%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% m3Dmanmac.tex.
% Auteur : Anthony PHAN.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\ifx\typofrmtversion\undefined\else\endinput\fi
\def\typofrmtversion{October 19, 2004}%
%
\catcode`\@=11
{\obeyspaces\def\@space{\leavevmode\space}\global\let =\@space}%
\def\claimsep{\ ---\ \ignorespaces}%
\def\claimbreak{\ifvmode\medbreak\fi}%
\def\breakupto#1{\vskip\z@ plus#1\penalty-250\vskip\z@ plus-#1}%
%
\def\meta#1#2{\expandafter\def\csname meta@#1\endcsname{#2}}%
\meta{school}{Universit\'e de Poitiers\\
	D\'epartement de Math\'ematiques}%
\let\meta@degree=\undefined
\let\meta@course=\undefined%
\meta{year}{Ann\'ee \anneescolaire}%
\meta{head}{\vtop{\let\\=\cr\halign{\strut##\hfil\cr
		\meta@school\crcr}}\hfill
		\vtop{\let\\=\cr\halign{\strut\hfil##\cr
		\ifx\meta@degree\undefined\else\meta@degree\cr\fi
		\meta@year\crcr}}}%
\def\anneescolaire{%
	\ifnum\month<7 {\count0=\year\advance\count0 by -1 
	\the\count0--\the\year}%
	\else{\count0=\year\advance\count0 by 1 
	\the\year--\the\count0}\fi}%
%
%\long\def\gobblepar#1{\ifx#1\par\let\@next=\relax
%	\else\def\@next{{#1}}\fi\@next}%
\def\setcounter#1#2{\csname c@#1\endcsname=#2\relax}%
%
% THE NEXT MACRO MUST BE INCLUDED
% IN THE \BYE COMMAND. FOR INSTANCE:
%
% \catcode`@=11
% \outer\def\bye{\close@aux
% 	\par\vfill\supereject\end}%
% \catcode`@=12
%
\def\addto#1#2{{\def\@addto##1\end@addto{\gdef#1{##1}}%
	\expandafter\@addto#1#2\end@addto}}%
%
\def\addtoreset#1#2{%
	\expandafter\ifx\csname cl@#1\endcsname\relax
	\expandafter\edef\csname cl@#1\endcsname%
	{\csname c@#2\endcsname=0\relax}\else
	\expandafter\@addtoreset\csname cl@#1\endcsname
	{\csname c@#2\endcsname=0\relax}\fi}%
\def\@addtoreset#1#2{\edef#1{#1#2}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% OPTIONS SYSTEM
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\documentclass#1{%
	\ifx[#1\let\AfterOptions=\documentclass
	\def\@next{\ProcessOptions[}\else\let\AfterOptions=\relax
	\def\@next{\expandafter\ifx\csname option@#1\endcsname\relax
	\message{documentclass "#1" is undefined !}%
	\option@article\else\csname option@#1\endcsname\fi}\fi\@next}%
\def\UseOptions#1{\let\AfterOptions=\relax\ProcessOptions[#1]}%
\def\useoptions{\UseOptions}%
\def\ProcessOptions[#1]{\@ProcessOptions[#1,\undefined,\undefined]%
	\AfterOptions}%
\def\@ProcessOptions[#1,#2]{\ifx#1\undefined\else
	\expandafter\ifx\csname option@#1\endcsname\relax
	\message{Option "#1" is  undefined !}%
	\else\csname option@#1\endcsname\fi
	\@ProcessOptions[#2]\fi}%	
\def\DefineOption#1{\expandafter\def\csname option@#1\endcsname}%
\let\AfterOptions=\relax
%\newwrite\tmp@out
%\def\IfFileExists#1#2#3{\immediate\openin\tmp@out=#1
%	\ifeof\tmp@out\immediate\closein\tmp@out
%	#3\relax
%	\else\immediate\closein\tmp@out
%	#2\relax
%	\fi}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% HYPERTEXT
%
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%
{\catcode`\#=12 \catcode`\*=6
\gdef\@HyperLinkRef*1{\special{html:<a href="#*1">}}%
\gdef\@HyperLinkName*1{\special{html:<a name="*1">}}%
\gdef\@endHyperLink{\special{html:</a>}}}%
\def\HyperLinkRef#1{}%
\def\HyperLinkName#1{}%
\let\endHyperLink=\relax
\DefineOption{hypertext}{%
	\let\HyperLinkRef=\@HyperLinkRef
	\let\HyperLinkName=\@HyperLinkName
	\let\endHyperLink=\@endHyperLink}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% POINT SIZE
%
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%
\DefineOption{magstep0}{\voffset=0.12 true cm
	\hoffset=0.31 true cm
	\vsize=24.2 true cm
	\hsize=15.3 true cm
	}%
\DefineOption{magstephalf}{\mag=\magstephalf
	\voffset=0.12 true cm
	\hoffset=0.31 true cm
	\vsize=24.2 true cm
	\hsize=15.3 true cm
	}%
\DefineOption{magstep1}{\mag=\magstep1
	\voffset=0.12 true cm
	\hoffset=0.31 true cm
	\vsize=24.2 true cm
	\hsize=15.3 true cm
	}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% LANGUAGE DEPENDENT
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\DefineOption{french}{\language=1
	\def\authorsep{\bigbreak}% par }%
	\def\seename{voir}%
	\def\indexname{Index}%
	\def\bibname{Bibliographie}%
	\def\refname{R\'ef\'erences}%
	\def\chaptername{Chapitre}%
	\def\chapvarname{Chap.}%
	\def\contentsname{Table des mati\`eres}%
	\def\remarkname{Remarque}%
	\def\remarksname{Remarques}%
	\def\proofname{D\'emonstration}%
	\def\figurename{Fig{\rm.}}%
	\def\theoremname{Th\'eor\`eme}%
	\def\propositionname{Proposition}%
	\def\definitionname{D\'efinition}%
	\def\corollaryname{Corollaire}%
	\def\lemmaname{Lemme}%
	\def\examplename{Exemple}%
	\def\examplesname{Exemples}%
	\def\exercicename{Exercice}%
	\def\chapternumeral##1{\ifcase##1 \or premier\else
		\uppercase\expandafter{\romannumeral##1}\fi}%
	\def\today{\number\day\space\ifcase\month\or
		janvier\or f\'evrier\or mars\or avril\or mai\or juin\or
		juillet\or ao\^ut\or septembre\or octobre\or novembre\or
		d\'ecembre\fi\space\number\year}%
	\let\og=\og@french\let\fg=\fg@french
	\frenchspacing}%
\DefineOption{english}{\language=0
	\def\authorsep{\bigbreak}% by }%
	\def\indexname{Index}%
	\def\seename{see}%
	\def\bibname{Bibliography}%
	\def\refname{References}%
	\def\chaptername{Chapter}%
	\def\chapvarname{Chap.}%
	\def\contentsname{Table of Contents}%
	\def\remarkname{Remark}%
	\def\remarksname{Remarks}%
	\def\proofname{Proof}%
	\def\figurename{Fig{\rm.}}%
	\def\theoremname{Theorem}%
	\def\propositionname{Proposition}%
	\def\definitionname{Definition}%
