--- /dev/null
+\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}}
+\newlabel{itm:1}{{1}{1}}[None]
+\newlabel{itm:2}{{2}{1}}[None]
--- /dev/null
+This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/Debian) (format=pdflatex 2013.4.28) 23 OCT 2013 16:18
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**main.tex
+(./main.tex
+LaTeX2e <2011/06/27>
+Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, lo
+aded.
+(/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/size10.clo
+File: size10.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 2008/07/08 v3.8m The Babel package
+
+(/usr/share/texlive/texmf-dist/tex/generic/babel/frenchb.ldf
+Language: frenchb 2010/08/21 v2.5a French support from the babel system
+
+(/usr/share/texlive/texmf-dist/tex/generic/babel/babel.def
+File: babel.def 2008/07/08 v3.8m Babel common definitions
+\babel@savecnt=\count87
+\U@D=\dimen103
+)
+
+Package babel Warning: No hyphenation patterns were loaded for
+(babel) the language `French'
+(babel) I will use the patterns loaded for \language=0 instead.
+
+\l@french = a dialect from \language0
+Package babel Info: Making : an active character on input line 234.
+Package babel Info: Making ; an active character on input line 235.
+Package babel Info: Making ! an active character on input line 236.
+Package babel Info: Making ? an active character on input line 237.
+\FB@Mht=\dimen104
+\std@mcc=\count88
+\dec@mcc=\count89
+\parindentFFN=\dimen105
+*************************************
+* Local config file frenchb.cfg used
+*
+(/usr/share/texlive/texmf-dist/tex/generic/babel/frenchb.cfg))
+(/usr/share/texlive/texmf-dist/tex/generic/babel/frenchb.ldf
+Language: frenchb 2010/08/21 v2.5a 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 2000/07/18 v2.13 AMS math features
+\@mathmargin=\skip43
+
+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=\count90
+LaTeX Info: Redefining \frac on input line 211.
+\uproot@=\count91
+\leftroot@=\count92
+LaTeX Info: Redefining \overline on input line 307.
+\classnum@=\count93
+\DOTSCASE@=\count94
+LaTeX Info: Redefining \ldots on input line 379.
+LaTeX Info: Redefining \dots on input line 382.
+LaTeX Info: Redefining \cdots on input line 467.
+\Mathstrutbox@=\box26
+\strutbox@=\box27
+\big@size=\dimen108
+LaTeX Font Info: Redeclaring font encoding OML on input line 567.
+LaTeX Font Info: Redeclaring font encoding OMS on input line 568.
+\macc@depth=\count95
+\c@MaxMatrixCols=\count96
+\dotsspace@=\muskip10
+\c@parentequation=\count97
+\dspbrk@lvl=\count98
+\tag@help=\toks18
+\row@=\count99
+\column@=\count100
+\maxfields@=\count101
+\andhelp@=\toks19
+\eqnshift@=\dimen109
+\alignsep@=\dimen110
+\tagshift@=\dimen111
+\tagwidth@=\dimen112
+\totwidth@=\dimen113
+\lineht@=\dimen114
+\@envbody=\toks20
+\multlinegap=\skip44
+\multlinetaggap=\skip45
+\mathdisplay@stack=\toks21
+LaTeX Info: Redefining \[ on input line 2666.
+LaTeX Info: Redefining \] on input line 2667.
+)
+(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty
+Package: amsfonts 2009/06/22 v3.00 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 96.
+)
+(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty
+Package: amssymb 2009/06/22 v3.00
+)
+(/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=\skip46
+\fb@frw=\dimen115
+\fb@frh=\dimen116
+\FrameRule=\dimen117
+\FrameSep=\dimen118
+)
+(/usr/share/texlive/texmf-dist/tex/latex/doublestroke/dsfont.sty
+Package: dsfont 1995/08/01 v0.1 Double stroke roman fonts
+)
+(/usr/share/texlive/texmf-dist/tex/latex/ntheorem/ntheorem.sty
+Style `ntheorem', Version 1.31 <2011/02/16>
+Package: ntheorem 2011/02/16 1.31
+(/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=\skip47
+\theorempostskipamount=\skip48
+\theoremframepreskipamount=\skip49
+\theoremframepostskipamount=\skip50
+\theoremindent=\dimen119
+\theorem@indent=\dimen120
+\theoremheaderfont=\toks26
+\theoremseparator=\toks27
+\theoremprework=\toks28
+\theorempostwork=\toks29
+\theoremsymbol=\toks30
+\qedsymbol=\toks31
+\theoremkeyword=\toks32
+\qedsymbol=\toks33
+\thm@topsepadd=\skip51
+Package ntheorem Info: Option `thmmarks' loaded on input line 1066.
+\c@endNonectr=\count102
+\c@currNonectr=\count103
+\mysavskip=\skip52
+Package ntheorem Info: Option `thref' loaded on input line 1066.
+\mysavskip=\skip53
+Package ntheorem Info: option `amsmath' handling for `thref' loaded on input li
+ne 1066.
+Package ntheorem Info: option `amsmath' handling for `thmmarks' loaded on input
+ line 1066.
+\thm@amstmpdepth=\dimen121
+\tagwidth=\dimen122
+\shadecolor=\toks34
+)
+(/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=\dimen123
+\Gin@req@width=\dimen124
+)
+\epsfxsize=\dimen125
+\epsfysize=\dimen126
+)
+(/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty
+Package: calc 2007/08/22 v4.3 Infix arithmetic (KKT,FJ)
+\calc@Acount=\count104
+\calc@Bcount=\count105
+\calc@Adimen=\dimen127
+\calc@Bdimen=\dimen128
+\calc@Askip=\skip54
+\calc@Bskip=\skip55
+LaTeX Info: Redefining \setlength on input line 76.
+LaTeX Info: Redefining \addtolength on input line 77.
+\calc@Ccount=\count106
+\calc@Cskip=\skip56
+)
+(/usr/share/texlive/texmf-dist/tex/latex/tabls/tabls.sty
+\tablinesep=\dimen129
+\arraylinesep=\dimen130
+\extrarulesep=\dimen131
+\@arstdepth=\dimen132
+\@arstheight=\dimen133
+\@skip@bove=\dimen134
+)
+
+! LaTeX Error: File `slashbox.sty' not found.
