From: couchot Date: Mon, 4 Nov 2013 19:26:49 +0000 (+0100) Subject: controle ensembles X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/cours-maths-dis.git/commitdiff_plain/381385111635a5d15f8bd60d6666f6c0f6a61bcc?ds=sidebyside controle ensembles --- diff --git a/partiels/131105S1/controle.aux b/partiels/131105S1/controle.aux new file mode 100644 index 0000000..bdcfa3a --- /dev/null +++ b/partiels/131105S1/controle.aux @@ -0,0 +1,13 @@ +\relax +\catcode `:\active +\catcode `;\active +\catcode `!\active +\catcode `?\active +\select@language{french} +\@writefile{toc}{\select@language{french}} +\@writefile{lof}{\select@language{french}} +\@writefile{lot}{\select@language{french}} +\@writefile{toc}{\contentsline {section}{\numberline {1}Cours (3pts) }{1}} +\@writefile{toc}{\contentsline {section}{\numberline {2}(5 pts) Simplification de formules bool\IeC {\'e}ennes (d'apr\IeC {\`e}s sujet de BTS-IG-2008)}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {3}(6 pts) D\IeC {\'e}monstrations ensemblistes}{1}} +\@writefile{toc}{\contentsline {section}{\numberline {4}(6 pts) Relation entre puissances d'\IeC {\'e}l\IeC {\'e}ments}{1}} diff --git a/partiels/131105S1/controle.log b/partiels/131105S1/controle.log new file mode 100644 index 0000000..8c27c7d --- /dev/null +++ b/partiels/131105S1/controle.log @@ -0,0 +1,1128 @@ +This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.3) 4 NOV 2013 20:22 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**controle.tex +(./controle.tex +LaTeX2e <2011/06/27> +Babel <3.9f> and hyphenation patterns for 4 languages loaded. +(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls +Document Class: article 2007/10/19 v1.4h Standard LaTeX document class +(/usr/share/texlive/texmf-dist/tex/latex/base/size11.clo +File: size11.clo 2007/10/19 v1.4h Standard LaTeX file (size option) +) +\c@part=\count79 +\c@section=\count80 +\c@subsection=\count81 +\c@subsubsection=\count82 +\c@paragraph=\count83 +\c@subparagraph=\count84 +\c@figure=\count85 +\c@table=\count86 +\abovecaptionskip=\skip41 +\belowcaptionskip=\skip42 +\bibindent=\dimen102 +) +(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.sty +Package: babel 2013/05/16 v3.9f The Babel package + +(/usr/share/texlive/texmf-dist/tex/generic/babel-french/frenchb.ldf +Language: frenchb 2013/07/06 v2.6e French support from the babel system + +(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.def +File: babel.def 2013/05/16 v3.9f Babel common definitions +\babel@savecnt=\count87 +\U@D=\dimen103 +) +\FB@interchartokenstateORI=\count88 +Package babel Info: Making : an active character on input line 240. +Package babel Info: Making ; an active character on input line 241. +Package babel Info: Making ! an active character on input line 242. +Package babel Info: Making ? an active character on input line 243. +\FB@Mht=\dimen104 +\std@mcc=\count89 +\dec@mcc=\count90 +\listindentFB=\skip43 +\labelwidthFB=\skip44 +\leftmarginFB=\skip45 +\parindentFFN=\dimen105 +) +(/usr/share/texlive/texmf-dist/tex/generic/babel-french/frenchb.ldf +Language: frenchb 2013/07/06 v2.6e French support from the babel system +)) +(/usr/share/texlive/texmf-dist/tex/latex/carlisle/scalefnt.sty) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty +Package: keyval 1999/03/16 v1.13 key=value parser (DPC) +\KV@toks@=\toks14 +) +(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty +Package: inputenc 2008/03/30 v1.1d Input encoding file +\inpenc@prehook=\toks15 +\inpenc@posthook=\toks16 + +(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def +File: utf8.def 2008/04/05 v1.1m UTF-8 support for inputenc +Now handling font encoding OML ... +... no UTF-8 mapping file for font encoding OML +Now handling font encoding T1 ... +... processing UTF-8 mapping file for font encoding T1 + +(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu +File: t1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc + defining Unicode char U+00A1 (decimal 161) + defining Unicode char U+00A3 (decimal 163) + defining Unicode char U+00AB (decimal 171) + defining Unicode char U+00BB (decimal 187) + defining Unicode char U+00BF (decimal 191) + defining Unicode char U+00C0 (decimal 192) + defining Unicode char U+00C1 (decimal 193) + defining Unicode char U+00C2 (decimal 194) + defining Unicode char U+00C3 (decimal 195) + defining Unicode char U+00C4 (decimal 196) + defining Unicode char U+00C5 (decimal 197) + defining Unicode char U+00C6 (decimal 198) + defining Unicode char U+00C7 (decimal 199) + defining Unicode char U+00C8 (decimal 200) + defining Unicode char U+00C9 (decimal 201) + defining Unicode char U+00CA (decimal 202) + defining Unicode char U+00CB (decimal 203) + defining Unicode char U+00CC (decimal 204) + defining Unicode char U+00CD (decimal 205) + defining Unicode char U+00CE (decimal 206) + defining Unicode char U+00CF (decimal 207) + defining Unicode char U+00D0 (decimal 208) + defining Unicode char U+00D1 (decimal 209) + defining Unicode char U+00D2 (decimal 210) + defining Unicode char U+00D3 (decimal 211) + defining Unicode char U+00D4 (decimal 212) + defining Unicode char U+00D5 (decimal 213) + defining Unicode char U+00D6 (decimal 214) + defining Unicode char U+00D8 (decimal 216) + defining Unicode char U+00D9 (decimal 217) + defining Unicode char U+00DA (decimal 218) + defining Unicode char U+00DB (decimal 219) + defining Unicode char U+00DC (decimal 220) + defining Unicode char U+00DD (decimal 221) + defining Unicode char U+00DE (decimal 222) + defining Unicode char U+00DF (decimal 223) + defining Unicode char U+00E0 (decimal 224) + defining Unicode char U+00E1 (decimal 225) + defining Unicode char U+00E2 (decimal 226) + defining Unicode char U+00E3 (decimal 227) + defining Unicode char U+00E4 (decimal 228) + defining Unicode char U+00E5 (decimal 229) + defining Unicode char U+00E6 (decimal 230) + defining Unicode char U+00E7 (decimal 231) + defining Unicode char U+00E8 (decimal 232) + defining Unicode char U+00E9 (decimal 233) + defining Unicode char U+00EA (decimal 234) + defining Unicode char U+00EB (decimal 235) + defining Unicode char U+00EC (decimal 236) + defining Unicode char U+00ED (decimal 237) + defining Unicode char U+00EE (decimal 238) + defining Unicode char U+00EF (decimal 239) + defining Unicode char U+00F0 (decimal 240) + defining Unicode char U+00F1 (decimal 241) + defining Unicode char U+00F2 (decimal 242) + defining Unicode char U+00F3 (decimal 243) + defining Unicode char U+00F4 (decimal 244) + defining Unicode char U+00F5 (decimal 245) + defining Unicode char U+00F6 (decimal 246) + defining Unicode char U+00F8 (decimal 248) + defining Unicode char U+00F9 (decimal 249) + defining Unicode char U+00FA (decimal 250) + defining Unicode char U+00FB (decimal 251) + defining Unicode char U+00FC (decimal 252) + defining Unicode char U+00FD (decimal 253) + defining Unicode char U+00FE (decimal 254) + defining Unicode char U+00FF (decimal 255) + defining Unicode char U+0102 (decimal 258) + defining Unicode char U+0103 (decimal 259) + defining Unicode char U+0104 (decimal 260) + defining Unicode char U+0105 (decimal 261) + defining