	\def\corollaryname{Corollary}%
	\def\lemmaname{Lemma}%
	\def\examplename{Example}%
	\def\examplesname{Examples}%
	\def\exercicename{Exercice}%
	\def\chapternumeral##1{\uppercase\expandafter{\romannumeral##1}}%
	\let\og=\og@english \let\fg=\fg@english
	\def\today{\ifcase\month\or
		January\or February\or March\or April\or May\or June\or
		July\or August\or September\or October\or November\or
		December\fi\space\number\day, \number\year}%
	\frenchspacing}%
\def\date{\today}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% FONTS' SECTION (typofont.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\DeclareMathSymbol#1#2#3#4{%
	\count@=#2\multiply\count@ by 16
	\advance\count@ by \csname#3fam\endcsname
	\multiply\count@ by 256\advance\count@ by #4
	\ifcat\noexpand#1\relax
		\mathchardef#1=\count@
	\else
		\expandafter\mathcode
		\expandafter`\csname#1\endcsname=\count@
	\fi}%
%
\def\DeclareFont#1#2#3#4#5{\ifx*#2%
	\expandafter\def\csname#1\endcsname{\font\current@font=#3%
		\current@font}\else
	\expandafter\font\csname#1@t\endcsname=#3
	\expandafter\font\csname#1@s\endcsname=#4
	\expandafter\font\csname#1@ss\endcsname=#5
	\textfont#2=\csname#1@t\endcsname
	\scriptfont#2=\csname#1@s\endcsname
	\scriptscriptfont#2=\csname#1@ss\endcsname
	\expandafter\def\csname#1\endcsname{\font\current@font=#3
		\fam#2\current@font}%
	\fi}%
%
%%\def\tenbig#1{{\hbox{$\left#1\vbox to8.5pt{}\right.\n@space$}}}%
%%\def\ninebig#1{{\hbox{$\textfont0=\tenrm\textfont2=\tensy
%%\left#1\vbox to7.25pt{}\right.\n@space$}}}%
%%\def\eightbig#1{{\hbox{$\textfont0=\ninerm\textfont2=\ninesy
%%\left#1\vbox to6.5pt{}\right.\n@space$}}}%
%
\font\headroman=cmr10%  headings
%
\def\eightpoint{%
	\DeclareFont{roman}{0}{cmr8}{cmr6}{cmr5}%
	\DeclareFont{italic}{*}{cmti8}{*}{*}%
	\DeclareFont{smallcaps}{*}{cmcsc8}{*}{*}%
	\DeclareFont{boldface}{4}{cmbx8}{cmbx6}{cmbx5}%
	\DeclareFont{monospace}{*}{cmtt8}{*}{*}%
	\DeclareFont{mit}{1}{cmmi8}{cmmi6}{cmmi5}%
	\DeclareFont{cal}{2}{cmsy8}{cmsy6}{cmsy5}%
	\DeclareFont{mathex}{3}{cmex8}{cmex8}{cmex8}%
	\ifx\mbbfam\undefined\else
	\DeclareFont{mbb}{\mbbfam}{mbb8}{mbb6}{mbb5}\fi
	\ifx\mathafam\undefined\else
	\DeclareFont{matha}{\mathafam}{matham8}{matham6}{matham5}\fi
	\ifx\mathbfam\undefined\else
	\DeclareFont{mathb}{\mathbfam}{mathbm8}{mathbm6}{mathbm5}\fi
%	\ifx\mathxfam\undefined\else
%	\DeclareFont{mathx}{\mathxfam}{mathx8}{mathx8}{mathx8}\fi
	\DeclareFont{timesroman}{*}{ptmr at 8\p@}{*}{*}%
	\DeclareFont{timesitalic}{*}{ptmri at 8\p@}{*}{*}%
	\DeclareFont{timesbold}{*}{ptmb at 8\p@}{*}{*}%
	% espacements
	\smallskipamount=2\p@ plus 1\p@ minus 1\p@
	\medskipamount=4\p@ plus 2\p@ minus 1\p@
	\bigskipamount=9\p@ plus 3\p@ minus 3\p@
	\abovedisplayskip=5\p@ plus 2.5\p@ minus 1\p@
	\belowdisplayskip=5\p@ plus 2.5\p@ minus 1\p@
	\abovedisplayshortskip=0\p@ plus 2.5\p@
	\belowdisplayshortskip=3\p@ plus 2.5\p@
	\normalbaselineskip=9\p@
	\setbox\strutbox=\hbox{\vrule
		height7\p@ depth2\p@ width0\p@}%
	\normalbaselines\rm}%
%
\def\ninepoint{%
	\DeclareFont{roman}{0}{cmr9}{cmr6}{cmr5}%
	\DeclareFont{italic}{*}{cmti9}{*}{*}%
	\DeclareFont{smallcaps}{*}{cmcsc9}{*}{*}%
	\DeclareFont{boldface}{4}{cmbx9}{cmbx6}{cmbx5}%
	\DeclareFont{monospace}{*}{cmtt9}{*}{*}%
	\DeclareFont{mit}{1}{cmmi9}{cmmi6}{cmmi5}%
	\DeclareFont{cal}{2}{cmsy9}{cmsy6}{cmsy5}%
	\DeclareFont{mathex}{3}{cmex9}{cmex9}{cmex9}%
	\ifx\mbbfam\undefined\else
	\DeclareFont{mbb}{\mbbfam}{mbb9}{mbb6}{mbb5}\fi
	\ifx\mathafam\undefined\else
	\DeclareFont{matham}{\mathafam}{matham9}{matham6}{matham5}\fi
	\ifx\mathbfam\undefined\else
	\DeclareFont{mathb}{\mathbfam}{mathbm9}{mathbm6}{mathbm5}\fi
%	\ifx\mathxfam\undefined\else
%	\DeclareFont{mathx}{\mathxfam}{mathx9}{mathx9}{mathx9}\fi
	\DeclareFont{timesroman}{*}{ptmr at 9\p@}{*}{*}%
	\DeclareFont{timesitalic}{*}{ptmri at 9\p@}{*}{*}%
	\DeclareFont{timesbold}{*}{ptmb at 9\p@}{*}{*}%
	% espacements
	\smallskipamount=2.5\p@ plus 1\p@ minus 1\p@
	\medskipamount=5\p@ plus 2\p@ minus 1.5\p@
	\bigskipamount=10.5\p@ plus 3.5\p@ minus 3.5\p@
	\abovedisplayskip=5.5\p@ plus 2.75\p@ minus 1\p@
	\belowdisplayskip=5.5\p@ plus 2.75\p@ minus 1\p@
	\abovedisplayshortskip=0\p@ plus 2.75\p@
	\belowdisplayshortskip=3.5\p@ plus 2.75\p@
	\normalbaselineskip=11\p@
	\setbox\strutbox=\hbox{\vrule
		height8\p@ depth3\p@ width0\p@}%
	\normalbaselines\rm}%
%
\def\tenpoint{%
	\DeclareFont{roman}{0}{cmr10}{cmr7}{cmr5}%
	\DeclareFont{italic}{*}{cmti10}{*}{*}%
	\DeclareFont{smallcaps}{*}{cmcsc10}{*}{*}%
	\DeclareFont{boldface}{4}{cmbx10}{cmbx7}{cmbx5}%
	\DeclareFont{monospace}{*}{cmtt10}{*}{*}%
	\DeclareFont{mit}{1}{cmmi10}{cmmi7}{cmmi5}%
	\DeclareFont{cal}{2}{cmsy10}{cmsy7}{cmsy5}%
	\DeclareFont{mathex}{3}{cmex10}{cmex10}{cmex10}%
	\ifx\mbbfam\undefined\else
	\DeclareFont{mbb}{\mbbfam}{mbb10}{mbb7}{mbb5}\fi
	\ifx\mathafam\undefined\else
	\DeclareFont{mathma}{\mathafam}{matham10}{matham7}{matham5}\fi
	\ifx\mathbfam\undefined\else
	\DeclareFont{mathb}{\mathbfam}{mathbm10}{mathbm7}{mathbm5}\fi
%	\ifx\mathxfam\undefined\else
%	\DeclareFont{mathx}{\mathxfam}{mathx10}{mathx10}{mathx10}\fi
	\DeclareFont{timesroman}{*}{ptmr at 10\p@}{*}{*}%
	\DeclareFont{timesitalic}{*}{ptmri at 10\p@}{*}{*}%
	\DeclareFont{timesbold}{*}{ptmb at 10\p@}{*}{*}%
	% espacements
	\smallskipamount=3\p@ plus 1\p@ minus 1\p@
	\medskipamount=6\p@ plus 2\p@ minus 2\p@
	\bigskipamount=12\p@ plus 4\p@ minus 4\p@
	\abovedisplayskip=6\p@ plus 3\p@ minus 1\p@
	\belowdisplayskip=6\p@ plus 3\p@ minus 1\p@
