        format: ''\n      };\n\n  _constructor();\n\n  /**\n   * Converter constructor\n   * @private\n   */\n  function _constructor () {\n    converterOptions = converterOptions || {};\n\n    for (var gOpt in globalOptions) {\n      if (globalOptions.hasOwnProperty(gOpt)) {\n        options[gOpt] = globalOptions[gOpt];\n      }\n    }\n\n    // Merge options\n    if (typeof converterOptions === 'object') {\n      for (var opt in converterOptions) {\n        if (converterOptions.hasOwnProperty(opt)) {\n          options[opt] = converterOptions[opt];\n        }\n      }\n    } else {\n      throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n      ' was passed instead.');\n    }\n\n    if (options.extensions) {\n      showdown.helper.forEach(options.extensions, _parseExtension);\n    }\n  }\n\n  /**\n   * Parse extension\n   * @param {*} ext\n   * @param {string} [name='']\n   * @private\n   */\n  function _parseExtension (ext, name) {\n\n    name = name || null;\n    // If it's a string, the extension was previously loaded\n    if (showdown.helper.isString(ext)) {\n      ext = showdown.helper.stdExtName(ext);\n      name = ext;\n\n      // LEGACY_SUPPORT CODE\n      if (showdown.extensions[ext]) {\n        console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n          'Please inform the developer that the extension should be updated!');\n        legacyExtensionLoading(showdown.extensions[ext], ext);\n        return;\n        // END LEGACY SUPPORT CODE\n\n      } else if (!showdown.helper.isUndefined(extensions[ext])) {\n        ext = extensions[ext];\n\n      } else {\n        throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n      }\n    }\n\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExt = validate(ext, name);\n    if (!validExt.valid) {\n      throw Error(validExt.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n      }\n      if (ext[i].hasOwnProperty('listeners')) {\n        for (var ln in ext[i].listeners) {\n          if (ext[i].listeners.hasOwnProperty(ln)) {\n            listen(ln, ext[i].listeners[ln]);\n          }\n        }\n      }\n    }\n\n  }\n\n  /**\n   * LEGACY_SUPPORT\n   * @param {*} ext\n   * @param {string} name\n   */\n  function legacyExtensionLoading (ext, name) {\n    if (typeof ext === 'function') {\n      ext = ext(new showdown.Converter());\n    }\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n    var valid = validate(ext, name);\n\n    if (!valid.valid) {\n      throw Error(valid.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n        default:// should never reach here\n          throw Error('Extension loader error: Type unrecognized!!!');\n      }\n    }\n  }\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   */\n  function listen (name, callback) {\n    if (!showdown.helper.isString(name)) {\n      throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n    }\n\n    if (typeof callback !== 'function') {\n      throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n    }\n\n    if (!listeners.hasOwnProperty(name)) {\n      listeners[name] = [];\n    }\n    listeners[name].push(callback);\n  }\n\n  function rTrimInputText (text) {\n    var rsp = text.match(/^\\s*/)[0].length,\n        rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n    return text.replace(rgx, '');\n  }\n\n  /**\n   * Dispatch an event\n   * @private\n   * @param {string} evtName Event name\n   * @param {string} text Text\n   * @param {{}} options Converter Options\n   * @param {{}} globals\n   * @returns {string}\n   */\n  this._dispatch = function dispatch (evtName, text, options, globals) {\n    if (listeners.hasOwnProperty(evtName)) {\n      for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n        var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n        if (nText && typeof nText !== 'undefined') {\n          text = nText;\n        }\n      }\n    }\n    return text;\n  };\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   * @returns {showdown.Converter}\n   */\n  this.listen = function (name, callback) {\n    listen(name, callback);\n    return this;\n  };\n\n  /**\n   * Converts a markdown string into HTML\n   * @param {string} text\n   * @returns {*}\n   */\n  this.makeHtml = function (text) {\n    //check if text is not falsy\n    if (!text) {\n      return text;\n    }\n\n    var globals = {\n      gHtmlBlocks:     [],\n      gHtmlMdBlocks:   [],\n      gHtmlSpans:      [],\n      gUrls:           {},\n      gTitles:         {},\n      gDimensions:     {},\n      gListLevel:      0,\n      hashLinkCounts:  {},\n      langExtensions:  langExtensions,\n      outputModifiers: outputModifiers,\n      converter:       this,\n      ghCodeBlocks:    [],\n      metadata: {\n        parsed: {},\n        raw: '',\n        format: ''\n      }\n    };\n\n    // This lets us use ¨ trema as an escape char to avoid md5 hashes\n    // The choice of character is arbitrary; anything that isn't\n    // magic in Markdown will work.