diff --git a/SimpleDocument.aux b/SimpleDocument.aux index 15423dd..b53dc07 100644 --- a/SimpleDocument.aux +++ b/SimpleDocument.aux @@ -16,6 +16,7 @@ \gdef\HyperFirstAtBeginDocument#1{#1} \providecommand\HyField@AuxAddToFields[1]{} \providecommand\HyField@AuxAddToCoFields[2]{} +\providecommand \oddpage@label [2]{} \@writefile{toc}{\contentsline {section}{\numberline {1}Modelli}{3}{section.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Cenni di Base}{3}{subsection.1.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Esercizi}{5}{subsection.1.2}\protected@file@percent } diff --git a/SimpleDocument.log b/SimpleDocument.log index 718fc4e..4444891 100644 --- a/SimpleDocument.log +++ b/SimpleDocument.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 20.12) (preloaded format=pdflatex 2021.1.16) 15 JUN 2021 14:43 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (MiKTeX 20.12) (preloaded format=pdflatex 2021.1.16) 15 JUN 2021 15:17 entering extended mode **./SimpleDocument.tex (SimpleDocument.tex @@ -172,6 +172,67 @@ Package: listings 2020/03/24 1.8d (Carsten Heinz) (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/base\textcomp.sty Package: textcomp 2020/02/02 v2.0n Standard LaTeX package ) +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/adjustbox\adjustbox.s +ty +Package: adjustbox 2020/08/19 v1.3 Adjusting TeX boxes (trim, clip, ...) + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/xkeyval\xkeyval.sty +Package: xkeyval 2020/11/20 v2.8 package option processing (HA) + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkeyval.tex + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkvutils.te +x +\XKV@toks=\toks23 +\XKV@tempa@toks=\toks24 +) +\XKV@depth=\count271 +File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) +)) +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/adjustbox\adjcalc.sty +Package: adjcalc 2012/05/16 v1.1 Provides advanced setlength with multiple back +-ends (calc, etex, pgfmath) +) +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/adjustbox\trimclip.st +y +Package: trimclip 2020/08/19 v1.2 Trim and clip general TeX material + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/collectbox\collectbox +.sty +Package: collectbox 2012/05/17 v0.4b Collect macro arguments as boxes +\collectedbox=\box51 +) +\tc@llx=\dimen154 +\tc@lly=\dimen155 +\tc@urx=\dimen156 +\tc@ury=\dimen157 +Package trimclip Info: Using driver 'tc-pdftex.def'. + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/adjustbox\tc-pdftex.d +ef +File: tc-pdftex.def 2019/01/04 v2.2 Clipping driver for pdftex +)) +\adjbox@Width=\dimen158 +\adjbox@Height=\dimen159 +\adjbox@Depth=\dimen160 +\adjbox@Totalheight=\dimen161 +\adjbox@pwidth=\dimen162 +\adjbox@pheight=\dimen163 +\adjbox@pdepth=\dimen164 +\adjbox@ptotalheight=\dimen165 + +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/ifoddpage\ifoddpage.s +ty +Package: ifoddpage 2016/04/23 v1.1 Conditionals for odd/even page detection +\c@checkoddpage=\count272 +) +(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/varwidth\varwidth.sty +Package: varwidth 2009/03/30 ver 0.92; Variable-width minipages +\@vwid@box=\box52 +\sift@deathcycles=\count273 +\@vwid@loff=\dimen166 +\@vwid@roff=\dimen167 +)) (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/hyperref\hyperref.sty Package: hyperref 2020-05-15 v7.00e Hypertext links for LaTeX @@ -219,9 +280,9 @@ Package: auxhook 2019-12-17 v1.6 Hooks for auxiliary files (HO) ty Package: kvoptions 2020-10-07 v3.14 Key value format for package options (HO) ) -\@linkdim=\dimen154 -\Hy@linkcounter=\count271 -\Hy@pagecounter=\count272 +\@linkdim=\dimen168 +\Hy@linkcounter=\count274 +\Hy@pagecounter=\count275 (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/hyperref\pd1enc.def File: pd1enc.def 2020-05-15 v7.00e Hyperref: PDFDocEncoding definition (HO) @@ -235,7 +296,7 @@ Package: intcalc 2019/12/15 v1.3 Expandable calculations with integers (HO) ty Package: etexcmds 2019/12/15 v1.7 Avoid name clashes with e-TeX commands (HO) ) -\Hy@SavedSpaceFactor=\count273 +\Hy@SavedSpaceFactor=\count276 Package hyperref Info: Hyper figures OFF on input line 4464. Package hyperref Info: Link nesting OFF on input line 4469. Package hyperref Info: Hyper index ON on input line 4472. @@ -243,13 +304,13 @@ Package hyperref Info: Plain pages OFF on input line 4479. Package hyperref Info: Backreferencing OFF on input line 4484. Package hyperref Info: Implicit mode ON; LaTeX internals redefined. Package hyperref Info: Bookmarks ON on input line 4717. -\c@Hy@tempcnt=\count274 +\c@Hy@tempcnt=\count277 (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/url\url.sty \Urlmuskip=\muskip17 Package: url 2013/09/16 ver 3.4 Verb mode for urls, etc. ) LaTeX Info: Redefining \url on input line 5076. -\XeTeXLinkMargin=\dimen155 +\XeTeXLinkMargin=\dimen169 (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/bitset\bitset.sty Package: bitset 2019/12/09 v1.3 Handle bit-vector datatype (HO) @@ -259,9 +320,9 @@ lc.sty Package: bigintcalc 2019/12/15 v1.5 Expandable calculations on big integers (HO ) )) -\Fld@menulength=\count275 -\Field@Width=\dimen156 -\Fld@charsize=\dimen157 +\Fld@menulength=\count278 +\Field@Width=\dimen170 +\Fld@charsize=\dimen171 Package hyperref Info: Hyper figures OFF on input line 6347. Package hyperref Info: Link nesting OFF on input line 6352. Package hyperref Info: Hyper index ON on input line 6355. @@ -277,9 +338,9 @@ Package: atbegshi-ltx 2020/08/17 v1.0a Emulation of the original atbegshi packa ge with kernel methods ) -\Hy@abspage=\count276 -\c@Item=\count277 -\c@Hfootnote=\count278 +\Hy@abspage=\count279 +\c@Item=\count280 +\c@Hfootnote=\count281 ) Package hyperref Info: Driver (autodetected): hpdftex. @@ -292,8 +353,8 @@ Package: atveryend-ltx 2020/08/19 v1.0a Emulation of the original atvery packag e with kernel methods ) -\Fld@listcount=\count279 -\c@bookmark@seq@number=\count280 +\Fld@listcount=\count282 +\c@bookmark@seq@number=\count283 (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/rerunfilecheck\rerunf ilecheck.sty @@ -311,19 +372,6 @@ Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2 (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/imakeidx\imakeidx.sty Package: imakeidx 2016/10/15 v1.3e Package for typesetting indices in a synchro nous mode -(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/xkeyval\xkeyval.sty -Package: xkeyval 2020/11/20 v2.8 package option processing (HA) - -(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkeyval.tex - -(C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/xkeyval\xkvutils.te -x -\XKV@toks=\toks23 -\XKV@tempa@toks=\toks24 -) -\XKV@depth=\count281 -File: xkeyval.tex 2014/12/03 v2.7a key=value parser (HA) -)) (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/generic/iftex\ifxetex.sty Package: ifxetex 2019/10/25 v0.7 ifxetex legacy package. Use iftex instead. ) @@ -331,29 +379,27 @@ Package: ifxetex 2019/10/25 v0.7 ifxetex legacy package. Use iftex instead. Package: ifluatex 2019/10/25 v1.5 ifluatex legacy package. Use iftex instead. ) (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/tools\multicol.sty