	\abovedisplayshortskip=0\p@ plus 3\p@
	\belowdisplayshortskip=4\p@ plus 3\p@
	\normalbaselineskip=12\p@
	\setbox\strutbox=\hbox{\vrule
		height8.5\p@ depth3.5\p@ width0\p@}%
	\normalbaselines\rm}%
%
\def\twelvepoint{%
	\DeclareFont{roman}{0}{cmr12}{cmr8}{cmr6}%
	\DeclareFont{italic}{*}{cmti12}{*}{*}%
	\DeclareFont{smallcaps}{*}{cmcsc10 at 12\p@}{*}{*}%
	\DeclareFont{boldface}{4}{cmbx10 at 12\p@}{cmbx8}{cmbx6}%
	\DeclareFont{monospace}{*}{cmtt12}{*}{*}%
	\DeclareFont{mit}{1}{cmmi10 at 12\p@}{cmmi8}{cmmi6}%
	\DeclareFont{cal}{2}{cmsy10 at 12\p@}{cmsy8}{cmsy6}%
	\DeclareFont{mathex}{3}%
		{cmex10 at 12\p@}{cmex10 at 12\p@}{cmex10 at 12\p@}%
	\ifx\mbbfam\undefined\else
	\DeclareFont{mbb}{\mbbfam}{mbb12}{mbb8}{mbb6}\fi
	\ifx\mathafam\undefined\else
	\DeclareFont{matha}{\mathafam}{matham10 at 12\p@}{matham8}{matham6}\fi
	\ifx\mathafam\undefined\else
	\DeclareFont{mathb}{\mathbfam}{mathbm10 at 12\p@}{mathbm8}{mathbm6}\fi
%	\ifx\mathxfam\undefined\else
%	\DeclareFont{mathx}{\mathxfam}%
%		{mathx10 at 12\p@}{mathx10 at 12\p@}{mathx10 at 12\p@}\fi
	\DeclareFont{timesroman}{*}{ptmr at 12\p@}{*}{*}%
	\DeclareFont{timesitalic}{*}{ptmri at 12\p@}{*}{*}%
	\DeclareFont{timesbold}{*}{ptmb at 12\p@}{*}{*}%
	% espacements
	\smallskipamount=3\p@ plus 1\p@ minus 1\p@
	\medskipamount=6\p@ plus 2\p@ minus 2\p@
	\bigskipamount=12\p@ plus 4\p@ minus 4\p@
	\abovedisplayskip=6\p@ plus 3\p@ minus 1\p@
	\belowdisplayskip=6\p@ plus 3\p@ minus 1\p@
	\abovedisplayshortskip=0\p@ plus 3\p@
	\belowdisplayshortskip=4\p@ plus 3\p@
	\normalbaselineskip=14.4\p@
	\setbox\strutbox=\hbox{\vrule
		height9.7\p@ depth4.2\p@ width0\p@}%
	\normalbaselines\rm}%
%
\def\rm{\let\current@face=\roman\roman}%
\def\it{\let\current@face=\italic\italic}%
\def\sc{\let\current@face=\smallcaps\smallcaps}%
\def\bf{\let\current@face=\boldface\boldface}%
\def\tt{\let\current@face=\monospace\monospace}%
%
\def\small{\ninepoint}\let\footnotesize=\small
\def\tiny{\eightpoint}%
\def\large{\twelvepoint}%
\def\normalsize{\tenpoint}%
%
\def\ExtraTextFont{\ifx\current@face\roman
	\timesroman\else\ifx\current@face\italic
	\timesitalic\else\ifx\current@face\boldface
	\timesbold\else\timesroman\fi\fi\fi}%
%
\def\guillemotleft{{\ExtraTextFont\char"AB}}%
\def\guillemotright{{\ExtraTextFont\char"BB}}%
%
%\def\guillemotleft{\leavevmode\raise.225ex\hbox{%
%	$\scriptscriptstyle\langle\!\langle$}}%
%\def\guillemotright{\leavevmode\raise.225ex\hbox{%
%	$\scriptscriptstyle\rangle\!\rangle$}}%
%
\def\em{\ifx\current@face\roman\it\else\rm\fi}%
%
\newcount\c@quot
%
\def\og@french{\ifnum\c@quot>0``\else\guillemotleft~\ignorespaces\fi
	\ignorespaces\global\advance\c@quot by 1}%
%
\def\fg@french{\global\advance\c@quot by -1\unskip
	\ifnum\c@quot>0''\else~\guillemotright\fi}%
%
\def\og@english{\ifnum\c@quot>0 `\else``\fi
	\ignorespaces\global\advance\c@quot by 1}%
\def\fg@english{\global\advance\c@quot by -1\unskip
	\ifnum\c@quot>0 '\else''\fi}%
%
\def\textsuperscript#1{\/\raise.82ex%
	\hbox{$\current@face\scriptscriptstyle#1$}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% MAIN FORMATING COMMANDS (typotex.tex)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\let\stop=\end
\def\begin#1{\csname #1\endcsname}%
\def\end#1{\csname end#1\endcsname}%
%
% num\'eration
%
\def\alphanumeral#1{\ifcase#1 ?\or a\or b\or c\or d%
	\or e\or f\or g\or h\or i\or j\or k\or l\or m\or n%
	\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x%
	\or y\or z\else xx\fi}%
\def\Alphanumeral#1{\ifcase#1 ?\or A\or B\or C\or D%
	\or E\or F\or G\or H\or I\or J\or K\or L\or M\or N%
	\or O\or P\or Q\or R\or S\or T\or U\or V\or W\or X%
	\or Y\or Z\else XX\fi}%
%
% punctuation
%
\def\,{\ifmmode\mskip\thinmuskip\else\thinspace\fi}%
\def\dots{\ifmmode\ldots\else
	.\kern\fontdimen3\font
	.\kern\fontdimen3\font
	.\fi}%
\def\Bigbreak{\par\ifdim\lastskip<1.5\bigskipamount
	\removelastskip\penalty-300\vskip1.5\bigskipamount\fi}%
%
% equations
%
\newcount\c@equation
\def\everyequationnumber{}%
\def\eqnum{\global\advance\c@equation by 1
	\edef\lastref{\everyequationnumber\number\c@equation}%
	\eqno{(\lastref)}}%
%
% sectionnement
%
\newcount\c@chapter
\newcount\c@section
\newcount\c@subsection
\newcount\c@subsubsection
\let\sectionnumber=\number
\def\lastref{}%
\def\titlemark{{}{}}%
%
\newif\iftitle\titletrue
\DefineOption{openright}{\def\titlepage{\ifvoid0\else\par\vfill\eject\fi
	\global\titletrue\gdef\titlemark{{}{}}\ifodd\pageno\else
	\null\par\vfill\eject\global\titletrue\fi}}%
\DefineOption{openleft}{\def\titlepage{\ifvoid0\else\par\vfill\eject\fi
	\global\titletrue\gdef\titlemark{{}{}}\ifodd\pageno
	\null\par\vfill\eject\global\titletrue\fi}}%
\DefineOption{openany}{\def\titlepage{\ifvoid0\else\par\vfill\eject\fi
	\global\titletrue\gdef\titlemark{{}{}}}}%
% \message{La page \the\pageno\space a ete sautee !}%
% \advance\pageno by 1\fi}%
%
\newif\ifnormalchapter
\normalchaptertrue
%
\let\@author=\undefined
\def\author#1{\def\@author{#1}}%
\let\@title=\relax
\def\title#1{\def\@title{#1}\def\@titlerunning{#1}}%
\def\institute#1{}%
\def\titlerunning#1{\def\@titlerunning{#1}}%
\let\chapterrunning=\titlerunning
\def\sectionrunning#1{\ifx*#1\let\@next=\@sectionrunning
	\else\let\@next=\relax\mark{{#1}{\S\ \sectionnumber\c@section}}\fi
	\@next}%
\def\@sectionrunning#1{\mark{{#1}{}}}%
%
\def\maketitle{\titlepage
	\normalchapterfalse
	\let\sectionnumber=\number
		\let\lastref=\@titlerunning
		\let\currentchapter=\lastref
	\edef\titlemark{{\@titlerunning}{}}%