+
+Type X to quit or <RETURN> to proceed,
+or enter new name. (Default extension: sty)
+
+Enter file name:
+(/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/multicol.sty
+Package: multicol 2011/06/27 v1.7a multicolumn formatting (FMi)
+\c@tracingmulticols=\count107
+\mult@box=\box28
+\multicol@leftmargin=\dimen135
+\c@unbalance=\count108
+\c@collectmore=\count109
+\doublecol@number=\count110
+\multicoltolerance=\count111
+\multicolpretolerance=\count112
+\full@width=\dimen136
+\page@free=\dimen137
+\premulticols=\dimen138
+\postmulticols=\dimen139
+\multicolsep=\skip57
+\multicolbaselineskip=\skip58
+\partial@page=\box29
+\last@line=\box30
+\mult@rightbox=\box31
+\mult@grightbox=\box32
+\mult@gfirstbox=\box33
+\mult@firstbox=\box34
+\@tempa=\box35
+\@tempa=\box36
+\@tempa=\box37
+\@tempa=\box38
+\@tempa=\box39
+\@tempa=\box40
+\@tempa=\box41
+\@tempa=\box42
+\@tempa=\box43
+\@tempa=\box44
+\@tempa=\box45
+\@tempa=\box46
+\@tempa=\box47
+\@tempa=\box48
+\@tempa=\box49
+\@tempa=\box50
+\@tempa=\box51
+\c@columnbadness=\count113
+\c@finalcolumnbadness=\count114
+\last@try=\dimen140
+\multicolovershoot=\dimen141
+\multicolundershoot=\dimen142
+\mult@nat@firstbox=\box52
+\colbreak@box=\box53
+\multicol@sort@counter=\count115
+)
+(/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=\dimen143
+\extrarowheight=\dimen144
+\NC@list=\toks35
+\extratabsurround=\skip59
+\backup@length=\skip60
+
+
+LaTeX Warning: Command \@xhline has changed.
+ Check if current package is valid.
+
+)
+\TX@col@width=\dimen145
+\TX@old@table=\dimen146
+\TX@old@col=\dimen147
+\TX@target=\dimen148
+\TX@delta=\dimen149
+\TX@cols=\count116
+\TX@ftn=\toks36
+) (/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 2011/10/31 v0.52 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 2008/08/13 v2.6a package option processing (HA)
+
+(/usr/share/texlive/texmf-dist/tex/generic/xkeyval/xkeyval.tex
+\XKV@toks=\toks37
+\XKV@tempa@toks=\toks38
+\XKV@depth=\count117
+File: xkeyval.tex 2008/08/13 v2.6a 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=\count118
+\pstFP@xia=\count119
+\pstFP@xib=\count120
+\pstFP@xfa=\count121
+\pstFP@xfb=\count122
+\pstFP@rega=\count123
+\pstFP@regb=\count124
+\pstFP@regs=\count125
+\pstFP@times=\count126
+)
+\psLoopIndex=\count127
+
+`PSTricks' v2.29 <2012/06/04> (tvz)
+\pst@dima=\dimen150
+\pst@dimb=\dimen151
+\pst@dimc=\dimen152
+\pst@dimd=\dimen153
+\pst@dimg=\dimen154
+\pst@dimh=\dimen155
+\pst@dimm=\dimen156
+\pst@dimn=\dimen157
+\pst@dimo=\dimen158
+\pst@dimp=\dimen159
+\pst@hbox=\box54
+\pst@ibox=\box55
+\pst@boxg=\box56
+\pst@cnta=\count128
+\pst@cntb=\count129
+\pst@cntc=\count130
+\pst@cntd=\count131
+\pst@cntg=\count132
+\pst@cnth=\count133
+\pst@cntm=\count134
+\pst@cntn=\count135
+\pst@cnto=\count136
+\pst@cntp=\count137
+\@zero=\count138
+\pst@toks=\toks39
+(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pstricks.con)
+\psunit=\dimen160
+\psxunit=\dimen161
+\psyunit=\dimen162
+\pst@C@@rType=\count139
+\pslinewidth=\dimen163
+\psk@startLW=\dimen164
+\psk@endLW=\dimen165
+\pst@customdefs=\toks40
+\pslinearc=\dimen166
+\pst@symbolStep=\dimen167
+\pst@symbolWidth=\dimen168
+\pst@symbolLinewidth=\dimen169
+\everypsbox=\toks41
+\psframesep=\dimen170
+\pslabelsep=\dimen171
+\pst@shift=\dimen172
+\theoverlaybox=\box57
+)
+File: pstricks.tex 2012/06/04 v2.29 `PSTricks' (tvz,hv)
+
+(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pst-fp.tex)
+File: pst-fp.tex 2012/06/04 v2.29 `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=\count140
+)
+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 <tvz>
+\multido@count=\count141
+\multidocount=\count142
+\multido@stuff=\toks42
+)
+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
+ v1.42, 2012/05/03 (tvz,hv)
+\pstRadUnit=\dimen173
+\pstRadUnitInv=\dimen174
+\pst@linecnt=\count143
+\psxlabelsep=\dimen175
+\psylabelsep=\dimen176
+\psk@subticksize=\dimen177
+\pst@xticksizeA=\dimen178
+\pst@xticksizeB=\dimen179
+\pst@xticksizeC=\dimen180
+\pst@yticksizeA=\dimen181
+\pst@yticksizeB=\dimen182
+\pst@yticksizeC=\dimen183
+\@digitcounter=\count144
+\psk@llx=\dimen184
+\psk@lly=\dimen185
+\psk@urx=\dimen186
+\psk@ury=\dimen187
+\pst@xunit=\dimen188
+\pst@yunit=\dimen189
+)
+File: pst-plot.tex 2012/05/03 1.42 `pst-plot' (tvz,hv)
+)
+(/usr/share/texlive/texmf-dist/tex/latex/pst-node/pst-node.sty
+Package: pst-node 2011/06/05 v1.00 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
+ v1.22, 2012/02/12
+\psrow=\count145
+\pscol=\count146
+\psmatrixcnt=\count147
+\psrowsep=\skip61
+\pscolsep=\skip62
+\pst@args=\count148
+\num@pts=\count149
+\pst@argcnt=\count150
+)
+File: pst-node.tex 2012/02/12 1.22 `pst-node' (tvz)
+)
+(/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=\box58
+\pstree@box=\box59
+\psnodecnt=\count151
+\pstreelevel=\count152
+\pstreecnt=\count153
+\pstree@cnt=\count154
+\pstree@stop=\count155
+)
+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=\box60
+)
+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' v3.55, 2011/12/11 (dr,hv)
+\pshooklength=\dimen190
+\pshookwidth=\dimen191
+\pst@cntC=\count156
+\chart@ColorIndex=\dimen192
+\chart@ColorStep=\dimen193
+\pst@chartHeight=\dimen194
+\pst@chartStackDepth=\dimen195
+\pst@chartStackWidth=\dimen196
+\chart@Toggle=\count157
+\psVectorCtr=\count158
+)
+File: pstricks-add.tex 2011/12/11 v3.55 `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=\count159
+\Gm@cntv=\count160
+\c@Gm@tempcnt=\count161
+\Gm@bindingoffset=\dimen197
+\Gm@wd@mp=\dimen198
+\Gm@odd@mp=\dimen199
+\Gm@even@mp=\dimen200
+\Gm@layoutwidth=\dimen201
+\Gm@layoutheight=\dimen202
+\Gm@layouthoffset=\dimen203
+\Gm@layoutvoffset=\dimen204
+\Gm@dimlist=\toks43
+)
+No file main.aux.