Package: multicol 2019/12/09 v1.8y multicolumn formatting (FMi) -\c@tracingmulticols=\count282 -\mult@box=\box51 -\multicol@leftmargin=\dimen158 -\c@unbalance=\count283 -\c@collectmore=\count284 -\doublecol@number=\count285 -\multicoltolerance=\count286 -\multicolpretolerance=\count287 -\full@width=\dimen159 -\page@free=\dimen160 -\premulticols=\dimen161 -\postmulticols=\dimen162 +\c@tracingmulticols=\count284 +\mult@box=\box53 +\multicol@leftmargin=\dimen172 +\c@unbalance=\count285 +\c@collectmore=\count286 +\doublecol@number=\count287 +\multicoltolerance=\count288 +\multicolpretolerance=\count289 +\full@width=\dimen173 +\page@free=\dimen174 +\premulticols=\dimen175 +\postmulticols=\dimen176 \multicolsep=\skip53 \multicolbaselineskip=\skip54 -\partial@page=\box52 -\last@line=\box53 -\maxbalancingoverflow=\dimen163 -\mult@rightbox=\box54 -\mult@grightbox=\box55 -\mult@gfirstbox=\box56 -\mult@firstbox=\box57 -\@tempa=\box58 -\@tempa=\box59 +\partial@page=\box54 +\last@line=\box55 +\maxbalancingoverflow=\dimen177 +\mult@rightbox=\box56 +\mult@grightbox=\box57 +\mult@gfirstbox=\box58 +\mult@firstbox=\box59 \@tempa=\box60 \@tempa=\box61 \@tempa=\box62 @@ -389,15 +435,17 @@ Package: multicol 2019/12/09 v1.8y multicolumn formatting (FMi) \@tempa=\box92 \@tempa=\box93 \@tempa=\box94 -\c@minrows=\count288 -\c@columnbadness=\count289 -\c@finalcolumnbadness=\count290 -\last@try=\dimen164 -\multicolovershoot=\dimen165 -\multicolundershoot=\dimen166 -\mult@nat@firstbox=\box95 -\colbreak@box=\box96 -\mc@col@check@num=\count291 +\@tempa=\box95 +\@tempa=\box96 +\c@minrows=\count290 +\c@columnbadness=\count291 +\c@finalcolumnbadness=\count292 +\last@try=\dimen178 +\multicolovershoot=\dimen179 +\multicolundershoot=\dimen180 +\mult@nat@firstbox=\box97 +\colbreak@box=\box98 +\mc@col@check@num=\count293 )) \SimpleDocument@idxfile=\write3 \openout3 = `SimpleDocument.idx'. @@ -407,41 +455,41 @@ Writing index file SimpleDocument.idx (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/l3backend\l3backend-p dftex.def File: l3backend-pdftex.def 2020-09-24 L3 backend support: PDF output (pdfTeX) -\l__kernel_color_stack_int=\count292 -\l__pdf_internal_box=\box97 +\l__kernel_color_stack_int=\count294 +\l__pdf_internal_box=\box99 ) (SimpleDocument.aux) \openout1 = `SimpleDocument.aux'. -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 24. -LaTeX Font Info: ... okay on input line 24. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 27. +LaTeX Font Info: ... okay on input line 27. (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/context/base/mkii\supp-pdf. mkii [Loading MPS to PDF converter (version 2006.09.02).] -\scratchcounter=\count293 -\scratchdimen=\dimen167 -\scratchbox=\box98 -\nofMPsegments=\count294 -\nofMParguments=\count295 +\scratchcounter=\count295 +\scratchdimen=\dimen181 +\scratchbox=\box100 +\nofMPsegments=\count296 +\nofMParguments=\count297 \everyMPshowfont=\toks25 -\MPscratchCnt=\count296 -\MPscratchDim=\dimen168 -\MPnumerator=\count297 -\makeMPintoPDFobject=\count298 +\MPscratchCnt=\count298 +\MPscratchDim=\dimen182 +\MPnumerator=\count299 +\makeMPintoPDFobject=\count300 \everyMPtoPDFconversion=\toks26 ) (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/epstopdf-pkg\epstopdf @@ -450,8 +498,8 @@ Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 85. ) -\c@lstlisting=\count299 -Package hyperref Info: Link coloring OFF on input line 24. +\c@lstlisting=\count301 +Package hyperref Info: Link coloring OFF on input line 