	\mark{{\@titlerunning}{}}%
	\def\@tmp{\sectionmark\title}%
	\expandafter\expandafter\expandafter\@tmp\expandafter{\@title}{}%
	\@@chapter\@title}%
\def\chapter#1{\titlepage
	\ifx*#1
		\let\@next=\@chapter
		\normalchapterfalse
		\let\sectionnumber=\Alphanumeral
	\else
		\def\@next{\@chapter{#1}}%
		\normalchaptertrue
		\global\advance\c@chapter by 1
		\let\sectionnumber=\number
	\fi\@next}%
%
\def\@chapter#1{%
	\def\@titlerunning{#1}%
	\ifnormalchapter
		\edef\lastref{\uppercase
			\expandafter{\romannumeral\c@chapter}}%
		\edef\currentchapter{\chapvarname~\lastref}%
		\edef\titlemark{{\@titlerunning}{\currentchapter}}%
		\mark{{\@titlerunning}{\currentchapter}}%
		\sectionmark\chapter{#1}{\the\c@chapter}%
	\else
		\edef\lastref{#1}%
		\let\currentchapter=\lastref
		\edef\titlemark{{\@titlerunning}{}}%
		\mark{{\@titlerunning}{}}%
		\sectionmark\chapter{#1}{}%
	\fi\@@chapter{#1}}%
\def\@@chapter#1{\titlepagetop
	\cl@chapter
	\center
	{\twelvepoint
	\ifnormalchapter
	{\sc\chaptername\unskip~\chapternumeral\c@chapter}%
	\vskip\bigskipamount\par
	\fi
	{\parskip=\smallskipamount
	\uppercase\expandafter{#1}}\par}%
	\ifx\@author\undefined
	\else\rm\authorsep\@author
	\global\let\@author=\undefined
	\fi
	\endcenter\vskip2\bigskipamount}%
\def\newsection#1#2{\expandafter\def\csname#1\endcsname
	{\@section{#1}#2}}%
\def\@section#1#2#3#4#5#6#7#8{#4\csname cl@#1\endcsname
	\ifx*#8%
	\def\@next{\@@sectionstar{#1}{#2}{#3}{#5}{#6}{#7}}%
	\else\def\@next{\@@section{#1}{#2}{#3}{#5}{#6}{#7}{#8}}\fi
	\@next}%
\def\@@section#1#2#3#4#5#6#7{%
	\global\advance\csname c@#2\endcsname by 1
	\edef\lastref{#3}\def\sectiontext{#7}%
	\expandafter\sectionmark\csname#1\endcsname{#7}\lastref
	{#4}#6}%
\def\@@sectionstar#1#2#3#4#5#6#7{%
	\def\sectiontext{#7}\def\\{\par\noindent\ignorespaces}%
	\expandafter\sectionmark\csname#1\endcsname{#7}{}%
	{#5}\let\\=\endgraf#6}%
%
\addtoreset{chapter}{section}%
\addtoreset{chapter}{equation}%
\addtoreset{section}{subsection}%
\addtoreset{subsection}{subsubsection}%
%
\DefineOption{defaultsectioning}{%
	\newsection{section}{{section}%
		{\sectionnumber\c@section}%
		{\Bigbreak\breakupto\baselineskip
		\noindent}%
		{\rm\lastref.\enspace\bf\sectiontext}%
		{\bf\sectiontext}%
		{\nobreak\bigskip}}%
	\newsection{subsection}{{subsection}%
		{\sectionnumber\c@section.\number\c@subsection}%
		{\bigbreak\noindent}%
		{\rm\lastref.\enspace\sc\sectiontext}%
		{\sc\sectiontext}%
		{\nobreak\medskip}}%
	\newsection{subsubsection}{{subsubsection}%
		{\number\c@subsubsection\petito}%
		{\medbreak}%
		{\noindent\rm\lastref\enspace\it\sectiontext\unskip.}%
		{\it\sectiontext\unskip.}%
		{\claimsep}}}%
\DefineOption{AMSsectioning}{%
	\newsection{section}{{section}%
		{\sectionnumber\c@section}%
		{\Bigbreak\breakupto\baselineskip}%
		{\center\rm\S\ \lastref.\enspace\sc\sectiontext\endcenter}%
		{\center\sc\sectiontext\endcenter}%
		{\nobreak\bigskip}}%
	\newsection{subsection}{{subsection}%
		{\sectionnumber\c@section.\number\c@subsection}%
		{\medbreak}%
		{\rm\lastref.\enspace\it\sectiontext\unskip.}%
		{\it\sectiontext\unskip.}%
		{\claimsep}}%
	\newsection{subsubsection}{{subsubsection}%
		{\number\c@subsubsection\petito}%
		{\medbreak}%
		{\rm\lastref\enspace\it\sectiontext\unskip.}%
		{\it\sectiontext\unskip.}%
		{\claimsep}}}%
\def\paragraph#1{\claimbreak{\it#1\unskip.}\claimsep}%
\let\endparagraph=\medbreak
\def\center{\par\bgroup\centering}%
\def\endcenter{\par\egroup}%
\def\centering{\leftskip=0\p@ plus 1fil
	\rightskip=0\p@ plus 1fil
	\parfillskip=0\p@
	\parindent=0\p@}
%
% lists
%
\newcount\c@item
\let\if@insidelist\iffalse
\newdimen\itemindent
\long\def\startlist#1#2{\c@item=0
	\expandafter\ifx\csname #1@item\endcsname\relax
	\roman@item\else\csname #1@item\endcsname\fi
	\ifx[#2\let\@next=\list@item@fix
	\else\def\@next{#2}\let\item@box=\relax\fi\@next}%
%
\let\item@box=\relax
\def\list@item@fix#1]{\setbox0=\hbox{#1}\edef\item@box##1{\noexpand\hbox
	to \the\wd0{\noexpand\hss##1}}}%
%
%\long\def\item@all@#1#2{\ifvmode\smallbreak\fi
%	\ifx#2[\let\@next\item@all@@
%	\else\def\@next{\advance\c@item by 1
%		\item@box{#1}\enspace\ignorespaces#2}\fi
%	\@next}%
%\long\def\item@all@@#1]{\item@box{#1}\enspace\ignorespaces}%
\long\def\item@all@#1{\ifvmode\smallbreak\fi
	\advance\c@item by 1
	\item@box{#1}\enspace\ignorespaces}%
%
\def\roman@item{\let\item=\item@roman}%
\def\item@roman{\item@all@{\rm(\romannumeral\c@item)}}%
%
\def\alpha@item{\let\item=\item@alpha}%
\def\item@alpha{\item@all@{\it\alphanumeral\c@item\/\rm)}}%
%
\def\arabic@item{\let\item=\item@arabic}%
\def\item@arabic{\item@all@{\rm\number\c@item.}}%
%
\def\bullet@item{\advance\leftskip by\itemindent
	\def\item{\ifvmode\smallbreak\fi
		\noindent\llap{$\bullet$\enspace}\ignorespaces}}%
%
\def\definitions@item{\advance\leftskip by\itemindent
	\def\item##1{\ifvmode\smallbreak\fi
		\noindent\leavevmode\hskip-\itemindent
		\item@box{##1}\enspace\ignorespaces}}%
\def\list#1{\bgroup\if@insidelist\par
	\advance\leftskip by\itemindent\fi
	\let\if@insidelist\iftrue
	\startlist{#1}}%
\def\endlist{\smallbreak\egroup}%
%
% verbatim
%
\newdimen\tabindent\tabindent=4em
\let\verbatimsep\quad
{\obeyspaces\gdef {\leavevmode\space}%
\catcode`\^^I=\active\gdef^^I{\hskip\tabindent\relax}}%
\def\rawverbatim{%
	\def\@numberedverbatimpar{\def\par{\ifvmode
		\endgraf\vskip\baselineskip\advance\count@ by 1
		\else\endgraf\fi}%
		\everypar={\advance\count@ by 1\leavevmode
		\llap{\the\count@\verbatimsep}}}%