+\openout1 = `main.aux'.
+
+LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 28.
+LaTeX Font Info: ... okay on input line 28.
+LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 28.
+LaTeX Font Info: Try loading font information for TS1+cmr on input line 28.
+(/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 28.
+LaTeX Font Info: Try loading font information for OT1+ptm on input line 28.
+
+(/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 28.
+LaTeX Info: Redefining \dots on input line 28.
+LaTeX Info: Redefining \up on input line 28.
+
+
+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 28.
+
+(/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=\count162
+\scratchdimen=\dimen205
+\scratchbox=\box61
+\nofMPsegments=\count163
+\nofMParguments=\count164
+\everyMPshowfont=\toks44
+\MPscratchCnt=\count165
+\MPscratchDim=\dimen206
+\MPnumerator=\count166
+\makeMPintoPDFobject=\count167
+\everyMPtoPDFconversion=\toks45
+)
+*geometry* driver: auto-detecting
+*geometry* detected driver: pdftex
+*geometry* verbose mode - [ preamble ] result:
+* driver: pdftex
+* paper: a4paper
+* layout: <same size as paper>
+* layoutoffset:(h,v)=(0.0pt,0.0pt)
+* modes:
+* h-part:(L,W,R)=(28.45274pt, 540.60239pt, 28.45274pt)
+* v-part:(T,H,B)=(28.45274pt, 773.91498pt, 42.67912pt)
+* \paperwidth=597.50787pt
+* \paperheight=845.04684pt
+* \textwidth=540.60239pt
+* \textheight=773.91498pt
+* \oddsidemargin=-43.81725pt
+* \evensidemargin=-43.81725pt
+* \topmargin=-80.81725pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=10.0pt
+* \footskip=30.0pt
+* \marginparwidth=72.26999pt
+* \marginparsep=11.0pt
+* \columnsep=10.0pt
+* \skip\footins=9.0pt 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 32.
+(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsa.fd
+File: umsa.fd 2009/06/22 v3.00 AMS symbols A
+)
+LaTeX Font Info: Try loading font information for U+msb on input line 32.
+
+(/usr/share/texlive/texmf-dist/tex/latex/amsfonts/umsb.fd
+File: umsb.fd 2009/06/22 v3.00 AMS symbols B
+)
+
+LaTeX Warning: No \author given.
+
+[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!{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}]
+LaTeX Font Info: Try loading font information for OT1+pcr on input line 102.
+
+
+(/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1pcr.fd
+File: ot1pcr.fd 2001/06/04 font definitions for OT1/pcr.
+)
+\tf@thm=\write5
+\openout5 = `main.thm'.
+
+ [2] (./main.aux)
+
+LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
+
+ )
+Here is how much of TeX's memory you used:
+ 9192 strings out of 495059
+ 132526 string characters out of 3182030
+ 280413 words of memory out of 3000000
+ 12116 multiletter control sequences out of 15000+200000
+ 14176 words of font info for 47 fonts, out of 3000000 for 9000
+ 14 hyphenation exceptions out of 8191
+ 44i,8n,64p,565b,270s stack positions out of 5000i,500n,10000p,200000b,50000s
+{/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc}</usr/share/texliv
+e/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texm
+f-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/texmf-dist/
+fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/t
+ype1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/fonts/type1/pub
+lic/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/am
+sfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1/urw/courier/ucrr
+8a.pfb></usr/share/texlive/texmf-dist/fonts/type1/urw/times/utmr8a.pfb>
+Output written on main.pdf (2 pages, 77459 bytes).
+PDF statistics:
+ 44 PDF objects out of 1000 (max. 8388607)
+ 31 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)
+
--- /dev/null
+\documentclass[10pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage{dsfont}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphics}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{slashbox}
+\usepackage{times}
+\usepackage{multicol}
+\usepackage{tabularx}
+\usepackage{textcomp}
+
+\usepackage{pst-all}
+
+\usepackage[a4paper]{geometry}
+
+
+\date{}
+\geometry{hmargin=1cm, tmargin=1cm,bmargin=1.5cm}
+\begin{document}
+\title{UE MESI, Master IMR 2ème année.\\
+ Novembre 2012 (durée 1h). J.-F. Couchot,}
+
+\maketitle
+\vspace{-5em}
+\begin{tabular}{ll}
+Nom:& ........................................\\
+Prénom:& ........................................\\
+\end{tabular}
+
+
+On s'intéresse à résoudre une équation de la forme $f(x)=0$ par la
+méthode de Müller. Dans cette méthode, on considère que l'on
+a le triplet de points $(x_{n-2},x_{n-1},x_{n})$. Pour calculer
+$x_{n+1}$, on fait comme suit:
+\begin{enumerate}
+\item \label{itm:1} on approche $f(x)$ par un polynôme $P(x)$ aux points
+ $(x_{n-2},x_{n-1},x_{n})$,
+\item\label{itm:2} on résout l'équation $P(x)=0$. La racine la plus proche de $x_n$ est $x_{n+1}$;
+\item on recommence avec le triplet $(x_{n-1},x_{n},x_{n+1})$\ldots
+\end{enumerate}
+
+
+
+
+
+
+Vos réponses seront données directement ci-dessous.
+
+\begin{enumerate}
+
+\item En utilisant une base de Lagrange, montrer que le polynôme $P(x)$
+ obtenu à l'étape 1. de la première itération est défini par
+$$
+P(x) = \dfrac{(x-x_{n-1})(x-x_{n-2})f(x_n)}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{(x-x_{n})(x-x_{n-2})f(x_{n-1})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{(x-x_{n})(x-x_{n-1})f(x_{n-2})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})}
+$$
+
+\vspace{4cm}
+
+\item Montrer que le polynôme de la question précédente est de degré 2.
+ Est-ce cohérent avec le fait qu'on veuille approximer $f$ en trois points?
+\vspace{4cm}
+
+\item Montrer que le polynôme de la première question peut s'écrire
+ sous la forme $P(x) = a_n x^2 + b_n x + c $ où
+\begin{eqnarray*}
+a_n & = & \dfrac{f(x_n)}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{f(x_{n-1})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{f(x_{n-2})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})} \\
+b_n & = &-\dfrac{f(x_n)(x_{n-1}+x_{n-2})}{(x_n-x_{n-1})(x_n-x_{n-2})} -
+\dfrac{f(x_{n-1})(x_{n}+x_{n-2})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} -
+\dfrac{f(x_{n-2})(x_{n}+x_{n-1})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})} \\
+c_n & = & \dfrac{f(x_n)x_{n-1}x_{n-2}}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{f(x_{n-1})x_{n}x_{n-2}}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{f(x_{n-2})x_{n}x_{n-1}}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})}
+\end{eqnarray*}
+\vspace{8cm}
+
+
+\item Exprimer les deux racines $x'_{n}$ et $x''_{n}$ du polynôme précédent
+en fonctions de $a_n$, $b_n$ et $c_n$ lorsqu'on itère dans les réels.