27. (C:\Users\Meschio\AppData\Local\Programs\MiKTeX\tex/latex/hyperref\nameref.sty Package: nameref 2019/09/16 v2.46 Cross-referencing by name of section @@ -463,28 +511,28 @@ Package: refcount 2019/12/15 v3.6 Data extraction from label references (HO) itlestring.sty Package: gettitlestring 2019/12/15 v1.6 Cleanup title references (HO) ) -\c@section@level=\count300 +\c@section@level=\count302 ) -LaTeX Info: Redefining \ref on input line 24. -LaTeX Info: Redefining \pageref on input line 24. -LaTeX Info: Redefining \nameref on input line 24. +LaTeX Info: Redefining \ref on input line 27. +LaTeX Info: Redefining \pageref on input line 27. +LaTeX Info: Redefining \nameref on input line 27. (SimpleDocument.out) (SimpleDocument.out) \@outlinefile=\write4 \openout4 = `SimpleDocument.out'. -LaTeX Font Info: Trying to load font information for U+msa on input line 26. +LaTeX Font Info: Trying to load font information for U+msa on input line 29. 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(rerunfilecheck) Checksum: E819F50BC83584E1FC153B9849328368;4516. ) Here is how much of TeX's memory you used: - 9579 strings out of 479697 - 147106 string characters out of 2866183 - 740037 words of memory out of 3000000 - 26198 multiletter control sequences out of 15000+200000 + 10427 strings out of 479697 + 161974 string characters out of 2866183 + 753231 words of memory out of 3000000 + 27022 multiletter control sequences out of 15000+200000 412403 words of font info for 62 fonts, out of 3000000 for 9000 1141 hyphenation exceptions out of 8191 66i,18n,74p,698b,2020s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -1629,7 +1677,7 @@ ers/Meschio/AppData/Local/Programs/MiKTeX/fonts/type1/public/amsfonts/cm/cmsy7. pfb> -Output written on SimpleDocument.pdf (61 pages, 2897175 bytes). +Output written on SimpleDocument.pdf (61 pages, 2897474 bytes). PDF statistics: 883 PDF objects out of 1000 (max. 8388607) 224 named destinations out of 1000 (max. 500000) diff --git a/SimpleDocument.pdf b/SimpleDocument.pdf index 22162d0..e71f413 100644 Binary files a/SimpleDocument.pdf and b/SimpleDocument.pdf differ diff --git a/SimpleDocument.synctex.gz b/SimpleDocument.synctex.gz index 9625986..4caaf3a 100644 Binary files a/SimpleDocument.synctex.gz and b/SimpleDocument.synctex.gz differ diff --git a/SimpleDocument.tex b/SimpleDocument.tex index e09c0d5..7f60bd0 100644 --- a/SimpleDocument.tex +++ b/SimpleDocument.tex @@ -10,6 +10,9 @@ \usepackage{textcomp} \lstset{upquote=true} +\usepackage{graphicx} %pacchetti per mettere immagini in equazioni +\usepackage[export]{adjustbox} + \usepackage{hyperref} %per gli hyperlink \usepackage{imakeidx} %per l'indice @@ -453,16 +456,16 @@ Reiteriamo per ogni colonna, il vettore colonna azzurro, ovvero il vettore dei t \begin{align*} max: &8u_1 - 2u_2 \\ &-u_1 \leqq 2 \\ -&3u_1 - u_2 \leqq 3 \\ +&3u_1 - u_2 \leqq 3 \\ &-2u_1 + u_2 \leqq 1 \\ &u_1, u_2 \geqq 0 \\ \end{align*} -\raisebox{-.5\height}{\includegraphics[width=5cm]{immagini/ProblemaDuale1.jpg}} +\raisebox{-.5\height}{\includegraphics[width=4cm]{immagini/ProblemaDuale1.jpg}} \end{center} Osservando l'ultima immagine per chiarezza col risultato finale che si riconduce al sistema iniziale.\\ -Se volessi risolvere il sistema invece, partendo dal sistema già orientato nel verso giusto e il suo problema duale:\\ +Se volessi risolvere il sistema invece, partendo dal sistema già orientato nel verso giusto e il suo problema duale con soluzione $x=(15,0,20,0,0)$ $z_P=-30$:\\ \begin{align*} min: &2x_1 + 4x_2 - 3x_3 & & & max: &5u_1 - 10u_2 \\