	\def\@verbatimpar{\def\par{\ifvmode
		\endgraf\vskip\baselineskip\else\endgraf\fi}%
		\everypar={}}}%
\def\smartverbatim{%
	\def\@numberedverbatimpar{%
		\def\par{\ifvmode\endgraf
			\ifdim\lastskip<\medskipamount
			\removelastskip\penalty-100\medskip
			\@verbatimskiptrue\fi\else\endgraf\fi}%
		\everypar={\advance\count@ by 1\leavevmode
			\@ifverbatimskip
			\llap{\the\count@\verbatimsep}%
			\@verbatimskipfalse\fi}}%
	\def\@verbatimpar{%
		\def\par{\ifvmode\endgraf
			\ifdim\lastskip<\medskipamount
			\removelastskip\penalty-100\medskip\fi
			\else\endgraf\fi}%
		\everypar={}}}%
%
\def\@verbatimskiptrue{\let\@ifverbatimskip\iftrue}%
\def\@verbatimskipfalse{\let\@ifverbatimskip\iffalse}%
\smartverbatim
\def\verb{\bgroup\tt\uncatcodespecials\obeyspaces\@verb}%
\def\verbatim{\medbreak\bgroup
	\rightskip=0\p@ minus 1000\p@
	\tt\uncatcodespecials\obeyspaces
	\catcode`\^^I=\active\@verbatim}%
\def\@verbatim#1{\ifx[#1%
	\@verbatimskiptrue
	\@numberedverbatimpar\obeylines\let\@next=\@@verbatim
	\else\@verbatimpar\obeylines\parindent=0\p@
	\def\@next{\@@@verbatim#1}\fi\@next}%
\def\@@verbatim#1]{\setbox0=\hbox{#1\verbatimsep}\parindent=\wd0
	\count@=0\@@@verbatim}%
\def\verbatimfile#1{\ifx[#1\let\@next\@verbatimfile
	\else\def\@next{\@@verbatimfile{\input #1}}\fi\@next}%
\def\@verbatimfile#1]#2{\@@verbatimfile{[#1]\input #2}}%
{\catcode`\|=0\catcode`\\=12
|gdef|@verb#1\endverb{#1|egroup}%
|gdef|@@@verbatim#1\endverbatim{#1|egroup|medbreak}%
|gdef|@@verbatimfile#1{|verbatim #1|relax\endverbatim}}%
\def\uncatcodespecials{\def\do##1{\catcode`##1=12 }\dospecials}%
%
% Theorems and such
%
% o  \theorem<text>    : Theorem 1. --- <text>
% o  \theorem*[<text>] : Theorem <text>. ---
% o  \theorem*<text>   : Theorem. --- <text>
% o  \theorem[<text>]  : Theorem 1 <text>. ---
%
\def\everyclaimnumber{}% one can put some chapter number
%\def\ensurenumbering{\global\let\@numbering=!}%
\long\def\@claim#1#2#3#4#5{\claimbreak
	\bgroup\startlist{roman}\sc#1%
	\ifx*#4%
		\def\lastref{}%
		\ifx[#5%
			\def\@next##1]{\unskip\ ##1\unskip\rm.#3\claimsep}%
		\else
			\def\@next{\rm.#3\claimsep#5}%
		\fi
	\else\ifx[#4%
		\def\@next##1]{\unskip\ #5##1\unskip\rm.#3\claimsep}%
		\global\advance#2 by 1
		\edef\lastref{\everyclaimnumber\number#2}%
		\ \lastref
	\else\global\advance#2 by 1
		\edef\lastref{\everyclaimnumber\number#2}%
		\ \lastref\unskip\rm.#3\claimsep\relax
		\def\@next{#4#5}\fi\fi\@next}%
\def\end@claim{\par\egroup
	\ifdim\lastskip<\medskipamount
	\removelastskip\penalty55\medskip\fi}%
%
\newcount\c@theorem \newcount\c@proposition \newcount\c@lemma
\newcount\c@definition \newcount\c@corollary \newcount\c@figure
%
\def\claim#1{\@claim{#1}*\it*}%
\let\endclaim=\end@claim
%
\def\newtheorem#1#2{\expandafter\let\csname end#1\endcsname=\end@claim
	\expandafter\def\csname#1\endcsname{\@claim#2}}%
%
\newtheorem{theorem}{\theoremname\c@theorem\it}%
\newtheorem{proposition}{\propositionname\c@proposition\it}%
\newtheorem{definition}{\definitionname\c@definition\relax}%
\newtheorem{corollary}{\corollaryname\c@corollary\it}%
\newtheorem{lemma}{\lemmaname\c@lemma\it}%
\newtheorem{remark}{{\it\remarkname}*{\let\item=\item@alpha}*}%
\newtheorem{remarks}{{\it\remarksname}*{\let\item=\item@alpha}*}%
\newtheorem{example}{{\it\examplename}*{\let\item=\item@alpha}*}%
\newtheorem{examples}{{\it\examplesname}*{\let\item=\item@alpha}*}%
\newtheorem{exercice}{{\it\exercicename}*{}*}%
%
\long\def\proof#1{\claimbreak
	\ifx[#1%
	\def\@next##1]{{\it\proofname\ ##1\unskip.}\claimsep}%
	\else\def\@next{{\it\proofname.}\claimsep#1}\fi\@next}%
\def\endproof{\medbreak}%
%\null\hfill$\Box$\medbreak}%
\def\qed{\relax\ifmmode\Box\else
	{\unskip\nobreak\hfil\penalty50\hskip1em\null\nobreak\hfil$\Box$%
	\parfillskip=\z@\finalhyphendemerits=0\endgraf}\fi}%
%
\long\def\skiptext#1\endskiptext{\ifx\proofmode\undefined
	\else
	\par
	{\ninepoint\leavevmode\llap{$^*$}\ignorespaces#1\unskip$_*$}%
	\par
	\fi}%
%
\def\figure{\global\advance\c@figure by 1
	\edef\lastref{\number\c@figure}%
	{\sc\figurename\unskip\ \lastref.}}%
%
\def\foreword{\skip@=\lastskip\hbox to \hsize\bgroup\hfill
	$\ifx\lfilet\undefined
		\vcenter\bgroup\advance\hsize by -2\parindent
	\else
		\setbox0=\hbox{$\left\lfilet\right.$}\dimen@=\parindent
		\advance\dimen@ by -\wd0
		\left\lfilet\hskip\dimen@
		\vcenter\bgroup
			\advance\hsize by -4\parindent\fi
			\ninepoint}%
\def\endforeword{\egroup\ifx\lfilet\undefined\else
	\hskip\dimen@\right\rfilet\fi$\hfill\egroup\par\vskip\skip@}%
\let\abstract=\foreword
\let\endabstract=\endforeword
%
\newcount\c@footnote
%
\def\footnoterule{\kern-3\p@
  \hrule width 2truein \kern 2.6\p@}% the \hrule is .4pt high
%
\def\footnote{%
	\edef\@sf{\spacefactor\the\spacefactor}%
	\global\advance\c@footnote by 1
	$^{\the\c@footnote}$\@sf
	\insert\footins\bgroup\ninepoint
	\interlinepenalty100 \let\par=\endgraf
	\leftskip=\z@skip \rightskip=\z@skip
	\splittopskip=10\p@ plus 1\p@ minus 1\p@
	\floatingpenalty=20000
	\smallskip$\the\c@footnote.$\enspace
	\bgroup\strut\aftergroup\@foot\let\@next}%
\skip\footins=12\p@ plus 2\p@ minus 4\p@ % space added when footnote is present
%\count\footins=1000 % footnote magnification factor (1 to 1)
\dimen\footins=30pc % maximum footnotes per page
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% BIBLIOGRAPHY SECTION
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \bibliographym@rk and \bibname must be defined somewhere
% (see much below).