Unicode char U+0106 (decimal 262) + defining Unicode char U+0107 (decimal 263) + defining Unicode char U+010C (decimal 268) + defining Unicode char U+010D (decimal 269) + defining Unicode char U+010E (decimal 270) + defining Unicode char U+010F (decimal 271) + defining Unicode char U+0110 (decimal 272) + defining Unicode char U+0111 (decimal 273) + defining Unicode char U+0118 (decimal 280) + defining Unicode char U+0119 (decimal 281) + defining Unicode char U+011A (decimal 282) + defining Unicode char U+011B (decimal 283) + defining Unicode char U+011E (decimal 286) + defining Unicode char U+011F (decimal 287) + defining Unicode char U+0130 (decimal 304) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0132 (decimal 306) + defining Unicode char U+0133 (decimal 307) + defining Unicode char U+0139 (decimal 313) + defining Unicode char U+013A (decimal 314) + defining Unicode char U+013D (decimal 317) + defining Unicode char U+013E (decimal 318) + defining Unicode char U+0141 (decimal 321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0143 (decimal 323) + defining Unicode char U+0144 (decimal 324) + defining Unicode char U+0147 (decimal 327) + defining Unicode char U+0148 (decimal 328) + defining Unicode char U+014A (decimal 330) + defining Unicode char U+014B (decimal 331) + defining Unicode char U+0150 (decimal 336) + defining Unicode char U+0151 (decimal 337) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+0154 (decimal 340) + defining Unicode char U+0155 (decimal 341) + defining Unicode char U+0158 (decimal 344) + defining Unicode char U+0159 (decimal 345) + defining Unicode char U+015A (decimal 346) + defining Unicode char U+015B (decimal 347) + defining Unicode char U+015E (decimal 350) + defining Unicode char U+015F (decimal 351) + defining Unicode char U+0160 (decimal 352) + defining Unicode char U+0161 (decimal 353) + defining Unicode char U+0162 (decimal 354) + defining Unicode char U+0163 (decimal 355) + defining Unicode char U+0164 (decimal 356) + defining Unicode char U+0165 (decimal 357) + defining Unicode char U+016E (decimal 366) + defining Unicode char U+016F (decimal 367) + defining Unicode char U+0170 (decimal 368) + defining Unicode char U+0171 (decimal 369) + defining Unicode char U+0178 (decimal 376) + defining Unicode char U+0179 (decimal 377) + defining Unicode char U+017A (decimal 378) + defining Unicode char U+017B (decimal 379) + defining Unicode char U+017C (decimal 380) + defining Unicode char U+017D (decimal 381) + defining Unicode char U+017E (decimal 382) + defining Unicode char U+200C (decimal 8204) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2018 (decimal 8216) + defining Unicode char U+2019 (decimal 8217) + defining Unicode char U+201A (decimal 8218) + defining Unicode char U+201C (decimal 8220) + defining Unicode char U+201D (decimal 8221) + defining Unicode char U+201E (decimal 8222) + defining Unicode char U+2030 (decimal 8240) + defining Unicode char U+2031 (decimal 8241) + defining Unicode char U+2039 (decimal 8249) + defining Unicode char U+203A (decimal 8250) + defining Unicode char U+2423 (decimal 9251) +) +Now handling font encoding OT1 ... +... processing UTF-8 mapping file for font encoding OT1 + +(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu +File: ot1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc + defining Unicode char U+00A1 (decimal 161) + defining Unicode char U+00A3 (decimal 163) + defining Unicode char U+00B8 (decimal 184) + defining Unicode char U+00BF (decimal 191) + defining Unicode char U+00C5 (decimal 197) + defining Unicode char U+00C6 (decimal 198) + defining Unicode char U+00D8 (decimal 216) + defining Unicode char U+00DF (decimal 223) + defining Unicode char U+00E6 (decimal 230) + defining Unicode char U+00EC (decimal 236) + defining Unicode char U+00ED (decimal 237) + defining Unicode char U+00EE (decimal 238) + defining Unicode char U+00EF (decimal 239) + defining Unicode char U+00F8 (decimal 248) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0141 (decimal 321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+2013 (decimal 8211) + defining Unicode char U+2014 (decimal 8212) + defining Unicode char U+2018 (decimal 8216) + defining Unicode char U+2019 (decimal 8217) + defining Unicode char U+201C (decimal 8220) + defining Unicode char U+201D (decimal 8221) +) +Now handling font encoding OMS ... +... processing UTF-8 mapping file for font encoding OMS + +(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu +File: omsenc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc + defining Unicode char U+00A7 (decimal 167) + defining Unicode char U+00B6 (decimal 182) + defining Unicode char U+00B7 (decimal 183) + defining Unicode char U+2020 (decimal 8224) + defining Unicode char U+2021 (decimal 8225) + defining Unicode char U+2022 (decimal 8226) +) +Now handling font encoding OMX ... +... no UTF-8 mapping file for font encoding OMX +Now handling font encoding U ... +... no UTF-8 mapping file for font encoding U + defining Unicode char U+00A9 (decimal 169) + defining Unicode char U+00AA (decimal 170) + defining Unicode char U+00AE (decimal 174) + defining Unicode char U+00BA (decimal 186) + defining Unicode char U+02C6 (decimal 710) + defining Unicode char U+02DC (decimal 732) + defining Unicode char U+200C (decimal 8204) + defining Unicode char U+2026 (decimal 8230) + defining Unicode char U+2122 (decimal 8482) + defining Unicode char U+2423 (decimal 9251) +)) +(/usr/share/texlive/texmf-dist/tex/latex/ntgclass/a4.sty +Package: a4 2004/04/15 v1.2g A4 based page layout +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty +Package: amsmath 2013/01/14 v2.14 AMS math features +\@mathmargin=\skip46 + +For additional information on amsmath, use the `?' option. +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty +Package: amstext 2000/06/29 v2.01 + +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty +File: amsgen.sty 1999/11/30 v2.0 +\@emptytoks=\toks17 +\ex@=\dimen106 +)) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty +Package: amsbsy 1999/11/29 v1.2d +\pmbraise@=\dimen107 +) +(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty +Package: amsopn 1999/12/14 v2.01 operator names +) +\inf@bad=\count91 +LaTeX Info: Redefining \frac on input line 210. +\uproot@=\count92 +\leftroot@=\count93 +LaTeX Info: Redefining \overline on input line 306. +\classnum@=\count94 +\DOTSCASE@=\count95 +LaTeX Info: Redefining \ldots on input line 378. +LaTeX Info: Redefining \dots on input line 381. +LaTeX Info: Redefining \cdots on input line 466. +\Mathstrutbox@=\box26 +\strutbox@=\box27 +\big@size=\dimen108 +LaTeX Font Info: Redeclaring font encoding OML on input line 566. +LaTeX Font Info: Redeclaring font encoding OMS on input line 567. +\macc@depth=\count96 +\c@MaxMatrixCols=\count97 +\dotsspace@=\muskip10 +\c@parentequation=\count98 +\dspbrk@lvl=\count99 +\tag@help=\toks18 +\row@=\count100 +\column@=\count101 +\maxfields@=\count102 +\andhelp@=\toks19 +\eqnshift@=\dimen109 +\alignsep@=\dimen110 +\tagshift@=\dimen111 +\tagwidth@=\dimen112 +\totwidth@=\dimen113 +\lineht@=\dimen114 +\@envbody=\toks20 +\multlinegap=\skip47 +\multlinetaggap=\skip48 +\mathdisplay@stack=\toks21 +LaTeX Info: Redefining \[ on input line 2665. +LaTeX Info: Redefining \] on input line 2666. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty +Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support +\symAMSa=\mathgroup4 +\symAMSb=\mathgroup5 +LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' +(Font) U/euf/m/n --> U/euf/b/n on input line 106. +) +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty +Package: amssymb 2013/01/14 v3.01 AMS font symbols +) +(/usr/share/texlive/texmf-dist/tex/latex/framed/framed.sty +Package: framed 2011/10/22 v 0.96: framed or shaded text with page breaks +\OuterFrameSep=\skip49 +\fb@frw=\dimen115 +\fb@frh=\dimen116 +\FrameRule=\dimen117 +\FrameSep=\dimen118 +) +(/usr/share/texlive/texmf-dist/tex/latex/ntheorem/ntheorem.sty +Style `ntheorem', Version 1.33 <2011/08/15> +Package: ntheorem 2011/08/15 1.33 +(/usr/share/texlive/texmf-dist/tex/latex/base/ifthen.sty +Package: ifthen 2001/05/26 v1.1c Standard LaTeX ifthen package (DPC) +) +\theorem@style=\toks22 +\theorem@@style=\toks23 +\theorembodyfont=\toks24 +\theoremnumbering=\toks25 +\theorempreskipamount=\skip50 +\theorempostskipamount=\skip51 +\theoremframepreskipamount=\skip52 +\theoremframepostskipamount=\skip53 +\theoreminframepreskipamount=\skip54 +\theoreminframepostskipamount=\skip55 +\theorem@preskip=\toks26 +\theorem@postskip=\toks27 +\theorem@framepreskip=\toks28 +\theorem@framepostskip=\toks29 +\theorem@inframepreskip=\toks30 +\theorem@inframepostskip=\toks31 +\theoremindent=\dimen119 +\theorem@indent=\dimen120 +\theoremrightindent=\dimen121 +\theorem@rightindent=\dimen122 +\theoremheaderfont=\toks32 +\theoremseparator=\toks33 +\theoremprework=\toks34 +\theorempostwork=\toks35 +\theoremsymbol=\toks36 +\qedsymbol=\toks37 +\theoremkeyword=\toks38 +\qedsymbol=\toks39 +\thm@topsep=\skip56 +\thm@topsepadd=\skip57 +Package ntheorem Info: Option `thmmarks' loaded on input line 1175. +\c@endNonectr=\count103 +\c@currNonectr=\count104 +\mysavskip=\skip58 +Package ntheorem Info: Option `thref' loaded on input line 1175. +\mysavskip=\skip59 +Package ntheorem Info: option `amsmath' handling for `thref' loaded on input li +ne 1175. +Package ntheorem Info: option `amsmath' handling for `thmmarks' loaded on input + line 1175. +\thm@amstmpdepth=\dimen123 +\tagwidth=\dimen124 +\shadecolor=\toks40 +) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty +Package: graphics 2009/02/05 v1.0o Standard LaTeX Graphics (DPC,SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty +Package: trig 1999/03/16 v1.09 sin cos tan (DPC) +) +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/graphics.cfg +File: graphics.cfg 2010/04/23 v1.9 graphics configuration of TeX Live +) +Package graphics Info: Driver file: dvips.def on input line 91. + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvips.def +File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR) +)) +(/usr/share/texlive/texmf-dist/tex/latex/graphics/epsfig.sty +Package: epsfig 1999/02/16 v1.7a (e)psfig emulation (SPQR) + +(/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty +Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR) +\Gin@req@height=\dimen125 +\Gin@req@width=\dimen126 +) +\epsfxsize=\dimen127 +\epsfysize=\dimen128 +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty +Package: calc 2007/08/22 v4.3 Infix arithmetic (KKT,FJ) +\calc@Acount=\count105 +\calc@Bcount=\count106 +\calc@Adimen=\dimen129 +\calc@Bdimen=\dimen130 +\calc@Askip=\skip60 +\calc@Bskip=\skip61 +LaTeX Info: Redefining \setlength on input line 76. +LaTeX Info: Redefining \addtolength on input line 77. +\calc@Ccount=\count107 +\calc@Cskip=\skip62 +) +(/usr/share/texlive/texmf-dist/tex/latex/tabls/tabls.sty +\tablinesep=\dimen131 +\arraylinesep=\dimen132 +\extrarulesep=\dimen133 +\@arstdepth=\dimen134 +\@arstheight=\dimen135 +\@skip@bove=\dimen136 +) +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/times.sty +Package: times 2005/04/12 PSNFSS-v9.2a (SPQR) +) +(/usr/share/texlive/texmf-dist/tex/latex/tools/tabularx.sty +Package: tabularx 1999/01/07 v2.07 `tabularx' package (DPC) + +(/usr/share/texlive/texmf-dist/tex/latex/tools/array.sty +Package: array 2008/09/09 v2.4c Tabular extension package (FMi) +\col@sep=\dimen137 +\extrarowheight=\dimen138 +\NC@list=\toks41 +\extratabsurround=\skip63 +\backup@length=\skip64 + + +LaTeX Warning: Command \@xhline has changed. + Check if current package is valid. + +) +\TX@col@width=\dimen139 +\TX@old@table=\dimen140 +\TX@old@col=\dimen141 +\TX@target=\dimen142 +\TX@delta=\dimen143 +\TX@cols=\count108 +\TX@ftn=\toks42 +) (/usr/share/texlive/texmf-dist/tex/latex/base/textcomp.sty +Package: textcomp 2005/09/27 v1.99g Standard LaTeX package +Package textcomp Info: Sub-encoding information: +(textcomp) 5 = only ISO-Adobe without \textcurrency +(textcomp) 4 = 5 + \texteuro +(textcomp) 3 = 4 + \textohm +(textcomp) 2 = 3 + \textestimated + \textcurrency +(textcomp) 1 = TS1 - \textcircled - \t +(textcomp) 0 = TS1 (full) +(textcomp) Font families with sub-encoding setting implement +(textcomp) only a restricted character set as indicated. +(textcomp) Family '?' is the default used for unknown fonts. +(textcomp) See the documentation for details. +Package textcomp Info: Setting ? sub-encoding to TS1/1 on input line 71. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.def +File: ts1enc.def 2001/06/05 v3.0e (jk/car/fm) Standard LaTeX file +Now handling font encoding TS1 ... +... processing UTF-8 mapping file for font encoding TS1 + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1enc.dfu +File: ts1enc.dfu 2008/04/05 v1.1m UTF-8 support for inputenc + defining Unicode char U+00A2 (decimal 162) + defining Unicode char U+00A3 (decimal 163) + defining Unicode char U+00A4 (decimal 164) + defining Unicode char U+00A5 (decimal 165) + defining Unicode char U+00A6 (decimal 166) + defining Unicode char U+00A7 (decimal 167) + defining Unicode char U+00A8 (decimal 168) + defining Unicode char U+00A9 (decimal 169) + defining Unicode char U+00AA (decimal 170) + defining Unicode char U+00AC (decimal 172) + defining Unicode char U+00AE (decimal 174) + defining Unicode char U+00AF (decimal 175) + defining Unicode char U+00B0 (decimal 176) + defining Unicode char U+00B1 (decimal 177) + defining Unicode char U+00B2 (decimal 178) + defining Unicode char U+00B3 (decimal 179) + defining Unicode char U+00B4 (decimal 180) + defining Unicode char U+00B5 (decimal 181) + defining Unicode char U+00B6 (decimal 182) + defining Unicode char U+00B7 (decimal 183) + defining Unicode char U+00B9 (decimal 185) + defining Unicode char U+00BA (decimal 186) + defining Unicode char U+00BC (decimal 188) + defining Unicode char U+00BD (decimal 189) + defining Unicode char U+00BE (decimal 190) + defining Unicode char U+00D7 (decimal 215) + defining Unicode char U+00F7 (decimal 247) + defining Unicode char U+0192 (decimal 402) + defining Unicode char U+02C7 (decimal 711) + defining Unicode char U+02D8 (decimal 728) + defining Unicode char U+02DD (decimal 733) + defining Unicode char U+0E3F (decimal 3647) + defining Unicode char U+2016 (decimal 8214) + defining Unicode char U+2020 (decimal 8224) + defining Unicode char U+2021 (decimal 8225) + defining Unicode char U+2022 (decimal 8226) + defining Unicode char U+2030 (decimal 8240) + defining Unicode char U+2031 (decimal 8241) + defining Unicode char U+203B (decimal 8251) + defining Unicode char U+203D (decimal 8253) + defining Unicode char U+2044 (decimal 8260) + defining Unicode char U+204E (decimal 8270) + defining Unicode char U+2052 (decimal 8274) + defining Unicode char U+20A1 (decimal 8353) + defining Unicode char U+20A4 (decimal 8356) + defining Unicode char U+20A6 (decimal 8358) + defining Unicode char U+20A9 (decimal 8361) + defining Unicode char U+20AB (decimal 8363) + defining Unicode char U+20AC (decimal 8364) + defining Unicode char U+20B1 (decimal 8369) + defining Unicode char U+2103 (decimal 8451) + defining Unicode char U+2116 (decimal 8470) + defining Unicode char U+2117 (decimal 8471) + defining Unicode char U+211E (decimal 8478) + defining Unicode char U+2120 (decimal 8480) + defining Unicode char U+2122 (decimal 8482) + defining Unicode char U+2126 (decimal 8486) + defining Unicode char U+2127 (decimal 8487) + defining Unicode char U+212E (decimal 8494) + defining Unicode char U+2190 (decimal 8592) + defining Unicode char U+2191 (decimal 8593) + defining Unicode char U+2192 (decimal 8594) + defining Unicode char U+2193 (decimal 8595) + defining Unicode char U+2329 (decimal 9001) + defining Unicode char U+232A (decimal 9002) + defining Unicode char U+2422 (decimal 9250) + defining Unicode char U+25E6 (decimal 9702) + defining Unicode char U+25EF (decimal 9711) + defining Unicode char U+266A (decimal 9834) +)) +LaTeX Info: Redefining \oldstylenums on input line 266. +Package textcomp Info: Setting cmr sub-encoding to TS1/0 on input line 281. +Package textcomp Info: Setting cmss sub-encoding to TS1/0 on input line 282. +Package textcomp Info: Setting cmtt sub-encoding to TS1/0 on input line 283. +Package textcomp Info: Setting cmvtt sub-encoding to TS1/0 on input line 284. +Package textcomp Info: Setting cmbr sub-encoding to TS1/0 on input line 285. +Package textcomp Info: Setting cmtl sub-encoding to TS1/0 on input line 286. +Package textcomp Info: Setting ccr sub-encoding to TS1/0 on input line 287. +Package textcomp Info: Setting ptm sub-encoding to TS1/4 on input line 288. +Package textcomp Info: Setting pcr sub-encoding to TS1/4 on input line 289. +Package textcomp Info: Setting phv sub-encoding to TS1/4 on input line 290. +Package textcomp Info: Setting ppl sub-encoding to TS1/3 on input line 291. +Package textcomp Info: Setting pag sub-encoding to TS1/4 on input line 292. +Package textcomp Info: Setting pbk sub-encoding to TS1/4 on input line 293. +Package textcomp Info: Setting pnc sub-encoding to TS1/4 on input line 294. +Package textcomp Info: Setting pzc sub-encoding to TS1/4 on input line 295. +Package textcomp Info: Setting bch sub-encoding to TS1/4 on input line 296. +Package textcomp Info: Setting put sub-encoding to TS1/5 on input line 297. +Package textcomp Info: Setting uag sub-encoding to TS1/5 on input line 298. +Package textcomp Info: Setting ugq sub-encoding to TS1/5 on input line 299. +Package textcomp Info: Setting ul8 sub-encoding to TS1/4 on input line 300. +Package textcomp Info: Setting ul9 sub-encoding to TS1/4 on input line 301. +Package textcomp Info: Setting augie sub-encoding to TS1/5 on input line 302. +Package textcomp Info: Setting dayrom sub-encoding to TS1/3 on input line 303. +Package textcomp Info: Setting dayroms sub-encoding to TS1/3 on input line 304. + +Package textcomp Info: Setting pxr sub-encoding to TS1/0 on input line 305. +Package textcomp Info: Setting pxss sub-encoding to TS1/0 on input line 306. +Package textcomp Info: Setting pxtt sub-encoding to TS1/0 on input line 307. +Package textcomp Info: Setting txr sub-encoding to TS1/0 on input line 308. +Package textcomp Info: Setting txss sub-encoding to TS1/0 on input line 309. +Package textcomp Info: Setting txtt sub-encoding to TS1/0 on input line 310. +Package textcomp Info: Setting lmr sub-encoding to TS1/0 on input line 311. +Package textcomp Info: Setting lmdh sub-encoding to TS1/0 on input line 312. +Package textcomp Info: Setting lmss sub-encoding to TS1/0 on input line 313. +Package textcomp Info: Setting lmssq sub-encoding to TS1/0 on input line 314. +Package textcomp Info: Setting lmvtt sub-encoding to TS1/0 on input line 315. +Package textcomp Info: Setting qhv sub-encoding to TS1/0 on input line 316. +Package textcomp Info: Setting qag sub-encoding to TS1/0 on input line 317. +Package textcomp Info: Setting qbk sub-encoding to TS1/0 on input line 318. +Package textcomp Info: Setting qcr sub-encoding to TS1/0 on input line 319. +Package textcomp Info: Setting qcs sub-encoding to TS1/0 on input line 320. +Package textcomp Info: Setting qpl sub-encoding to TS1/0 on input line 321. +Package textcomp Info: Setting qtm sub-encoding to TS1/0 on input line 322. +Package textcomp Info: Setting qzc sub-encoding to TS1/0 on input line 323. +Package textcomp Info: Setting qhvc sub-encoding to TS1/0 on input line 324. +Package textcomp Info: Setting futs sub-encoding to TS1/4 on input line 325. +Package textcomp Info: Setting futx sub-encoding to TS1/4 on input line 326. +Package textcomp Info: Setting futj sub-encoding to TS1/4 on input line 327. +Package textcomp Info: Setting hlh sub-encoding to TS1/3 on input line 328. +Package textcomp Info: Setting hls sub-encoding to TS1/3 on input line 329. +Package textcomp Info: Setting hlst sub-encoding to TS1/3 on input line 330. +Package textcomp Info: Setting hlct sub-encoding to TS1/5 on input line 331. +Package textcomp Info: Setting hlx sub-encoding to TS1/5 on input line 332. +Package textcomp Info: Setting hlce sub-encoding to TS1/5 on input line 333. +Package textcomp Info: Setting hlcn sub-encoding to TS1/5 on input line 334. +Package textcomp Info: Setting hlcw sub-encoding to TS1/5 on input line 335. +Package textcomp Info: Setting hlcf sub-encoding to TS1/5 on input line 336. +Package textcomp Info: Setting pplx sub-encoding to TS1/3 on input line 337. +Package textcomp Info: Setting pplj sub-encoding to TS1/3 on input line 338. +Package textcomp Info: Setting ptmx sub-encoding to TS1/4 on input line 339. +Package textcomp Info: Setting ptmj sub-encoding to TS1/4 on input line 340. +) +(/usr/share/texlive/texmf-dist/tex/latex/pstricks/pst-all.sty +Package: pst-all 2008/01/01 the main pstricks tools + +(/usr/share/texlive/texmf-dist/tex/latex/pstricks/pstricks.sty +Package: pstricks 2013/05/22 v0.57 LaTeX wrapper for `PSTricks' (RN,HV) + +(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pstricks.tex +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/pst-xkey.tex +File: pst-xkey.tex 2005/11/25 v1.6 PSTricks specialization of xkeyval (HA) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/xkeyval.sty +Package: xkeyval 2012/10/14 v2.6b package option processing (HA) + +(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex +\XKV@toks=\toks43 +\XKV@tempa@toks=\toks44 +\XKV@depth=\count109 +File: xkeyval.tex 2012/10/14 v2.6b key=value parser (HA) +))) +(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex +`pst-fp' v0.05, 2010/01/17 (hv) +\pstFP@xs=\count110 +\pstFP@xia=\count111 +\pstFP@xib=\count112 +\pstFP@xfa=\count113 +\pstFP@xfb=\count114 +\pstFP@rega=\count115 +\pstFP@regb=\count116 +\pstFP@regs=\count117 +\pstFP@times=\count118 +) +(/usr/share/texmf/tex/generic/pgf/utilities/pgfutil-common.tex +\pgfutil@everybye=\toks45 +) +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeys.code.tex +\pgfkeys@pathtoks=\toks46 +\pgfkeys@temptoks=\toks47 + +(/usr/share/texmf/tex/generic/pgf/utilities/pgfkeysfiltered.code.tex +\pgfkeys@tmptoks=\toks48 +)) +(/usr/share/texmf/tex/generic/pgf/utilities/pgffor.code.tex +\pgffor@iter=\dimen144 +\pgffor@skip=\dimen145 +\pgffor@stack=\toks49 +\pgffor@toks=\toks50 +) +\psLoopIndex=\count119 + +`PSTricks' v2.45 <2013/07/09> (tvz) +\pst@dima=\dimen146 +\pst@dimb=\dimen147 +\pst@dimc=\dimen148 +\pst@dimd=\dimen149 +\pst@dimg=\dimen150 +\pst@dimh=\dimen151 +\pst@dimm=\dimen152 +\pst@dimn=\dimen153 +\pst@dimo=\dimen154 +\pst@dimp=\dimen155 +\pst@hbox=\box28 +\pst@ibox=\box29 +\pst@boxg=\box30 +\pst@cnta=\count120 +\pst@cntb=\count121 +\pst@cntc=\count122 +\pst@cntd=\count123 +\pst@cntg=\count124 +\pst@cnth=\count125 +\pst@cntm=\count126 +\pst@cntn=\count127 +\pst@cnto=\count128 +\pst@cntp=\count129 +\@zero=\count130 +\pst@toks=\toks51 +(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pstricks.con) +\psunit=\dimen156 +\psxunit=\dimen157 +\psyunit=\dimen158 +\pst@C@@rType=\count131 +\pslinewidth=\dimen159 +\psk@startLW=\dimen160 +\psk@endLW=\dimen161 +\pst@customdefs=\toks52 +\pslinearc=\dimen162 +\pst@symbolStep=\dimen163 +\pst@symbolWidth=\dimen164 +\pst@symbolLinewidth=\dimen165 +\everypsbox=\toks53 +\psframesep=\dimen166 +\pslabelsep=\dimen167 +\sh@wgridXunit=\dimen168 +\sh@wgridYunit=\dimen169 +\pst@shift=\dimen170 +) +File: pstricks.tex 2013/07/09 v2.45 `PSTricks' (tvz,hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex) +File: pst-fp.tex 2013/07/09 v2.45 `PST-fp' (hv) + +(/usr/share/texmf/tex/latex/xcolor/xcolor.sty +Package: xcolor 2007/01/21 v2.11 LaTeX color extensions (UK) + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg +File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive +) +Package xcolor Info: Driver file: pdftex.def on input line 225. + +(/usr/share/texlive/texmf-dist/tex/latex/pdftex-def/pdftex.def +File: pdftex.def 2011/05/27 v0.06d Graphics/color for pdfTeX + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/infwarerr.sty +Package: infwarerr 2010/04/08 v1.3 Providing info/warning/error messages (HO) +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ltxcmds.sty +Package: ltxcmds 2011/11/09 v1.22 LaTeX kernel commands for general use (HO) +) +\Gread@gobject=\count132 +) +Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1337. +Package xcolor Info: Model `RGB' extended on input line 1353. +Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1355. +Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1356. +Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1357. +Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1358. +Package xcolor Info: Model `Gray' substituted by `gray' on input line 1359. +Package xcolor Info: Model `wave' substituted by `hsb' on input line 1360. +)) +(/usr/share/texlive/texmf-dist/tex/latex/pst-plot/pst-plot.sty +Package: pst-plot 2011/06/05 v1.00 LaTeX wrapper for `pst-plot' (HV) + +(/usr/share/texlive/texmf-dist/tex/latex/xkeyval/pst-xkey.sty +Package: pst-xkey 2005/11/25 v1.6 package wrapper for pst-xkey.tex (HA) +) +(/usr/share/texlive/texmf-dist/tex/latex/multido/multido.sty +Package: multido 2004/05/17 package wrapper for PSTricks `multido.tex', (HV/RN) + + +(/usr/share/texlive/texmf-dist/tex/generic/multido/multido.tex + v1.42, 2010/05/14 +\multido@count=\count133 +\multidocount=\count134 +\multido@stuff=\toks54 +) +File: multido.tex 2010/05/14 v1.42 `multido' (tvz,hv) +) +Package: pst-plot 2011/04/13 package wrapper for pst-plot.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-plot/pst-plot.tex + v1.47, 2013/07/08 (tvz,hv) +\pstRadUnit=\dimen171 +\pstRadUnitInv=\dimen172 +\pst@linecnt=\count135 +\RCD@file=\read1 +\psxlabelsep=\dimen173 +\psylabelsep=\dimen174 +\psk@subticksize=\dimen175 +\pst@xticksizeA=\dimen176 +\pst@xticksizeB=\dimen177 +\pst@xticksizeC=\dimen178 +\pst@yticksizeA=\dimen179 +\pst@yticksizeB=\dimen180 +\pst@yticksizeC=\dimen181 +\@digitcounter=\count136 +\psk@llx=\dimen182 +\psk@lly=\dimen183 +\psk@urx=\dimen184 +\psk@ury=\dimen185 +\pst@xunit=\dimen186 +\pst@yunit=\dimen187 +) +File: pst-plot.tex 2013/07/08 1.47 `pst-plot' (tvz,hv) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-node/pst-node.sty +Package: pst-node 2012/09/18 v1.01 LaTeX wrapper for `pst-node' (HV) +Package: pst-node 2010/04/22 package wrapper for pst-node.tex + +(/usr/share/texlive/texmf-dist/tex/generic/pst-node/pst-node.tex + v1.29, 2013/07/13 +\psrow=\count137 +\pscol=\count138 +\psmatrixcnt=\count139 +\psrowsep=\skip65 +\pscolsep=\skip66 +\pst@args=\count140 +\num@pts=\count141 +\pst@argcnt=\count142 +) +File: pst-node.tex 2013/07/13 1.29 `pst-node' (tvz,hv) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-tree/pst-tree.sty +Package: pst-tree 2009/01/25 package wrapper for pst-tree.tex + +(/usr/share/texlive/texmf-dist/tex/generic/pst-tree/pst-tree.tex + v1.12, 2011/02/28(tvz,dg,hv) +\pstree@rootbox=\box31 +\pstree@box=\box32 +\psnodecnt=\count143 +\pstreelevel=\count144 +\pstreecnt=\count145 +\pstree@cnt=\count146 +\pstree@stop=\count147 +) +File: pst-tree.tex 2011/02/28 1.12 `pst-tree' (tvz,hv) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-grad/pst-grad.sty +Package: pst-grad 2004/07/15 package wrapper for pst-grad.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-grad/pst-grad.tex +`pst-grad' v1.06, 2006/11/27 (tvz,dg,hv)) +File: pst-grad.tex 2006/11/27 1.06 `pst-grad' (tvz) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-coil/pst-coil.sty +Package: pst-coil 2010/02/01 package wrapper for pst-coil.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-coil/pst-coil.tex + v1.06, 2006/11/27 +(/usr/share/texlive/texmf-dist/tex/generic/pst-node/pst-node.tex)) +File: pst-coil.tex 2011/09/17 v1.06 `PST-coil' (tvz,hv) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-text/pst-text.sty +Package: pst-text 2006/01/01 package wrapper for pst-text.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-text/pst-text.tex + v1.00, 2006/11/05(tvz,hv)) +File: pst-text.tex 2006/11/05 1.00 `pst-text' (tvz) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-3d/pst-3d.sty +Package: pst-3d 2009/07/28 package wrapper for pst-3d.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-3d/pst-3d.tex +`PST-3d' v1.11, 2010/02/14 (tvz)) +File: pst-3d.tex 2010/02/14 v1.11 `PST-3d' (hv) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-eps/pst-eps.sty +Package: pst-eps 2005/05/20 package wrapper for pst-eps.