+\vspace{3cm}
+
+\item Comment est alors défini $x_{n+1}$?
+\vspace{3cm}
+
+\item On pourrait montrer que l'ordre de la convergence est 1,84. Comparer cette vitesse de convergence avec celle de Newton et celle de Lagrange.
+\vspace{3cm}
+
+
+\item Donner le code Python de la fonction
+ $\verb+[n,X] = iteration_muller(x+_{\verb+0+},\verb+x+_{\verb+1+},\verb+x+_{\verb+2+}\verb+,m,epsilon,f)+$ où
+\begin{itemize}
+\item $\verb+x+_{\verb+0+}$, $\verb+x+_{\verb+1+}$ et $\verb+x+_{\verb+2+}$ sont les trois premières valeurs des itérés, \verb+m+
+ est le nombre maximal
+ d'itérations, \texttt{epsilon} est la précision souhaitée
+ et \verb+f+ la fonction à itérer;
+\item \verb+n+ est le nombre d'itérations réalisées pour que
+\verb+f(+$\verb+x+_{\verb+n+}$\verb+)+=0 ou que
+$|\verb+x+_{\verb+n+}- \verb+x+_{\verb+n-1+}| \leq \verb+epsilon+$, \verb+n+ étant inférieur à \verb+m+ et \verb+X+ est
+ le vecteur contenant les
+ valeurs $\verb+x+_{\verb+0+},\ldots,\verb+x+_{\verb+n+}$.
+\end{itemize}
+\end{enumerate}
+
+
+\end{document}
\ No newline at end of file
--- /dev/null
+<?xml version="1.0" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
+"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
+<!-- Creator: fig2dev Version 3.2 Patchlevel 5-alpha7 -->
+<!-- CreationDate: Mon Jun 19 22:27:10 2006 -->
+<!-- Magnification: 1.050 -->
+<svg xmlns="http://www.w3.org/2000/svg" width="3.9in" height="3.5in" viewBox="456 270 4681 4158">
+<g style="stroke-width:.025in; stroke:black; fill:none">
+<!-- Line -->
+<polyline points="527,2362
+5125,2362
+" style="stroke:#000000;stroke-width:8;
+stroke-linejoin:miter; stroke-linecap:butt;
+"/>
+<!-- Line -->
+<polyline points="1417,283
+1417,4416
+" style="stroke:#000000;stroke-width:8;
+stroke-linejoin:miter; stroke-linecap:butt;
+"/>
+<!-- Line -->
+<polyline points="4708,486
+4708,2369
+" style="stroke:#000000;stroke-width:8;
+stroke-linejoin:miter; stroke-linecap:butt;
+stroke-dasharray:50 50;
+"/>
+<!-- Line -->
+<polyline points="3298,1195
+3298,2353
+" style="stroke:#000000;stroke-width:8;
+stroke-linejoin:miter; stroke-linecap:butt;
+stroke-dasharray:50 50;
+"/>
+<!-- Line -->
+<polyline points="1881,4267
+1881,2362
+" style="stroke:#000000;stroke-width:8;
+stroke-linejoin:miter; stroke-linecap:butt;
+stroke-dasharray:50 50;
+"/>
+<!-- Line -->
+<polyline points="1889,4251
+4719,474
+" style="stroke:#0000ff;stroke-width:16;
+stroke-linejoin:miter; stroke-linecap:butt;
+"/>
+<!-- Line -->
+<polyline points="1874,4259
+3307,1196
+" style="stroke:#0000ff;stroke-width:16;
+stroke-linejoin:miter; stroke-linecap:butt;
+"/>
+<!-- Circle -->
+<circle cx="1881" cy="4259" r="43"
+ style="fill:#ff0000;stroke:#000000;stroke-width:0;"/>
+<!-- Circle -->
+<circle cx="4716" cy="479" r="43"
+ style="fill:#ff0000;stroke:#000000;stroke-width:0;"/>
+<!-- Circle -->
+<circle cx="3307" cy="1196" r="43"
+ style="fill:#ff0000;stroke:#000000;stroke-width:0;"/>
+<!-- Circle -->
+<circle cx="3291" cy="2369" r="43"
+ style="fill:#0000ff;stroke:#000000;stroke-width:0;"/>
+<!-- Circle -->
+<circle cx="2760" cy="2362" r="43"
+ style="fill:#0000ff;stroke:#000000;stroke-width:0;"/>
+<!-- Line -->
+<polyline points="5070,393
+5068,393
+5063,395
+5054,397
+5040,401
+5019,405
+4994,411
+4961,418
+4923,428
+4880,437
+4834,449
+4784,460
+4732,473
+4679,487
+4626,499
+4574,512
+4522,525
+4472,538
+4424,551
+4379,562
+4334,574
+4293,585
+4254,596
+4217,606
+4181,617
+4148,627
+4115,637
+4085,647
+4054,658
+4025,667
+3996,678
+3968,688
+3939,700
+3909,711
+3880,723
+3850,735
+3821,749
+3792,763
+3762,777
+3733,793
+3704,810
+3675,827
+3646,846
+3616,866
+3588,886
+3560,908
+3532,931
+3505,954
+3478,979
+3453,1005
+3426,1032
+3402,1060
+3379,1088
+3356,1118
+3334,1149
+3313,1180
+3293,1212
+3274,1246
+3255,1280
+3237,1315
+3220,1352
+3205,1391
+3192,1421
+3180,1454
+3167,1486
+3155,1521
+3144,1556
+3132,1593
+3121,1631
+3109,1671
+3098,1711
+3087,1753
+3076,1795
+3065,1839
+3055,1884
+3043,1929
+3033,1975
+3022,2023
+3012,2070
+3001,2118
+2991,2166
+2980,2215
+2971,2263
+2960,2311
+2951,2360
+2941,2407
+2931,2454
+2921,2501
+2912,2548
+2902,2593
+2894,2637
+2885,2680
+2876,2723
+2867,2764
+2858,2805
+2849,2845
+2840,2883
+2831,2921
+2823,2958
+2813,2994
+2803,3036
+2791,3077
+2780,3118
+2768,3158
+2755,3196
+2743,3235
+2730,3274
+2717,3312
+2703,3350
+2689,3386
+2675,3423
+2660,3459
+2644,3495
+2628,3529
+2613,3563
+2597,3596
+2580,3629
+2563,3659
+2548,3690
+2531,3719
+2514,3748
+2497,3774
+2480,3800
+2464,3824
+2447,3848
+2430,3870
+2413,3892
+2397,3913
+2381,3932
+2365,3951
+2348,3970
+2331,3987
+2311,4008
+2290,4028
+2268,4048
+2246,4067
+2223,4086
+2200,4103
+2175,4121
+2150,4139
+2123,4155
+2096,4171
+2068,4186
+2039,4201
+2010,4215
+1981,4227
+1950,4239
+1919,4250
+1888,4260
+1857,4269
+1825,4278
+1794,4285
+1762,4291
+1731,4297
+1698,4301
+1667,4305
+1634,4308
+1602,4310
+1574,4312