% \refsp@ce is the spacing command that appens between multiple
% references.
%
\let\refsp@ce=\
\def\citeopen{[}%
\def\citeclose{]}%
%
%\let\refsp@ce=\thinspace
%\def\citeopen{$^\bgroup}%
%\def\citeclose{\egroup}}%
%
% new variables
%
\newcount\c@bibitem
\newif\ifref@changes\ref@changesfalse
\newif\ifpageref@changes\ref@changesfalse
\newif\ifbib@changes\bib@changesfalse
\newif\ifref@undefined\ref@undefinedfalse
\newif\ifpageref@undefined\ref@undefinedfalse
\newif\ifbib@undefined\bib@undefinedfalse
%
% One can reference anything, just copy the former macro
% and use it so: \machin \label{truc}%
% In machin you would have defined \lastref by some number
% or any text.
%
% References macros
%
% The next macros are the core of \ref and \cite commands.
% Its first argument may be ref, pageref or bib.
%
% It is too tricky to be explained.
% (It is a bit recursive.)
% It allows using \cite or \ref or ...
% with arbitrary many arguments,
% for instance:
% \cite{knuth1,knuth2,ma pomme}%
%
% First argument is always ref, pageref or bib.
%
% Note that \meaning\@next is there to allow active things
% or control sequences within the referencing tag.
%
\def\re@dreferences#1#2{{%
	\re@dreferenceslist{#1}#2,\undefined\@@}}%
\def\re@dreferenceslist#1#2,#3\@@{\def\@next{#2}%
	\expandafter\ifx\csname#1@@\meaning\@next\endcsname\relax
	??\immediate\write16
	{Warning, #1-reference "\@next" on page \folio\space
	is undefined.}%
	\global\csname#1@undefinedtrue\endcsname
	\else\HyperLinkRef{#1@@#2}\csname#1@@\meaning\@next\endcsname
		\endHyperLink\fi
	\ifx#3\undefined\relax
	\else,\refsp@ce\re@dreferenceslist{#1}#3\@@\fi}%
%
% notice that the former ``,\refsp@ce'' will separate
% multiple arguments. But beware of spaces
% while defining a reference or calling for it!
%
% tricky thing: \newlabel has two arguments
% {labelname}{{\lastref}{\pageref}}%
% The second argument is read as two arguments
% by \newl@bel. This was necessary to get
% a jobname.aux containing the same syntax
% LaTeX would produce and use.
%
\def\newlabel#1#2{{\def\@next{#1}\newl@bel#2}}%
\def\newl@bel#1#2{%
	\expandafter\xdef\csname ref@@\meaning\@next\endcsname{#1}%
	\expandafter\xdef\csname pageref@@\meaning\@next\endcsname{#2}}%
% \immediate can cause nasty things with \pageref...
\def\label#1{{\init@aux
	\toks0={#1}\message{ref(\lastref) \the\toks0,}%
	\immediate\write\aux@out%
	{\noexpand\newlabel{\the\toks0}{{\lastref}{\folio}}}%
	\HyperLinkName{ref@@#1}\endHyperLink\def\@next{#1}%
	\expandafter\ifx\csname ref@@\meaning\@next\endcsname\lastref
	\else\message{former label is to be checked,}%
	\global\ref@changestrue\fi%
	\newlabel{#1}{{\lastref}{\folio}}}}%
\def\ref#1{\re@dreferences{ref}{#1}}%
\def\pageref#1{\re@dreferences{pageref}{#1}}%
%
% bibliography macros
%
\def\bibcite#1#2{{\def\@next{#1}%
	\expandafter\xdef\csname bib@@\meaning\@next\endcsname{#2}}}%
\def\cite#1{\citeopen\re@dreferences{bib}{#1}\citeclose}%
%
% The argument of \thebibliography
% is any sequence of numerals which will represent
% the maximum \item's length. If you have less than 9
% \bibitem's, this argument may be {any numeral}.
% if you have between 100 and 999 \bibitem's
% this argument may be {any three numerals},
% and so on.
%
\def\thebibliography#1{\bibliographym@rk
	\setbox0\hbox{\citeopen#1\citeclose\enspace}%
	\parindent=\wd0
	\global\c@bibitem=0
	\def\bibitem##1{\init@aux
		\global\advance\c@bibitem by 1
		\edef\lastref{\number\c@bibitem}%
		{\toks0={##1}%
		\message{bib[\lastref] \the\toks0,}%
		\immediate\write\aux@out
		{\noexpand\bibcite{\the\toks0}{\lastref}}}%
		\def\@next{##1}%
		\expandafter\ifx
		\csname bib@@\meaning\@next\endcsname\lastref
		\else\global\bib@changestrue\fi%
		\bibcite{##1}{\lastref}%
		\medbreak
		\item{\hfill\citeopen
			\HyperLinkName{bib@@##1}\lastref
			\endHyperLink\citeclose}%
		}%
	\def\idem{\vrule width 4em height 0.222\p@ depth 0pt\,}%
	}%
\def\endthebibliography{\par\egroup\par}%
%
\def\extra@end{}%
%
% initialization of jobname.aux
%
\newwrite\aux@out
\def\init@aux{%
	\immediate\openin\aux@out=\jobname.aux
	\ifeof\aux@out
		\immediate\write16{Creating file \jobname.aux}%
		\immediate\closein\aux@out
		\immediate\openout\aux@out=\jobname.aux
		\immediate\write\aux@out{\relax}%
		\immediate\closeout\aux@out
	\else
		\immediate\closein\aux@out
	\fi
	\gdef\@toc{}%
	\input\jobname.aux
	\immediate\openout\aux@out=\jobname.aux
	\global\let\init@aux=\relax
	\global\let\sectionmark=\@sectionmark
	\addto\extra@end{\closeout\aux@out
		\ifref@changes\immediate\write16%
		{Warning, changes in references.}\fi
		\ifpageref@changes\immediate\write16%
		{Warning, changes in page references.}\fi
		\ifbib@changes\immediate\write16%
		{Warning, changes in bibliography.}\fi
		\ifref@undefined\immediate\write16%
		{Warning, references undefined.}\fi
		\ifpageref@undefined\immediate\write16%
		{Warning, page references undefined.}\fi
		\ifbib@undefined\immediate\write16%
		{Warning, citations undefined.}\fi}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% LAYOUT COMMANDS
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Table des matieres
%
\def\content#1#2#3#4{\addto\@toc{#1{#2}{#3}{#4}}}%
%
\def\ignorecontentstitles{\def\contents@title##1##2##3{}}%
\def\usecontentstitles{\def\contents@title##1##2##3{\chapter{##1}{##2}{##3}}}%
\ignorecontentstitles
\def\tableofcontents{%
	\init@aux
	\tableofcontentsm@rk
	\def\\{\par\noindent\ignorespaces}% 
	\def\smartdot##1{{\def\@arg{##1}%
		\ifx\@arg\empty\relax\else##1\unskip.\enspace\fi}}%