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-eps/pst-eps.tex + v1.00, 2006/11/04 +\pst@epsout=\write3 +\pst@tempout=\write4 +) +File: pst-eps.tex 2006/11/04 1.00 `pst-eps' (tvz) +) +(/usr/share/texlive/texmf-dist/tex/latex/pst-fill/pst-fill.sty +Package: pst-fill 2005/09/13 package wrapper for pst-fill.tex (hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pst-fill/pst-fill.tex +`PST-Fill' v1.01, 2007/03/10 (tvz,dg,hv) +\pst@fillbox=\box33 +) +File: pst-fill.tex 2007/03/10 v1.01 `PST-fill' (tvz,dg) +) +(/usr/share/texlive/texmf-dist/tex/latex/pstricks-add/pstricks-add.sty +(/usr/share/texlive/texmf-dist/tex/latex/pst-math/pst-math.sty +Package: pst-math 2009/01/20 package wrapper for PSTricks pst-math.tex + +(/usr/share/texlive/texmf-dist/tex/generic/pst-math/pst-math.tex +`pst-math' v0.62 , (CJ,hv)) +File: pst-math.tex 2010/10/20 v0.62 `PST-math' (hv) +) +Package: pstricks-add 2010/02/11 v. 0.14 package wrapper for pstricks-add.tex ( +hv) + +(/usr/share/texlive/texmf-dist/tex/generic/pstricks-add/pstricks-add.tex +`pstricks-add' v3.60, 2013/01/01 (dr,hv) +\psparallelogramsep=\dimen188 +\pshooklength=\dimen189 +\pshookwidth=\dimen190 +\pst@cntC=\count148 +\chart@ColorIndex=\dimen191 +\chart@ColorStep=\dimen192 +\pst@chartHeight=\dimen193 +\pst@chartStackDepth=\dimen194 +\pst@chartStackWidth=\dimen195 +\chart@Toggle=\count149 +\psVectorCtr=\count150 +) +File: pstricks-add.tex 2013/01/01 v3.60 `PSTricks-add' (hv) +)) +(/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty +Package: geometry 2010/09/12 v5.6 Page Geometry + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifpdf.sty +Package: ifpdf 2011/01/30 v2.3 Provides the ifpdf switch (HO) +Package ifpdf Info: pdfTeX in PDF mode is detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifvtex.sty +Package: ifvtex 2010/03/01 v1.5 Detect VTeX and its facilities (HO) +Package ifvtex Info: VTeX not detected. +) +(/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty +Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional +) +\Gm@cnth=\count151 +\Gm@cntv=\count152 +\c@Gm@tempcnt=\count153 +\Gm@bindingoffset=\dimen196 +\Gm@wd@mp=\dimen197 +\Gm@odd@mp=\dimen198 +\Gm@even@mp=\dimen199 +\Gm@layoutwidth=\dimen200 +\Gm@layoutheight=\dimen201 +\Gm@layouthoffset=\dimen202 +\Gm@layoutvoffset=\dimen203 +\Gm@dimlist=\toks55 +) +(./symboles.sty) (./controle.aux) +\openout1 = `controle.aux'. + +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 29. +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 29. +LaTeX Font Info: Try loading font information for TS1+cmr on input line 29. + +(/usr/share/texlive/texmf-dist/tex/latex/base/ts1cmr.fd +File: ts1cmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions +) +LaTeX Font Info: ... okay on input line 29. +LaTeX Font Info: Try loading font information for OT1+ptm on input line 29. + +(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ptm.fd +File: ot1ptm.fd 2001/06/04 font definitions for OT1/ptm. +) +LaTeX Info: Redefining \degres on input line 29. +LaTeX Info: Redefining \dots on input line 29. +LaTeX Info: Redefining \up on input line 29. + + +Package frenchb.ldf Warning: OT1 encoding should not be used for French. +(frenchb.ldf) Add \usepackage[T1]{fontenc} to the preamble +(frenchb.ldf) of your document, on input line 29. + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/pdftexcmds.sty +Package: pdftexcmds 2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO +) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/ifluatex.sty +Package: ifluatex 2010/03/01 v1.3 Provides the ifluatex switch (HO) +Package ifluatex Info: LuaTeX not detected. +) +Package pdftexcmds Info: LuaTeX not detected. +Package pdftexcmds Info: \pdf@primitive is available. +Package pdftexcmds Info: \pdf@ifprimitive is available. +Package pdftexcmds Info: \pdfdraftmode found. +) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty +Package: epstopdf-base 2010/02/09 v2.5 Base part for package epstopdf + +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty +Package: grfext 2010/08/19 v1.1 Manage graphics extensions (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvdefinekeys.sty +Package: kvdefinekeys 2011/04/07 v1.3 Define keys (HO) +)) +(/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty +Package: kvoptions 2011/06/30 v3.11 Key value format for package options (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/kvsetkeys.sty +Package: kvsetkeys 2012/04/25 v1.16 Key value parser (HO) + +(/usr/share/texlive/texmf-dist/tex/generic/oberdiek/etexcmds.sty +Package: etexcmds 2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO) +Package etexcmds Info: Could not find \expanded. +(etexcmds) That can mean that you are not using pdfTeX 1.50 or +(etexcmds) that some package has redefined \expanded. +(etexcmds) In the latter case, load this package earlier. +))) +Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 +34. +Package grfext Info: Graphics extension search list: +(grfext) [.png,.pdf,.jpg,.mps,.jpeg,.jbig2,.jb2,.PNG,.PDF,.JPG,.JPE +G,.JBIG2,.JB2,.eps] +(grfext) \AppendGraphicsExtensions on input line 452. + +(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg +File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv +e +)) +(/usr/share/texlive/texmf-dist/tex/context/base/supp-pdf.mkii +[Loading MPS to PDF converter (version 2006.09.02).] +\scratchcounter=\count154 +\scratchdimen=\dimen204 +\scratchbox=\box34 +\nofMPsegments=\count155 +\nofMParguments=\count156 +\everyMPshowfont=\toks56 +\MPscratchCnt=\count157 +\MPscratchDim=\dimen205 +\MPnumerator=\count158 +\makeMPintoPDFobject=\count159 +\everyMPtoPDFconversion=\toks57 +) +*geometry* driver: auto-detecting +*geometry* detected driver: pdftex +*geometry* verbose mode - [ preamble ] result: +* driver: pdftex +* paper: a4paper +* layout: +* layoutoffset:(h,v)=(0.0pt,0.0pt) +* modes: +* h-part:(L,W,R)=(28.45274pt, 540.60239pt, 28.45274pt) +* v-part:(T,H,B)=(-14.22636pt, 816.59409pt, 42.67912pt) +* \paperwidth=597.50787pt +* \paperheight=845.04684pt +* \textwidth=540.60239pt +* \textheight=816.59409pt +* \oddsidemargin=-43.81725pt +* \evensidemargin=-43.81725pt +* \topmargin=-123.49635pt +* \headheight=12.0pt +* \headsep=25.0pt +* \topskip=11.0pt +* \footskip=30.0pt +* \marginparwidth=72.26999pt +* \marginparsep=10.0pt +* \columnsep=10.0pt +* \skip\footins=10.0pt plus 4.0pt minus 2.0pt +* \hoffset=0.0pt +* \voffset=0.0pt +* \mag=1000 +* \@twocolumnfalse +* \@twosidefalse +* \@mparswitchfalse +* \@reversemarginfalse +* (1in=72.27pt=25.4mm, 1cm=28.453pt) + +LaTeX Font Info: Try loading font information for U+msa on input line 30. +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd +File: umsa.fd 2013/01/14 v3.01 AMS symbols A +) +LaTeX Font Info: Try loading font information for U+msb on input line 30. + +(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd +File: umsb.fd 2013/01/14 v3.01 AMS symbols B +) + +LaTeX Warning: No \author given. + +LaTeX Font Info: Font shape `OT1/ptm/bx/n' in size <14.4> not available +(Font) Font shape `OT1/ptm/b/n' tried instead on input line 42. +\tf@thm=\write5 +\openout5 = `controle.thm'. + +[1 +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! + + +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored! +Non-PDF special ignored!