+1546,4313
+1518,4313
+1488,4313
+1458,4313
+1425,4312
+1392,4310
+1356,4308
+1318,4306
+1278,4303
+1236,4299
+1192,4295
+1145,4289
+1097,4284
+1045,4279
+993,4272
+938,4266
+883,4259
+829,4251
+775,4245
+724,4238
+676,4232
+632,4225
+593,4220
+559,4216
+532,4212
+511,4208
+496,4206
+487,4205
+481,4204
+479,4204
+" style="stroke:#ff0000;stroke-width:16;
+stroke-linejoin:bevel; stroke-linecap:butt;
+"/>
+<!-- Text -->
+<text xml:space="preserve" x="525" y="4121" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">f(x)</text>
+<!-- Text -->
+<text xml:space="preserve" x="2503" y="2270" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">a</text>
+<!-- Text -->
+<text xml:space="preserve" x="2653" y="2322" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">2</text>
+<!-- Text -->
+<text xml:space="preserve" x="4629" y="2578" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">b</text>
+<!-- Text -->
+<text xml:space="preserve" x="4779" y="2645" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">0</text>
+<!-- Text -->
+<text xml:space="preserve" x="2157" y="2554" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="normal" font-weight="normal" font-size="177" text-anchor="start">=</text>
+<!-- Text -->
+<text xml:space="preserve" x="2061" y="2605" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">0</text>
+<!-- Text -->
+<text xml:space="preserve" x="2479" y="2605" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">1</text>
+<!-- Text -->
+<text xml:space="preserve" x="3504" y="2601" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="normal" font-weight="normal" font-size="177" text-anchor="start">=</text>
+<!-- Text -->
+<text xml:space="preserve" x="3408" y="2692" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">1</text>
+<!-- Text -->
+<text xml:space="preserve" x="2330" y="2554" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">a</text>
+<!-- Text -->
+<text xml:space="preserve" x="1912" y="2554" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">a</text>
+<!-- Text -->
+<text xml:space="preserve" x="3259" y="2624" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">b</text>
+<!-- Text -->
+<text xml:space="preserve" x="3669" y="2624" stroke="#000000" fill="#000000" font-family="Helvetica" font-style="italic" font-weight="normal" font-size="177" text-anchor="start">b</text>
+<!-- Text -->
+<text xml:space="preserve" x="3818" y="2692" stroke="#000000" fill="#000000" font-family="Times" font-style="normal" font-weight="normal" font-size="114" text-anchor="start">2</text>
+</g>
+</svg>
--- /dev/null
+\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}}
+\newlabel{itm:1}{{1}{1}}[None]
+\newlabel{itm:2}{{2}{1}}[None]
--- /dev/null
+This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) (format=pdflatex 2013.11.3) 3 NOV 2013 21:53
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**main.tex
+(./main.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/size10.clo
+File: size10.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/doublestroke/dsfont.sty
+Package: dsfont 1995/08/01 v0.1 Double stroke roman fonts
+)
+(/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/graphicx.sty
+Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
+
+(/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)
+))
+\Gin@req@height=\dimen125
+\Gin@req@width=\dimen126
+)
+(/usr/share/texlive/texmf-dist/tex/latex/graphics/epsfig.sty
+Package: epsfig 1999/02/16 v1.7a (e)psfig emulation (SPQR)
+\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/multicol.sty
+Package: multicol 2011/06/27 v1.7a multicolumn formatting (FMi)
+\c@tracingmulticols=\count108
+\mult@box=\box28
+\multicol@leftmargin=\dimen137
+\c@unbalance=\count109
+\c@collectmore=\count110
+\doublecol@number=\count111
+\multicoltolerance=\count112
+\multicolpretolerance=\count113
+\full@width=\dimen138
+\page@free=\dimen139
+\premulticols=\dimen140
+\postmulticols=\dimen141
+\multicolsep=\skip63
+\multicolbaselineskip=\skip64
+\partial@page=\box29
+\last@line=\box30
+\mult@rightbox=\box31
+\mult@grightbox=\box32
+\mult@gfirstbox=\box33
+\mult@firstbox=\box34
+\@tempa=\box35
+\@tempa=\box36
+\@tempa=\box37
+\@tempa=\box38
+\@tempa=\box39
+\@tempa=\box40
+\@tempa=\box41
+\@tempa=\box42
+\@tempa=\box43
+\@tempa=\box44
+\@tempa=\box45
+\@tempa=\box46
+\@tempa=\box47
+\@tempa=\box48
+\@tempa=\box49
+\@tempa=\box50
+\@tempa=\box51
+\c@columnbadness=\count114
+\c@finalcolumnbadness=\count115
+\last@try=\dimen142
+\multicolovershoot=\dimen143
+\multicolundershoot=\dimen144
+\mult@nat@firstbox=\box52
+\colbreak@box=\box53
+\multicol@sort@counter=\count116
+)
+(/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=\dimen145
+\extrarowheight=\dimen146
+\NC@list=\toks41
+\extratabsurround=\skip65
+\backup@length=\skip66
+
+
+LaTeX Warning: Command \@xhline has changed.
+ Check if current package is valid.