\n    text = text.replace(/¨/g, '¨T');\n\n    // Replace $ with ¨D\n    // RegExp interprets $ as a special character\n    // when it's in a replacement string\n    text = text.replace(/\\$/g, '¨D');\n\n    // Standardize line endings\n    text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n    text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n    // Stardardize line spaces\n    text = text.replace(/\\u00A0/g, ' ');\n\n    if (options.smartIndentationFix) {\n      text = rTrimInputText(text);\n    }\n\n    // Make sure text begins and ends with a couple of newlines:\n    text = '\\n\\n' + text + '\\n\\n';\n\n    // detab\n    text = showdown.subParser('detab')(text, options, globals);\n\n    /**\n     * Strip any lines consisting only of spaces and tabs.\n     * This makes subsequent regexs easier to write, because we can\n     * match consecutive blank lines with /\\n+/ instead of something\n     * contorted like /[ \\t]*\\n+/\n     */\n    text = text.replace(/^[ \\t]+$/mg, '');\n\n    //run languageExtensions\n    showdown.helper.forEach(langExtensions, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // run the sub parsers\n    text = showdown.subParser('metadata')(text, options, globals);\n    text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n    text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n    text = showdown.subParser('hashCodeTags')(text, options, globals);\n    text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n    text = showdown.subParser('blockGamut')(text, options, globals);\n    text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n    text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n    // attacklab: Restore dollar signs\n    text = text.replace(/¨D/g, '$$');\n\n    // attacklab: Restore tremas\n    text = text.replace(/¨T/g, '¨');\n\n    // render a complete html document instead of a partial if the option is enabled\n    text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n    // Run output modifiers\n    showdown.helper.forEach(outputModifiers, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // update metadata\n    metadata = globals.metadata;\n    return text;\n  };\n\n  /**\n   * Converts an HTML string into a markdown string\n   * @param src\n   * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n   * @returns {string}\n   */\n  this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n    // replace \\r\\n with \\n\n    src = src.replace(/\\r\\n/g, '\\n');\n    src = src.replace(/\\r/g, '\\n'); // old macs\n\n    // due to an edge case, we need to find this: > <\n    // to prevent removing of non silent white spaces\n    // ex: this is sparta\n    src = src.replace(/>[ \\t]+¨NBSP;<');\n\n    if (!HTMLParser) {\n      if (window && window.document) {\n        HTMLParser = window.document;\n      } else {\n        throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n      }\n    }\n\n    var doc = HTMLParser.createElement('div');\n    doc.innerHTML = src;\n\n    var globals = {\n      preList: substitutePreCodeTags(doc)\n    };\n\n    // remove all newlines and collapse spaces\n    clean(doc);\n\n    // some stuff, like accidental reference links must now be escaped\n    // TODO\n    // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n    var nodes = doc.childNodes,\n        mdDoc = '';\n\n    for (var i = 0; i < nodes.length; i++) {\n      mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n    }\n\n    function clean (node) {\n      for (var n = 0; n < node.childNodes.length; ++n) {\n        var child = node.childNodes[n];\n        if (child.nodeType === 3) {\n          if (!/\\S/.test(child.nodeValue)) {\n            node.removeChild(child);\n            --n;\n          } else {\n            child.nodeValue = child.nodeValue.split('\\n').join(' ');\n            child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n          }\n        } else if (child.nodeType === 1) {\n          clean(child);\n        }\n      }\n    }\n\n    // find all pre tags and replace contents with placeholder\n    // we need this so that we can remove all indentation from html\n    // to ease up parsing\n    function substitutePreCodeTags (doc) {\n\n      var pres = doc.querySelectorAll('pre'),\n          presPH = [];\n\n      for (var i = 0; i < pres.length; ++i) {\n\n        if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n          var content = pres[i].firstChild.innerHTML.trim(),\n              language = pres[i].firstChild.getAttribute('data-language') || '';\n\n          // if data-language attribute is not defined, then we look for class language-*\n          if (language === '') {\n            var classes = pres[i].firstChild.className.split(' ');\n            for (var c = 0; c < classes.length; ++c) {\n              var matches = classes[c].match(/^language-(.