{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +(./controle.aux) ) +Here is how much of TeX's memory you used: + 10058 strings out of 495002 + 148793 string characters out of 6180262 + 302980 words of memory out of 5000000 + 13008 multiletter control sequences out of 15000+600000 + 15942 words of font info for 47 fonts, out of 8000000 for 9000 + 14 hyphenation exceptions out of 8191 + 44i,7n,64p,599b,199s stack positions out of 5000i,500n,10000p,200000b,80000s +{/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc} +Output written on controle.pdf (1 page, 88472 bytes). +PDF statistics: + 45 PDF objects out of 1000 (max. 8388607) + 32 compressed objects within 1 object stream + 0 named destinations out of 1000 (max. 500000) + 1 words of extra memory for PDF output out of 10000 (max. 10000000) + diff --git a/partiels/131105S1/controle.pdf b/partiels/131105S1/controle.pdf new file mode 100644 index 0000000..8f6d573 Binary files /dev/null and b/partiels/131105S1/controle.pdf differ diff --git a/partiels/131105S1/controle.tex b/partiels/131105S1/controle.tex new file mode 100644 index 0000000..057bddb --- /dev/null +++ b/partiels/131105S1/controle.tex @@ -0,0 +1,135 @@ +\documentclass[11pt,a4paper,french]{article} +\usepackage[francais]{babel} +\usepackage[utf8]{inputenc} +\usepackage{a4} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{framed} +\usepackage[amsmath,thmmarks,thref,framed]{ntheorem} +\usepackage[dvips]{graphics} +\usepackage{epsfig} +\usepackage{calc} +\usepackage{tabls} +\usepackage{times} +\usepackage{tabularx} +\usepackage{textcomp} +\usepackage{pst-all} +\usepackage[a4paper]{geometry} + +\input{symboles.sty} +\geometry{hmargin=1cm, tmargin=-0.5cm, bmargin=1.5cm} + +\title{ +DUT d'informatique. Contrôle de mathématiques discrètes.\\ +Semestre 1 (Novembre 2013). Durée 1h.} + +\date{} + +\begin{document} +\maketitle + +\vspace{-3em} +\noindent Seule une fiche manuscrite de format A5 est autorisée. +Tous les exercices de ce sujet sont indépendants les uns des autres. +Dans tout ce qui suit, on considère une algèbre de Boole +munie des opérateurs classiques ``+'', ``.'', +``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes +$a$, $b$, $c$, $d$. + + +\vspace{-1em} +\section{Cours (3pts) } + +\begin{enumerate} +\item Soit $A$ et $B$ deux ensembles d'un +univers $\Omega$ tels que $A \subseteq B$. Définir $B\setminus A$ en compréhension. +\item L'ensemble vide appartient-il à tout ensemble? Justifier. +\end{enumerate} + + + + +\vspace{-1em} +\section{(5 pts) Simplification de formules booléennes (d'après sujet de BTS-IG-2008)} +La société Jurabois exploite des forêts d'arbres constituées exclusivement de +feuillus et de résineux. Elle désire simplifier le règlement que les salariés +doivent appliquer pour la coupe du bois. +Actuellement, le règlement dit qu'un arbre est à abattre dans les quatre cas +suivants: +\begin{itemize} +\item si c'est un résineux au tronc droit mesurant plus de 20 m de hauteur; +\item si c'est un feuillus de 50 ans ou plus; +\item s'il a moins de 50 ans et mesure plus de 20 m de hauteur; +\item s'il est tordu. +\end{itemize} +Pour un arbre quelconque, on définit les variables booléennes suivantes par: +\begin{itemize} +\item $a=1$ si l'arbre est un résineux; +\item $b=1$ si l'arbre a moins de 50 ans; +\item $c=1$ si l'arbre mesure plus de 20 m de hauteur; +\item $d=1$ si l'arbre est tordu. +\end{itemize} + + +\begin{enumerate} +\item Écrire sans justifier + la fonction booléenne $f(a,b,c,d)$ qui traduit le règlement + actuel d'abattage d'un arbre. + +\item Grâce à une bonne gestion des forêts que la société exploite, + il n'y a maintenant plus d'arbre tordu. +\begin{enumerate} +\item Montrer que le nouveau règlement d'abattage se traduit par la fonction +$ +g(a,b,c) = ac + \overline{a}\overline{b} + bc +$. +\item A l'aide d'une table de Karnaugh, donner sans justifier + l'expression $G$ qui + est la forme la plus réduite de $g$. + + +\item Écrire la nouvelle règle d'abattage d'un arbre sous la forme + la plus simple possible. +\end{enumerate} +\end{enumerate} + + + +\vspace{-1em} +\section{(6 pts) Démonstrations ensemblistes} +Soit $A$ et $B$ deux sous-ensembles de $\Omega$. +\begin{enumerate} +\item Soit $A_0=\{1,2,3\}$ et $B_0=\{3,4\}$. +Définir en extension $A_0 \cup B_0$, $P(A_0)$, $P(B_0)$, $P(A_0\cup B_0)$ et +$P(A_0) \cup P(B_0)$. +\item A-t-on l'égalité $P(A \cup B) = P(A) \cup P(B)$? Justifier. +\item Montrer que l'on a $P(A \cap B) = P(A) \cap P(B)$. +\end{enumerate} + + + +\vspace{-1em} +\section{(6 pts) Relation entre puissances d'éléments} + + +Sur $\N^*$ on définit la relation +$a \mathcal{R} b$ si $a^b \leq b ^a$. +\begin{enumerate} +\item A-t-on $2 \mathcal{R} 3$? $2 \mathcal{R} 7$? $2 \mathcal{R} 4$? $4 \mathcal{R} 2$? Justifier à chaque fois. + +\item La relation est-elle réflexive? Le démontrer. + +\item La fonction logarithme népérien $\ln: \R^{+*} \rightarrow \R$ étant + croissante, montrer que sur $\N^*$ + $a \mathcal{R} b$ si $\dfrac{\ln(a)}{a} \leq \dfrac{\ln(b)}{b}$. +\item La relation est-elle transitive? Pour justifier votre réponse, on + pourra utiliser la question précédente. +\item La relation est-elle antisymétrique? Le justifier. +\end{enumerate} + + + + + +\end{document} diff --git a/partiels/131105S1/controle.tex.bak b/partiels/131105S1/controle.tex.bak new file mode 100644 index 0000000..40a3f55 --- /dev/null +++ b/partiels/131105S1/controle.tex.bak @@ -0,0 +1,134 @@ +\documentclass[11pt,a4paper,french]{article} +\usepackage[francais]{babel} +\usepackage[utf8]{inputenc} +\usepackage{a4} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{framed} +\usepackage[amsmath,thmmarks,thref,framed]{ntheorem} +\usepackage[dvips]{graphics} +\usepackage{epsfig} +\usepackage{calc} +\usepackage{tabls} +\usepackage{times} +\usepackage{tabularx} +\usepackage{textcomp} +\usepackage{pst-all} +\usepackage[a4paper]{geometry} + +\input{symboles.sty} +\geometry{hmargin=1cm, tmargin=-0.5cm, bmargin=1.5cm} + +\title{ +DUT d'informatique. Contrôle de mathématiques discrètes.\\ +Semestre 1 (Novembre 2013). Durée 1h.