+
+)
+\TX@col@width=\dimen147
+\TX@old@table=\dimen148
+\TX@old@col=\dimen149
+\TX@target=\dimen150
+\TX@delta=\dimen151
+\TX@cols=\count117
+\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=\count118
+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=\count119
+\pstFP@xia=\count120
+\pstFP@xib=\count121
+\pstFP@xfa=\count122
+\pstFP@xfb=\count123
+\pstFP@rega=\count124
+\pstFP@regb=\count125
+\pstFP@regs=\count126
+\pstFP@times=\count127
+)
+(/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=\dimen152
+\pgffor@skip=\dimen153
+\pgffor@stack=\toks49
+\pgffor@toks=\toks50
+)
+\psLoopIndex=\count128
+
+`PSTricks' v2.45 <2013/07/09> (tvz)
+\pst@dima=\dimen154
+\pst@dimb=\dimen155
+\pst@dimc=\dimen156
+\pst@dimd=\dimen157
+\pst@dimg=\dimen158
+\pst@dimh=\dimen159
+\pst@dimm=\dimen160
+\pst@dimn=\dimen161
+\pst@dimo=\dimen162
+\pst@dimp=\dimen163
+\pst@hbox=\box54
+\pst@ibox=\box55
+\pst@boxg=\box56
+\pst@cnta=\count129
+\pst@cntb=\count130
+\pst@cntc=\count131
+\pst@cntd=\count132
+\pst@cntg=\count133
+\pst@cnth=\count134
+\pst@cntm=\count135
+\pst@cntn=\count136
+\pst@cnto=\count137
+\pst@cntp=\count138
+\@zero=\count139
+\pst@toks=\toks51
+(/usr/share/texlive/texmf-dist/tex/generic/pstricks/pstricks.con)
+\psunit=\dimen164
+\psxunit=\dimen165
+\psyunit=\dimen166
+\pst@C@@rType=\count140
+\pslinewidth=\dimen167
+\psk@startLW=\dimen168
+\psk@endLW=\dimen169
+\pst@customdefs=\toks52
+\pslinearc=\dimen170
+\pst@symbolStep=\dimen171
+\pst@symbolWidth=\dimen172
+\pst@symbolLinewidth=\dimen173
+\everypsbox=\toks53
+\psframesep=\dimen174
+\pslabelsep=\dimen175
+\sh@wgridXunit=\dimen176
+\sh@wgridYunit=\dimen177
+\pst@shift=\dimen178
+)
+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=\count141
+)
+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 <tvz>
+\multido@count=\count142
+\multidocount=\count143
+\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=\dimen179
+\pstRadUnitInv=\dimen180
+\pst@linecnt=\count144
+\RCD@file=\read1
+\psxlabelsep=\dimen181
+\psylabelsep=\dimen182
+\psk@subticksize=\dimen183
+\pst@xticksizeA=\dimen184
+\pst@xticksizeB=\dimen185
+\pst@xticksizeC=\dimen186
+\pst@yticksizeA=\dimen187
+\pst@yticksizeB=\dimen188
+\pst@yticksizeC=\dimen189
+\@digitcounter=\count145
+\psk@llx=\dimen190
+\psk@lly=\dimen191
+\psk@urx=\dimen192
+\psk@ury=\dimen193
+\pst@xunit=\dimen194
+\pst@yunit=\dimen195
+)
+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=\count146
+\pscol=\count147
+\psmatrixcnt=\count148
+\psrowsep=\skip67
+\pscolsep=\skip68
+\pst@args=\count149
+\num@pts=\count150
+\pst@argcnt=\count151
+)
+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=\box57
+\pstree@box=\box58
+\psnodecnt=\count152
+\pstreelevel=\count153
+\pstreecnt=\count154
+\pstree@cnt=\count155
+\pstree@stop=\count156
+)
+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=\box59
+)
+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=\dimen196
+\pshooklength=\dimen197
+\pshookwidth=\dimen198
+\pst@cntC=\count157
+\chart@ColorIndex=\dimen199
+\chart@ColorStep=\dimen200
+\pst@chartHeight=\dimen201
+\pst@chartStackDepth=\dimen202
+\pst@chartStackWidth=\dimen203
+\chart@Toggle=\count158
+\psVectorCtr=\count159
+)
+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=\count160
+\Gm@cntv=\count161
+\c@Gm@tempcnt=\count162
+\Gm@bindingoffset=\dimen204
+\Gm@wd@mp=\dimen205
+\Gm@odd@mp=\dimen206
+\Gm@even@mp=\dimen207
+\Gm@layoutwidth=\dimen208
+\Gm@layoutheight=\dimen209
+\Gm@layouthoffset=\dimen210
+\Gm@layoutvoffset=\dimen211
+\Gm@dimlist=\toks55
+) (./main.aux)
+\openout1 = `main.aux'.
+
+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 T1/cmr/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 OMS/cmsy/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 TS1/cmr/m/n on input line 27.
+LaTeX Font Info: Try loading font information for TS1+cmr on input line 27.
+
+(/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 27.
+LaTeX Font Info: Try loading font information for OT1+ptm on input line 27.
+
+(/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 27.
+LaTeX Info: Redefining \dots on input line 27.
+LaTeX Info: Redefining \up on input line 27.
+
+
+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 27.
+
+(/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=\count163
+\scratchdimen=\dimen212
+\scratchbox=\box60
+\nofMPsegments=\count164
+\nofMParguments=\count165
+\everyMPshowfont=\toks56
+\MPscratchCnt=\count166
+\MPscratchDim=\dimen213
+\MPnumerator=\count167
+\makeMPintoPDFobject=\count168
+\everyMPtoPDFconversion=\toks57
+)
+*geometry* driver: auto-detecting
+*geometry* detected driver: pdftex
+*geometry* verbose mode - [ preamble ] result:
+* driver: pdftex
+* paper: a4paper
+* layout: <same size as paper>
+* layoutoffset:(h,v)=(0.0pt,0.0pt)
+* modes:
+* h-part:(L,W,R)=(28.45274pt, 540.60239pt, 28.45274pt)
+* v-part:(T,H,B)=(28.45274pt, 773.91498pt, 42.67912pt)
+* \paperwidth=597.50787pt
+* \paperheight=845.04684pt
+* \textwidth=540.60239pt
+* \textheight=773.91498pt
+* \oddsidemargin=-43.81725pt
+* \evensidemargin=-43.81725pt
+* \topmargin=-80.81725pt
+* \headheight=12.0pt
+* \headsep=25.0pt
+* \topskip=10.0pt
+* \footskip=30.0pt
+* \marginparwidth=72.26999pt
+* \marginparsep=11.0pt
+* \columnsep=10.0pt
+* \skip\footins=9.0pt 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 31.
+(/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 31.
+
+(/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.
+
+<False_position_method.pdf, id=1, 281.74008pt x 252.945pt>
+File: False_position_method.pdf Graphic file (type pdf)
+
+<use False_position_method.pdf>
+Package pdftex.def Info: False_position_method.pdf used on input line 66.
+(pdftex.def) Requested size: 187.32301pt x 168.17929pt.
+LaTeX Font Info: Try loading font information for U+dsrom on input line 100.
+
+
+(/usr/share/texlive/texmf-dist/tex/latex/doublestroke/Udsrom.fd
+File: Udsrom.fd 1995/08/01 v0.1 Double stroke roman font definitions
+) [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} <./
+False_position_method.pdf>]
+\tf@thm=\write5
+\openout5 = `main.thm'.
+
+ [2] (./main.aux) )
+Here is how much of TeX's memory you used:
+ 10017 strings out of 495002
+ 150021 string characters out of 6180262
+ 301242 words of memory out of 5000000
+ 12956 multiletter control sequences out of 15000+600000
+ 13949 words of font info for 48 fonts, out of 8000000 for 9000
+ 14 hyphenation exceptions out of 8191
+ 44i,6n,64p,565b,257s stack positions out of 5000i,500n,10000p,200000b,80000s
+{/usr/share/texlive/texmf-dist/fonts/enc/dvips/base/8r.enc}<
+/usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/s
+hare/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi5.pfb></usr/share/te
+xlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></usr/share/texlive/t
+exmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-di
+st/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/fonts
+/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1
+/public/amsfonts/cm/cmsy7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public
+/doublestroke/dsrom10.pfb></usr/share/texlive/texmf-dist/fonts/type1/urw/times/
+utmr8a.pfb>
+Output written on main.pdf (2 pages, 113686 bytes).