+)$/);\n              if (matches !== null) {\n                language = matches[1];\n                break;\n              }\n            }\n          }\n\n          // unescape html entities in content\n          content = showdown.helper.unescapeHTMLEntities(content);\n\n          presPH.push(content);\n          pres[i].outerHTML = '';\n        } else {\n          presPH.push(pres[i].innerHTML);\n          pres[i].innerHTML = '';\n          pres[i].setAttribute('prenum', i.toString());\n        }\n      }\n      return presPH;\n    }\n\n    return mdDoc;\n  };\n\n  /**\n   * Set an option of this Converter instance\n   * @param {string} key\n   * @param {*} value\n   */\n  this.setOption = function (key, value) {\n    options[key] = value;\n  };\n\n  /**\n   * Get the option of this Converter instance\n   * @param {string} key\n   * @returns {*}\n   */\n  this.getOption = function (key) {\n    return options[key];\n  };\n\n  /**\n   * Get the options of this Converter instance\n   * @returns {{}}\n   */\n  this.getOptions = function () {\n    return options;\n  };\n\n  /**\n   * Add extension to THIS converter\n   * @param {{}} extension\n   * @param {string} [name=null]\n   */\n  this.addExtension = function (extension, name) {\n    name = name || null;\n    _parseExtension(extension, name);\n  };\n\n  /**\n   * Use a global registered extension with THIS converter\n   * @param {string} extensionName Name of the previously registered extension\n   */\n  this.useExtension = function (extensionName) {\n    _parseExtension(extensionName);\n  };\n\n  /**\n   * Set the flavor THIS converter should use\n   * @param {string} name\n   */\n  this.setFlavor = function (name) {\n    if (!flavor.hasOwnProperty(name)) {\n      throw Error(name + ' flavor was not found');\n    }\n    var preset = flavor[name];\n    setConvFlavor = name;\n    for (var option in preset) {\n      if (preset.hasOwnProperty(option)) {\n        options[option] = preset[option];\n      }\n    }\n  };\n\n  /**\n   * Get the currently set flavor of this converter\n   * @returns {string}\n   */\n  this.getFlavor = function () {\n    return setConvFlavor;\n  };\n\n  /**\n   * Remove an extension from THIS converter.\n   * Note: This is a costly operation. It's better to initialize a new converter\n   * and specify the extensions you wish to use\n   * @param {Array} extension\n   */\n  this.removeExtension = function (extension) {\n    if (!showdown.helper.isArray(extension)) {\n      extension = [extension];\n    }\n    for (var a = 0; a < extension.length; ++a) {\n      var ext = extension[a];\n      for (var i = 0; i < langExtensions.length; ++i) {\n        if (langExtensions[i] === ext) {\n          langExtensions[i].splice(i, 1);\n        }\n      }\n      for (var ii = 0; ii < outputModifiers.length; ++i) {\n        if (outputModifiers[ii] === ext) {\n          outputModifiers[ii].splice(i, 1);\n        }\n      }\n    }\n  };\n\n  /**\n   * Get all extension of THIS converter\n   * @returns {{language: Array, output: Array}}\n   */\n  this.getAllExtensions = function () {\n    return {\n      language: langExtensions,\n      output: outputModifiers\n    };\n  };\n\n  /**\n   * Get the metadata of the previously parsed document\n   * @param raw\n   * @returns {string|{}}\n   */\n  this.getMetadata = function (raw) {\n    if (raw) {\n      return metadata.raw;\n    } else {\n      return metadata.parsed;\n    }\n  };\n\n  /**\n   * Get the metadata format of the previously parsed document\n   * @returns {string}\n   */\n  this.getMetadataFormat = function () {\n    return metadata.format;\n  };\n\n  /**\n   * Private: set a single key, value metadata pair\n   * @param {string} key\n   * @param {string} value\n   */\n  this._setMetadataPair = function (key, value) {\n    metadata.parsed[key] = value;\n  };\n\n  /**\n   * Private: set metadata format\n   * @param {string} format\n   */\n  this._setMetadataFormat = function (format) {\n    metadata.format = format;\n  };\n\n  /**\n   * Private: set metadata raw text\n   * @param {string} raw\n   */\n  this._setMetadataRaw = function (raw) {\n    metadata.raw = raw;\n  };\n};\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n  var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n    if (showdown.helper.isUndefined(title)) {\n      title = '';\n    }\n    linkId = linkId.toLowerCase();\n\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n    } else if (!url) {\n      if (!linkId) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n        url = globals.gUrls[linkId];\n        if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n          title = globals.gTitles[linkId];\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n    var result = '';\n\n    return result;\n  };\n\n  // First, handle reference-style links: [link text] [id]\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n  // Next, inline-style links: [link text](url \"optional title\")\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // normal cases\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // handle reference-style shortcuts: [link text]\n  // These must come last in case you've also got [link test][1]\n  // or [link test](/foo)\n  text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n  // Lastly handle GithubMentions if option is enabled\n  if (options.ghMentions) {\n    text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n      if (escape === '\\\\') {\n        return st + mentions;\n      }\n\n      //check if options.ghMentionsLink is a string\n      if (!showdown.helper.isString(options.ghMentionsLink)) {\n        throw new Error('ghMentionsLink option must be a string');\n      }\n      var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n          target = '';\n      if (options.openLinksInNewWindow) {\n        target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n      }\n      return st + '' + mentions + '';\n    });\n  }\n\n  text = globals.converter._dispatch('anchors.after', text, options, globals);\n  return text;\n});\n","// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex  = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    delimUrlRegex   = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n    simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n    delimMailRegex  = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n    replaceLink = function (options) {\n      'use strict';\n      return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n        link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n        var lnkTxt = link,\n            append = '',\n            target = '',\n            lmc    = leadingMagicChars || '',\n            tmc    = trailingMagicChars || '';\n        if (/^www\\./i.test(link)) {\n          link = link.replace(/^www\\./i, 'http://www.');\n        }\n        if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n          append = trailingPunctuation;\n        }\n        if (options.openLinksInNewWindow) {\n          target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n        }\n        return lmc + '' + lnkTxt + '' + append + tmc;\n      };\n    },\n\n    replaceMail = function (options, globals) {\n      'use strict';\n      return function (wholeMatch, b, mail) {\n        var href = 'mailto:';\n        b = b || '';\n        mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n        if (options.encodeEmails) {\n          href = showdown.helper.encodeEmailAddress(href + mail);\n          mail = showdown.helper.encodeEmailAddress(mail);\n        } else {\n          href = href + mail;\n        }\n        return b + '' + mail + '';\n      };\n    };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n  text = text.replace(delimUrlRegex, replaceLink(options));\n  text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n  return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n  'use strict';\n\n  if (!options.simplifiedAutoLink) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n  if (options.excludeTrailingPunctuationFromURLs) {\n    text = text.replace(simpleURLRegex2, replaceLink(options));\n  } else {\n    text = text.replace(simpleURLRegex, replaceLink(options));\n  }\n  text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n  return text;\n});\n","/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n  // we parse blockquotes first so that we can have headings and hrs\n  // inside blockquotes\n  text = showdown.subParser('blockQuotes')(text, options, globals);\n  text = showdown.subParser('headers')(text, options, globals);\n\n  // Do Horizontal Rules:\n  text = showdown.subParser('horizontalRule')(text, options, globals);\n\n  text = showdown.subParser('lists')(text, options, globals);\n  text = showdown.subParser('codeBlocks')(text, options, globals);\n  text = showdown.subParser('tables')(text, options, globals);\n\n  // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n  // was to escape raw HTML in the original Markdown source. This time,\n  // we're escaping the markup we've just created, so that we don't wrap\n  // 