	\def\leaderfill{\leaders\hbox to 1em{\hss.\hss}\hfill}%
%	\let\normalchapterfalse=\relax\let\normalchaptertrue=\relax
	\let\title=\contents@title
	\def\chapter##1##2##3{\bigbreak\noindent%\let\endgraf=\relax
		{\parindent=0\p@
		\bf\ifx##2\relax\else
			\chaptername\unskip\
			\smartdot{\chapternumeral{##2}}\fi##1}%
		\leaderfill##3\nobreak\medskip}%
	\def\section##1##2##3{\medbreak\noindent
		{\rm\smartdot{##2}\sc##1}\leaderfill
			##3\nobreak\smallskip}%
	\def\subsection##1##2##3{\smallbreak
		\hangindent\parindent
		{\rm\smartdot{##2}\it##1}\leaderfill##3\par}%
	\def\subsubsection##1##2##3{\par\indent\indent
		\hangindent3\parindent
		{\rm##2\enspace##1}\leaderfill##3\par}%
	\@toc
	\egroup\endtableofcontents}%
%
\def\\{\let\stoken= }\\
\long\def\unexpandwrite#1#2{\def\writ@{\write#1}%
	{\aftergroup\writ@\aftergroup{\s@nitize#2\ends@nity}}}%
\def\s@nitize{\futurelet\@next\s@nswitch}%
\def\s@nswitch{\ifx\@next\ends@nity
	\else\ifcat\noexpand\@next\stoken\aftergroup\space\let\@next\e@t
	\else\ifcat\noexpand\@next\bgroup\aftergroup{\let\@next\e@t
	\else\ifcat\noexpand\@next\egroup\aftergroup}\let\@next\e@t
	\else\let\@next\copyt@ken\fi\fi\fi\fi
	\@next}%
\def\e@t{\afterassignment\s@nitize\let\@next= }%
\long\def\copyt@ken#1{\ifcat\noexpand#1\relax\aftergroup\noexpand
	\else\ifcat\noexpand#1\noexpand~\aftergroup\noexpand\fi\fi
	\aftergroup#1\s@nitize}%
\def\ends@nity\ends@nity{}%
\long\def\semiexpandwrite#1#2#3{%
	\def\writ@{\write#1}\def\toexp@nd{#3}%
	% beware, a \gdef may replace the last \def
	{\aftergroup\writ@\aftergroup{\s@nitize#2\ends@nity
	\aftergroup\toexp@nd}}}%
%
\long\def\unexpandmark#1#2{\def\writ@{\mark}%
	{\aftergroup\writ@\aftergroup{\s@nitize{#2}{#1}\ends@nity}}}%
\def\semiexpandmark#1#2{\edef\@next{\noexpand\unexpandmark{#2}}%
	\@next{#1}}%
%
% The next macro must be used in sectionning commands
% as: \sectionmark\section{name of the section}\lastref.
% When \jobname.aux is initialized, it becomes \@sectionmark
% and then writes in \jobname.aux informations for the table
% of contents (and changes headings as it always should do).
%
\def\sectionmark#1#2#3{\ifnum\pageno>-1
 	\ifx#1\section\semiexpandmark{#2}{#3}\fi\fi}%
%
\def\@sectionmark#1#2#3{\ifnum\pageno>-1
 	\ifx#1\section\semiexpandmark{#2}{#3}\fi
	\edef\@next{\noexpand\@@sectionmark{#3}}% section number is expanded
	\@next{#1}{#2}\relax\fi}%
%
\def\@@sectionmark#1#2#3{%
	\semiexpandwrite\aux@out{\content#2{#3}{#1}}{{\folio}}}%
%
% sections and al. will be marked if and only if
% the current page number is strictly positive.
%
% headings
%
\def\righthead#1#2{\if#2\relax\relax\else\rlap{\headroman\S\ #2}\fi
	\hfil{\ninepoint\it#1}\hfil\llap{\headroman\folio}}%
\def\lefthead#1#2{\rlap{\headroman\folio}\hfil{\ninepoint\it#1}\hfil
		\llap{\headroman#2}}%
\def\mixedmarks{\def\@tmp##1##2##3##4{%
	% A REVOIR
	\ifx##2\relax\relax
		\ifx##4\relax\relax
			\def\firstbotmark{{##1/##3}{}}%
		\else
			\def\firstbotmark{{##1/##3}{##4}}%
		\fi
	\else
		\ifx##4\relax\relax
			\def\firstbotmark{{##1/##3}{##2}}%
		\else\def\firstbotmark{{##1/##3}{##2\,--\,##4}}%
		\fi
	\fi}%
	\expandafter\expandafter\expandafter
	\@tmp\expandafter\firstmark\botmark}%
%
% changes in output
%
% \documentclass
%
\DefineOption{book}{%
	\def\titlepagetop{\topglue 2\bigskipamount}%
	\def\tableofcontentsm@rk{\chapter*{\contentsname}\bgroup}%
	\let\endtableofcontents=\relax%\newpage
	\def\bibliographym@rk{\chapter*{\bibname}\bgroup}%
	\def\everyclaimnumber{}%
	\def\everyequationnumber{\ifnormalchapter\number\c@chapter.\else
		\sectionnumber\c@section.\fi}%
	\headline={\iftitle\hfil\global\titlefalse
		\ifodd\pageno\advance\pageno by 1\fi
	\else
		\ifodd\pageno
			\edef\tmp@a{\firstmark}%
			\edef\tmp@b{\botmark}%
			\ifx\tmp@a\tmp@b
				\expandafter\righthead\botmark
			\else\mixedmarks
				\expandafter\righthead\firstbotmark\fi
		\else\expandafter\lefthead\titlemark
		\fi
	\fi}%
	\footline={\hfil}}%
%
\DefineOption{article}{%
	\def\titlepagetop{\topglue 2\bigskipamount}%
	\def\tableofcontentsm@rk{\Bigbreak\centerline{\sc\contentsname}%
%		\sectionmark\section{\contentsname}{}%
		\bigbreak\bgroup\ninepoint}%
	\let\endtableofcontents=\Bigbreak
	\def\bibliographym@rk{\Bigbreak\centerline{\sc\refname}%
		\sectionmark\section{\refname}{}%
		\bigbreak\bgroup\ninepoint}%
	\def\everyclaimnumber{}%
	\def\everyequationnumber{}%
	\headline={\hfil}%
	\footline={\hfil{\headroman\folio}\hfil}}%
%
\DefineOption{preprint}{\option@article
	\headline={\iftitle\hfil\global\titlefalse
		\else\ifnum\pageno>1\ifodd\pageno
		\righthead{\today}{}\else
		\expandafter\lefthead\titlemark\fi
		\else\hfil\fi\fi}%
	\footline={\hfil}}%
%
\DefineOption{enseignement}{\option@article
	\mag=\magstep1
	\hoffset=-0.54truecm\hsize=17truecm
	\voffset=-0.54truecm\vsize=25.7truecm
	\headline={\iftitle\hfil\global\titlefalse
		\else\ifnum\pageno>1\ifodd\pageno
		\righthead{\ifx\meta@degree\undefined\titlemark
		\else\meta@degree\fi}{}\else
		\expandafter\lefthead\titlemark\fi
		\else\hfil\fi\fi}%
	\def\titlepagetop{\noindent\leavevmode
		\meta@head\vskip2\bigskipamount}%
	\footline={\hfil}}%
%
\def\onepageout{\ifodd\pageno \advance\hoffset by \offsetcorrection
	\else\advance\hoffset by -\offsetcorrection\fi
	\shipout\vbox{\makeheadline\pagebody\makefootline}%
	\advancepageno
	\ifnum\outputpenalty>-\@MM \else\dosupereject\fi}%
%
\output={\onepageout}%
%
\newdimen\offsetcorrection\offsetcorrection=\z@
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% typoindx.tex. Version : 28 octobre 2002.