+PDF statistics:
+ 58 PDF objects out of 1000 (max. 8388607)
+ 40 compressed objects within 1 object stream
+ 0 named destinations out of 1000 (max. 500000)
+ 6 words of extra memory for PDF output out of 10000 (max. 10000000)
+
--- /dev/null
+\documentclass[10pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage{dsfont}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphicx}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{times}
+\usepackage{multicol}
+\usepackage{tabularx}
+\usepackage{textcomp}
+
+\usepackage{pst-all}
+
+\usepackage[a4paper]{geometry}
+
+
+\date{}
+\geometry{hmargin=1cm, tmargin=1cm,bmargin=1.5cm}
+\begin{document}
+\title{UE MESI, Master IMR 2ème année.\\
+ Novembre 2013 (durée 45 mn). J.-F. Couchot,}
+
+\maketitle
+\vspace{-5em}
+% \begin{tabular}{ll}
+% Nom:& ........................................\\
+% Prénom:& ........................................\\
+% \end{tabular}
+
+
+\begin{minipage}{0.6\textwidth}
+
+On cherche à résoudre une équation de la forme $f(x)=0$ par la
+méthode de la fausse position.
+Cette méthode commence par deux points $a_0$ et $b_0$
+tels que $f(a_0)$ et $f(b_0)$ sont de signes opposés.
+Comme la fonction $f$ est continue, elle possède au moins une racine
+dans l’intervalle $[a_0, b_0]$.
+
+Dans cette méthode, on considère que l'on
+a l'intervalle $[a_n,b_n]$. Pour calculer
+$[a_{n+1},b_{n+1}]$, on fait comme suit:
+
+\begin{enumerate}
+\item \label{itm:1} on construit la droite $(D_n)$ qui passe par les points
+$(a_n,f(a_n))$ et $(b_n,f(b_n))$;
+\item\label{itm:2} on construit $X(x_n,0)$ le point d'intersection entre
+ la droite $(D_n)$ et l'axe de $x$;
+\item si $f(a_n)f(x_n)\leq 0$, alors $a_{n+1} = a_{n}$ et $b_{n+1}=x_n$;
+\item si $f(a_n)f(x_n)> 0$, alors $a_{n+1} = x_{n}$ et $b_{n+1}=b_n$.
+\end{enumerate}
+
+
+\end{minipage}
+\begin{minipage}{0.35\textwidth}
+%\begin{figure}
+%\includegraphics[width=0.99\textwidth]{Regula_falsi_method.png}
+\includegraphics[width=0.99\textwidth]{False_position_method}
+%\caption{Deux itérations de la méthode de la fausse postion.}\label{fig:iter}
+%\end{figure}
+\end{minipage}
+
+
+
+
+
+
+
+
+Vos réponses seront données directement ci-dessous.
+
+\begin{enumerate}
+
+\item (2pts) Montrer que l'équation de la droite $(D_n)$ est
+$y - f(b_n) = \frac{f(b_n)-f(a_n)}{b_n-a_n} (x-b_n)$.
+
+\vspace{4cm}
+
+\item (2pts) Montrer que le nombre $x_n$ est donné par l'équation
+$x_n = a_n - \frac{a_n-b_n}{f(a_n)-f(b_n)} f(a_n)$.
+
+\vspace{4cm}
+
+
+\item (2pts) En moyenne, l'ordre de cette méthode est 1,618.
+ Comparer cet ordre avec celui des autres méthodes du cours.
+\vspace{4cm}
+
+\item (5pts) Quelle partie de cette méthode est commune avec la
+ méthode par dichotomie? Est-elle toujours plus efficace?
+ Comparer les approches par exemple
+ sur l'intervalle $[-1,1]$ avec fonction $f$ définie sur $\mathds{R}$ par
+ $f(x)= 2x^3-4x^2+3x$.
+\vspace{6cm}
+
+\item (4pts) Quelle partie de cette méthode est commune avec la méthode de Lagrange?
+Est-ce la même méthode? Si ce n'est pas le cas, Expliquer ce qui diffère.
+\vspace{4cm}
+
+
+\item (5pts) Donner le code d'un programme qui implanterait cette méthode.
+
+\vspace{4cm}
+
+
+
+\end{enumerate}
+
+
+
+
+
+\end{document}
\ No newline at end of file
--- /dev/null
+\documentclass[10pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage{dsfont}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphicx}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{times}
+\usepackage{multicol}
+\usepackage{tabularx}
+\usepackage{textcomp}
+
+\usepackage{pst-all}
+
+\usepackage[a4paper]{geometry}
+
+
+\date{}
+\geometry{hmargin=1cm, tmargin=1cm,bmargin=1.5cm}
+\begin{document}
+\title{UE MESI, Master IMR 2ème année.\\
+ Novembre 2013 (durée 45 mn). J.-F. Couchot,}
+
+\maketitle
+\vspace{-5em}
+% \begin{tabular}{ll}
+% Nom:& ........................................\\
+% Prénom:& ........................................\\
+% \end{tabular}
+
+
+\begin{minipage}{0.6\textwidth}
+
+On cherche à résoudre une équation de la forme $f(x)=0$ par la
+méthode de la fausse position.
+Cette méthode commence par deux points $a_0$ et $b_0$
+tels que $f(a_0)$ et $f(b_0)$ sont de signes opposés.
+Comme la fonction $f$ est continue, elle possède au moins une racine
+dans l’intervalle $[a_0, b_0]$.
+
+Dans cette méthode, on considère que l'on
+a l'intervalle $[a_n,b_n]$. Pour calculer
+$[a_{n+1},b_{n+1}]$, on fait comme suit:
+
+\begin{enumerate}
+\item \label{itm:1} on construit la droite $(D_n)$ qui passe par les points
+$(a_n,f(a_n))$ et $(b_n,f(b_n))$;
+\item\label{itm:2} on construit $X(x_n,0)$ le point d'intersection entre
+ la droite $(D_n)$ et l'axe de $x$;
+\item si $f(a_n)f(x_n)\leq 0$, alors $a_{n+1} = a_{n}$ et $b_{n+1}=x_n$;
+\item si $f(a_n)f(x_n)> 0$, alors $a_{n+1} = x_{n}$ et $b_{n+1}=b_n$.
+\end{enumerate}
+
+
+\end{minipage}
+\begin{minipage}{0.35\textwidth}
+%\begin{figure}
+%\includegraphics[width=0.99\textwidth]{Regula_falsi_method.png}
+\includegraphics[width=0.99\textwidth]{False_position_method}
+%\caption{Deux itérations de la méthode de la fausse postion.}\label{fig:iter}
+%\end{figure}
+\end{minipage}
+
+
+
+
+
+
+
+
+Vos réponses seront données directement ci-dessous.