} + +\date{} + +\begin{document} +\maketitle + +\vspace{-3em} +\noindent Seule une fiche manuscrite de format A5 est autorisée. +Tous les exercices de ce sujet sont indépendants les uns des autres. +Dans tout ce qui suit, on considère une algèbre de Boole +munie des opérateurs classiques ``+'', ``.'', +``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes +$a$, $b$, $c$, $d$. + + +\vspace{-1em} +\section{Cours (3pts) } + +\begin{enumerate} +\item Soit $A$ et $B$ deux ensembles d'un +univers $\Omega$ tels que $A \subseteq B$. Définir $B\setminus A$ en compréhension. +\item L'ensemble vide appartient-il à tout ensemble? Justifier. +\end{enumerate} + + + + +\vspace{-1em} +\section{(6pts) Simplification de formules booléennes (d'après sujet de BTS-IG-2008)} +La société Jurabois exploite des coupes d'arbres constitués exclusivement de +feuillus et de résineux. Elle désire simplifier le réglement que les salariés +doivent appliquerr pour la coupe du bois. +Actuellement, le réglement dit qu'un arbre est à abattre dans les quatre cas +suivants: +\begin{itemize} +\item si c'est un résineux au tronc droit mesurant plus de 20 m de hauteur; +\item si c'est un feuillus de 50 ans ou plus; +\item s'il a moins de 50 ans et mesure plus de 20 m de hauteur; +\item s'il est tordu. +\end{itemize} +Pour un arbre quelconque, on définit les variables booléennes suivantes par: +\begin{itemize} +\item $a=1$ si l'arbre est un résineux; +\item $b=1$ si l'arbre a moins de 50 ans; +\item $c=1$ si l'arbre mesure plus de 20 m de hauteur; +\item $d=1$ si l'arbre est tordu. +\end{itemize} + + +\begin{enumerate} +\item Ecrire la fonction booléenne $f(a,b,c,d)$ qui traduit le réglement + actuel d'abattage d'un arbre. + +\item Grâce à une bonne gestion des forêts que la société exploite, + il n'y a maintenant plus d'arbre tordu. +\begin{enumerate} +\item Montrer que le nouveau réglement d'abattage se traduit par la fonction +$ +g(a,b,c) = ac + \overline{a}\overline{b} + bc +$. +\item A l'aide d'une table de Karnaugh donner l'expression $G$ qui + serait la forme la plus réduite de $g$. + +\item Justifier algébriquement que l'on a l'égalité $G = g$. + +\item Ecrire la nouvelle règle d'abattage d'un arbre sous la forme + la plus simple possible. +\end{enumerate} +\end{enumerate} + + + +\vspace{-1em} +\section{(5pts) Démonstrations ensemblistes} +Soit $A$ et $B$ deux sous-ensembles de $\Omega$. +\begin{enumerate} +\item Soit $A_0=\{1,2,3\}$ et $B_0=\{3,4\}$. +Définir $A_0 \cup B_0$, $P(A_0)$, $P(B_0)$, $P(A_0\cup B_0)$ et +$P(A_0) \cup P(B_0)$. +\item A-t-on l'égalité $P(A \cup B) = P(A) \cup P(B)$? Justifier. +\item Montrer que l'on a $P(A \cap B) = P(A) \cap P(B)$. +\end{enumerate} + + + +\vspace{-1em} +\section{(6 pts) Relation entre puissances d'éléments} + + +Sur $\N^*$ on définit la relation +$a \mathcal{R} b$ si $a^b \leq b ^a$. +\begin{enumerate} +\item A-t-on $2 \mathcal{R} 3$? $2 \mathcal{R} 7$? $2 \mathcal{R} 4$? $3 \mathcal{R} 3$? $4 \mathcal{R} 2$? Justifier à chaque-fois. + +\item La relation est-elle réflexive? Le démontrer. + +\item La fonction logarithme népérien $\ln: \R^{+*} \rightarrow \R$ étant + croissante, montrer que sur $\N^*$ + $a \mathcal{R} b$ si $\dfrac{\ln(a)}{a} \leq \dfrac{\ln(b)}{b}$. +\item La relation est-elle transitive? Pour justifier votre réponse, on + pourra utiliser la question précédente. +\item La relation est-elle antisymétrique? Le justifier. +\end{enumerate} + + + + + +\end{document} diff --git a/partiels/131105S1/controle.tex~ b/partiels/131105S1/controle.tex~ new file mode 100644 index 0000000..efd326f --- /dev/null +++ b/partiels/131105S1/controle.tex~ @@ -0,0 +1,134 @@ +\documentclass[11pt,a4paper,french]{article} +\usepackage[francais]{babel} +\usepackage[utf8]{inputenc} +\usepackage{a4} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{framed} +\usepackage[amsmath,thmmarks,thref,framed]{ntheorem} +\usepackage[dvips]{graphics} +\usepackage{epsfig} +\usepackage{calc} +\usepackage{tabls} +\usepackage{times} +\usepackage{tabularx} +\usepackage{textcomp} +\usepackage{pst-all} +\usepackage[a4paper]{geometry} + +\input{symboles.sty} +\geometry{hmargin=1cm, tmargin=-0.5cm, bmargin=1.5cm} + +\title{ +DUT d'informatique. Contrôle de mathématiques discrètes.\\ +Semestre 1 (Novembre 2013). Durée 1h.} + +\date{} + +\begin{document} +\maketitle + +\vspace{-3em} +\noindent Seule une fiche manuscrite de format A5 est autorisée. +Tous les exercices de ce sujet sont indépendants les uns des autres. +Dans tout ce qui suit, on considère une algèbre de Boole +munie des opérateurs classiques ``+'', ``.'', +``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes +$a$, $b$, $c$, $d$. + + +\vspace{-1em} +\section{Cours (3pts) } + +\begin{enumerate} +\item Soit $A$ et $B$ deux ensembles d'un +univers $\Omega$ tels que $A \subseteq B$. Définir $B\setminus A$ en compréhension. +\item L'ensemble vide appartient-il à tout ensemble? Justifier. +\end{enumerate} + + + + +\vspace{-1em} +\section{(6pts) Simplification de formules booléennes (d'après sujet de BTS-IG-2008)} +La société Jurabois exploite des coupes d'arbres constitués exclusivement de +feuillus et de résineux. Elle désire simplifier le règlement que les salariés +doivent appliquer pour la coupe du bois. +Actuellement, le règlement dit qu'un arbre est à abattre dans les quatre cas +suivants: +\begin{itemize} +\item si c'est un résineux au tronc droit mesurant plus de 20 m de hauteur; +\item si c'est un feuillus de 50 ans ou plus; +\item s'il a moins de 50 ans et mesure plus de 20 m de hauteur; +\item s'il est tordu. +\end{itemize} +Pour un arbre quelconque, on définit les variables booléennes suivantes par: +\begin{itemize} +\item $a=1$ si l'arbre est un résineux; +\item $b=1$ si l'arbre a moins de 50 ans; +\item $c=1$ si l'arbre mesure plus de 20 m de hauteur; +\item $d=1$ si l'arbre est tordu. +\end{itemize} + + +\begin{enumerate} +\item Écrire la fonction booléenne $f(a,b,c,d)$ qui traduit le règlement + actuel d'abattage d'un arbre. + +\item Grâce à une bonne gestion des forêts que la société exploite, + il n'y a maintenant plus d'arbre tordu. +\begin{enumerate} +\item Montrer que le nouveau règlement d'abattage se traduit par la fonction +$ +g(a,b,c) = ac + \overline{a}\overline{b} + bc +$. +\item A l'aide d'une table de Karnaugh donner l'expression $G$ qui + serait la forme la plus réduite de $g$. + +\item Justifier algébriquement que l'on a l'égalité $G = g$. + +\item Écrire la nouvelle règle d'abattage d'un arbre sous la forme + la plus simple possible. +\end{enumerate} +\end{enumerate} + + + +\vspace{-1em} +\section{(5pts) Démonstrations ensemblistes} +Soit $A$ et $B$ deux sous-ensembles de $\Omega$. +\begin{enumerate} +\item Soit $A_0=\{1,2,3\}$ et $B_0=\{3,4\}$. +Définir $A_0 \cup B_0$, $P(A_0)$, $P(B_0)$, $P(A_0\cup B_0)$ et +$P(A_0) \cup P(B_0)$. +\item A-t-on l'égalité $P(A \cup B) = P(A) \cup P(B)$? Justifier. +\item Montrer que l'on a $P(A \cap B) = P(A) \cap P(B)$. +\end{enumerate} + + + +\vspace{-1em} +\section{(6 pts) Relation entre puissances d'éléments} + + +Sur $\N^*$ on définit la relation +$a \mathcal{R} b$ si $a^b \leq b ^a$. +\begin{enumerate} +\item A-t-on $2 \mathcal{R} 3$? $2 \mathcal{R} 7$? $2 \mathcal{R} 4$? $3 \mathcal{R} 3$? $4 \mathcal{R} 2$? Justifier à chaque fois. + +\item La relation est-elle réflexive? Le démontrer. + +\item La fonction logarithme népérien $\ln: \R^{+*} \rightarrow \R$ étant + croissante, montrer que sur $\N^*$ + $a \mathcal{R} b$ si $\dfrac{\ln(a)}{a} \leq \dfrac{\ln(b)}{b}$. +\item La relation est-elle transitive? Pour justifier votre réponse, on + pourra utiliser la question précédente. +\item La relation est-elle antisymétrique? Le justifier. +\end{enumerate} + + + + + +\end{document} diff --git a/partiels/131105S1/controle.thm b/partiels/131105S1/controle.thm new file mode 100644 index 0000000..e69de29 diff --git a/partiels/131105S1/symboles.sty b/partiels/131105S1/symboles.sty new file mode 120000 index 0000000..a4e1afa --- /dev/null +++ b/partiels/131105S1/symboles.sty @@ -0,0 +1 @@ +/home/couchot/enseignement/stats/partiels/111103/symboles.sty \ No newline at end of file