     tags around block-level tags.\n  text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n  text = showdown.subParser('paragraphs')(text, options, globals);\n\n  text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('blockQuotes', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n  // add a couple extra lines after the text and endtext mark\n  text = text + '\\n\\n';\n\n  var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n  if (options.splitAdjacentBlockquotes) {\n    rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n  }\n\n  text = text.replace(rgx, function (bq) {\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n    // attacklab: clean up hack\n    bq = bq.replace(/¨0/g, '');\n\n    bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n    bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n    bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n    bq = bq.replace(/(^|\\n)/g, '$1  ');\n    // These leading spaces screw with 
     content, so we need to fix that:\n    bq = bq.replace(/(\\s*
    [^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
    \\n' + bq + '\\n
    ', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n","/**\n * Process Markdown `
    ` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
    Just type foo `bar` baz at the prompt.
    \n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n","/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n","/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n","/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n","/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n","/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n","showdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n","showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape 
     elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
    \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
    ', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
    ', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n","/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n","/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n","/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n","/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n","/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n","/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n","/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n","showdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n","showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n","showdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n","showdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n","showdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n","showdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n","\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n","showdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
    ' + globals.preList[num] + '
    ';\n});\n","showdown.subParser('makeMarkdown.strikethrough', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '~~';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '~~';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.strong', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '**';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '**';\n  }\n  return txt;\n});\n","showdown.subParser('makeMarkdown.table', function (node, globals) {\n  'use strict';\n\n  var txt = '',\n      tableArray = [[], []],\n      headings   = node.querySelectorAll('thead>tr>th'),\n      rows       = node.querySelectorAll('tbody>tr'),\n      i, ii;\n  for (i = 0; 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diff --git a/docs/route-vldigeometria.chunk.e95fc.css b/docs/route-vldigeometria.chunk.e95fc.css
deleted file mode 100644
index a96cbe6..0000000
--- a/docs/route-vldigeometria.chunk.e95fc.css
+++ /dev/null
@@ -1 +0,0 @@
-.panel__1ubJw{background-color:rgba(160,204,255,.1);padding:4px;border-radius:4px;margin:4px;height:calc(100% - 8px);min-width:256px}
\ No newline at end of file
diff --git a/docs/sw-esm.js b/docs/sw-esm.js
index 801e4e3..c6fb378 100644
--- a/docs/sw-esm.js
+++ b/docs/sw-esm.js
@@ -1,4 +1,4 @@
-importScripts("/precache-manifest.01e323f5778dc7abb82cf3d35c59f3c3.esm.js", "https://storage.googleapis.com/workbox-cdn/releases/4.3.1/workbox-sw.js");
+importScripts("/precache-manifest.d5b9b83a383fd46375c30c19ae5399b0.esm.js", "https://storage.googleapis.com/workbox-cdn/releases/4.3.1/workbox-sw.js");
 
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diff --git a/docs/sw.js b/docs/sw.js
index db5112b..dc49b18 100644
--- a/docs/sw.js
+++ b/docs/sw.js
@@ -1,4 +1,4 @@
-importScripts("/precache-manifest.c81ea7c2741dedd3fafc34056e5ab75c.js", "https://storage.googleapis.com/workbox-cdn/releases/4.3.1/workbox-sw.js");
+importScripts("/precache-manifest.d70c8ac2ebf9c8612909cb2648f39798.js", "https://storage.googleapis.com/workbox-cdn/releases/4.3.1/workbox-sw.js");
 
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