+
+\begin{enumerate}
+
+\item (2pts) Montrer que l'équation de la droite $(D_n)$ est
+$y - f(b_n) = \frac{f(b_n)-f(a_n)}{b_n-a_n} (x-b_n)$.
+
+\vspace{4cm}
+
+\item (2pts) Montrer que le nombre $x_n$ est donné par l'équation
+$x_n = a_n - \frac{a_n-b_n}{f(a_n)-f(b_n)} f(a_n)$.
+
+\vspace{4cm}
+
+
+\item (2pts) En moyenne, l'ordre de cette méthode est 1,618.
+ Comparer cet ordre avec celui des autres methodes du cours.
+\vspace{4cm}
+
+\item (5pts) Quelle partie de cette méthode est commune avec la
+ méthode par dichotomie? Est-elle toujours plus efficace?
+ Comparer les approches par exemple
+ sur l'intervalle $[-1,1]$ avec fonction $f$ définie sur $\mathds{R}$ par
+ $f(x)= 2x^3-4x^2+3x$.
+\vspace{6cm}
+
+\item (4pts) Quelle partie de cette méthode est commune avec la méthode de Lagrange?
+Est-ce la même méthode? Si ce n'est pas le cas, Expliquer ce qui difère.
+\vspace{4cm}
+
+
+\item (5pts) Donner le code d'un programme qui implanterait cette méthode.
+
+\vspace{4cm}
+
+
+
+\end{enumerate}
+
+
+
+
+
+\end{document}
\ No newline at end of file
--- /dev/null
+\documentclass[10pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage{dsfont}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphics}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{slashbox}
+\usepackage{times}
+\usepackage{multicol}
+\usepackage{tabularx}
+\usepackage{textcomp}
+
+\usepackage{pst-all}
+
+\usepackage[a4paper]{geometry}
+
+
+\date{}
+\geometry{hmargin=1cm, tmargin=1cm,bmargin=1.5cm}
+\begin{document}
+\title{UE MESI, Master IMR 2ème année.\\
+ Novembre 2012 (durée 1h). J.-F. Couchot,}
+
+\maketitle
+\vspace{-5em}
+\begin{tabular}{ll}
+Nom:& ........................................\\
+Prénom:& ........................................\\
+\end{tabular}
+
+
+On s'intéresse à résoudre une équation de la forme $f(x)=0$ par la
+méthode de Müller. Dans cette méthode, on considère que l'on
+a le triplet de points $(x_{n-2},x_{n-1},x_{n})$. Pour calculer
+$x_{n+1}$, on fait comme suit:
+\begin{enumerate}
+\item \label{itm:1} on approche $f(x)$ par un polynôme $P(x)$ aux points
+ $(x_{n-2},x_{n-1},x_{n})$,
+\item\label{itm:2} on résout l'équation $P(x)=0$. La racine la plus proche de $x_n$ est $x_{n+1}$;
+\item on recommence avec le triplet $(x_{n-1},x_{n},x_{n+1})$\ldots
+\end{enumerate}
+
+
+
+
+
+
+Vos réponses seront données directement ci-dessous.
+
+\begin{enumerate}
+
+\item En utilisant une base de Lagrange, montrer que le polynôme $P(x)$
+ obtenu à l'étape 1. de la première itération est défini par
+$$
+P(x) = \dfrac{(x-x_{n-1})(x-x_{n-2})f(x_n)}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{(x-x_{n})(x-x_{n-2})f(x_{n-1})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{(x-x_{n})(x-x_{n-1})f(x_{n-2})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})}
+$$
+
+\vspace{4cm}
+
+\item Montrer que le polynôme de la question précédente est de degré 2.
+ Est-ce cohérent avec le fait qu'on veuille approximer $f$ en trois points?
+\vspace{4cm}
+
+\item Montrer que le polynôme de la première question peut s'écrire
+ sous la forme $P(x) = a_n x^2 + b_n x + c $ où
+\begin{eqnarray*}
+a_n & = & \dfrac{f(x_n)}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{f(x_{n-1})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{f(x_{n-2})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})} \\
+b_n & = &-\dfrac{f(x_n)(x_{n-1}+x_{n-2})}{(x_n-x_{n-1})(x_n-x_{n-2})} -
+\dfrac{f(x_{n-1})(x_{n}+x_{n-2})}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} -
+\dfrac{f(x_{n-2})(x_{n}+x_{n-1})}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})} \\
+c_n & = & \dfrac{f(x_n)x_{n-1}x_{n-2}}{(x_n-x_{n-1})(x_n-x_{n-2})} +
+\dfrac{f(x_{n-1})x_{n}x_{n-2}}{(x_{n-1}-x_{n})(x_{n-1}-x_{n-2})} +
+\dfrac{f(x_{n-2})x_{n}x_{n-1}}{(x_{n-2}-x_{n})(x_{n-2}-x_{n-1})}
+\end{eqnarray*}
+\vspace{8cm}
+
+
+\item Exprimer les deux racines $x'_{n}$ et $x''_{n}$ du polynôme précédent
+en fonctions de $a_n$, $b_n$ et $c_n$ lorsqu'on itère dans les réels.
+\vspace{3cm}
+
+\item Comment est alors défini $x_{n+1}$?
+\vspace{3cm}
+
+\item On pourrait montrer que l'ordre de la convergence est 1,84. Comparer cette vitesse de convergence avec celle de Newton et celle de Lagrange.
+\vspace{3cm}
+
+
+\item Donner le code Python de la fonction
+ $\verb+[n,X] = iteration_muller(x+_{\verb+0+},\verb+x+_{\verb+1+},\verb+x+_{\verb+2+}\verb+,m,epsilon,f)+$ où
+\begin{itemize}
+\item $\verb+x+_{\verb+0+}$, $\verb+x+_{\verb+1+}$ et $\verb+x+_{\verb+2+}$ sont les trois premières valeurs des itérés, \verb+m+
+ est le nombre maximal
+ d'itérations, \texttt{epsilon} est la précision souhaitée
+ et \verb+f+ la fonction à itérer;
+\item \verb+n+ est le nombre d'itérations réalisées pour que
+\verb+f(+$\verb+x+_{\verb+n+}$\verb+)+=0 ou que
+$|\verb+x+_{\verb+n+}- \verb+x+_{\verb+n-1+}| \leq \verb+epsilon+$, \verb+n+ étant inférieur à \verb+m+ et \verb+X+ est
+ le vecteur contenant les
+ valeurs $\verb+x+_{\verb+0+},\ldots,\verb+x+_{\verb+n+}$.
+\end{itemize}
+\end{enumerate}
+
+
+\end{document}
\ No newline at end of file