% Auteur : Anthony PHAN.
%
% (inspir� de manmac.tex, book.cls)
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\index#1{\init@aux
	\semiexpandwrite\aux@out{\indexentry{#1}}{{\folio}}}%
\def\indexentry#1#2{}%
%
\def\theindex{\chapter*{\indexname}%
	%\vskip-20pt
	\nobreak\doublecolumns\raggedright
	\parskip\z@ plus .3\p@
	\parindent\z@
	\def\bold##1{{\bf##1}}\def\see##1##2{{\it\seename}\/~##1}%
	\def\item{\par\hangindent 40\p@}%
	\def\subitem{\item \vrule width\z@\nobreak
                \hskip 20\p@\hskip \z@skip}%
	\def\subsubitem{\item \vrule width\z@\nobreak
                \hskip 30\p@\hskip \z@skip}%
	\def\indexspace{\par\vskip10\p@ plus5\p@ minus3\p@\relax}}%
%	\let\indexspace\medbreak}%
\def\endtheindex{\enddoublecolumns\par\vfill\eject}%
\def\printindex{\input\jobname.ind
	\relax}%
%
\newbox\partialpage
\newdimen\pagewidth
\newdimen\pageheight
\pagewidth=\hsize\pageheight=\vsize
%
\def\doublecolumns{\pagewidth=\hsize\pageheight=\vsize\begingroup
%	\tolerance 9999 \emergencystretch 3em%
%	\hfuzz .5\p@\vfuzz\hfuzz
	\output={\global\setbox\partialpage=\vbox{\unvbox255}}\eject
	\output={\doublecolumnout}%
	\divide\hsize by 2\advance\hsize by -1em
	\multiply\vsize by 2}
%
\def\enddoublecolumns{\output={\balancecolumns}\eject
	\endgroup \pagegoal=\vsize}%
%
\def\doublecolumnout{\splittopskip=\topskip \splitmaxdepth=\maxdepth
	\dimen@=\pageheight\advance\dimen@ by-\ht\partialpage
%	\advance\dimen@ by -0.5ex
	\setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@
	{\setbox255=\vbox{\pagesofar}% compatible avec plain ou presque
	\hsize=\pagewidth\vsize=\pageheight\onepageout}%
	\unvbox255\penalty\outputpenalty}%
%
\def\pagesofar{\unvbox\partialpage\vskip\z@ plus\z@ minus3\p@
	\wd0=\hsize \wd2=\hsize \hbox to\pagewidth{\box0\hfil\box2}}%
%
\def\balancecolumns{\setbox0=\vbox{\unvbox255} \dimen@=\ht0
	\advance\dimen@ by\topskip \advance\dimen@ by-\baselineskip
	\divide\dimen@ by2 \splittopskip=\topskip
	{\vbadness=10000 \loop \global\setbox3=\copy0
		\global\setbox1=\vsplit3 to\dimen@
		\ifdim\ht3>\dimen@ \global\advance\dimen@ by1pt \repeat}%
	\setbox0=\vbox to\dimen@{\unvbox1}%
	\setbox2=\vbox to\dimen@{\unvbox3}%
	\pagesofar}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% BOXES
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newdimen\fboxrule\fboxrule0.8pt
\newdimen\fboxsep\fboxsep2pt
\long\def\fbox#1{\hbox{\setbox0\hbox{#1}\dimen@\dp0\advance\dimen@\fboxsep
	\advance\dimen@\fboxrule\lower\dimen@\hbox{\vrule width\fboxrule
	\vbox{\hrule height\fboxrule\kern\fboxsep
		\hbox{\kern\fboxsep\box0\kern\fboxsep}%
		\kern\fboxsep\hrule height\fboxrule}\vrule width\fboxrule}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% PERSONAL STUFF
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\hyphenation{pro-ba-bi-li-ste pro-ba-bi-li-stes
	sto-chas-tique sto-chas-tiques pro-ces-sus
	lip-schi-tzien lip-schi-tziens lip-schi-tzien-ne
	lip-schi-tzien-nes
	mar-tin-gale mar-tin-gales
	brow-nien brow-niens brow-nien-ne brow-nien-nes
	li-mi-te li-mi-tes
	mar-ko-vien mar-ko-viens mar-ko-vienne mar-ko-viennes
	ins-tant ins-tants
	ca-no-nique ca-no-niques}%
%
% frenchy stuff
%
\def\petito{\textsuperscript o}%
\def\numero{n\textsuperscript o~\ignorespaces}%
%
% extending math commands (LaTeX-like)
%
\ifx\mathbb\undefined
	\def\mathbb#1{{\bf#1}}\fi
\def\mathcal#1{{\cal#1}}%
\def\mathbf#1{{\bf#1}}%
\def\mathrm#1{{\rm#1}}%
%
\ifx\euro\undefined
\def\euro{\leavevmode{% Poor but complex Euro symbol
		\setbox0=\hbox{$\vcenter{\null}$}\dimen@=-\ht0
		\setbox0=\hbox{C}\advance\dimen@ by 0.5\ht0
		\rlap{\raise\dimen@\hbox{=}}%
		% taking slant into account
		\dimen@i=1pt\divide\dimen@ by \dimen@i
		\dimen@i=\fontdimen1\the\font
		\multiply\dimen@ by -\dimen@i
		\advance\dimen@ by 0.16em 
		\kern\dimen@ C}}%
\fi
\ifx\Box\undefined
\def\Box{{\setbox0\hbox{$+$}\dimen0=\ht0
	\advance\dimen0 by \dp0 \advance\dimen0 by -0.8\p@
	\vcenter{\hbox to \wd0{\hss\vbox{%
		\hrule height 0.4pt\hbox{%
			\vrule width 0.4\p@
			\vbox to \dimen0{\hbox to \dimen0{\hss}\vss}%
			\vrule width 0.4\p@}%
		\hrule height 0.4\p@}\hss}}}}%
\fi
\ifx\lbbbrack\undefined\def\lbbbrack{[\![}\def\rbbbrack{]\!]}\fi
%\def\indic@trice{\mathop{\mathbb 1\null}\mskip-\thinmuskip\mathord{\null}}%
\def\indic@trice{\mathbb 1}%
\def\indicatrice#1{\ifx*#1
	\def\@next{\indic@trice_}\else
	\let\@next=\relax\indic@trice_{\{#1\}}\fi\@next}%
\def\dd{\mathop{\rm d\null}\mskip-\thinmuskip\mathord{\null}}%
\def\ee{\mathop{\rm e\null}\mskip-\thinmuskip\mathord{\null}}%
\mathchardef\ii="7069% i imaginaire
\def\Proba{\mathop{\mathbb P\null}\nolimits}%
\def\Expect{\mathop{\mathbb E\null}\nolimits}%
\def\Var{\mathop{\rm Var}\nolimits}%
\def\Bor{\mathop{\rm\mathcal Bor}\nolimits}%
\def\pBor{\mathop{\rm p\mathcal Bor}\nolimits}%
\def\bBor{\mathop{\rm b\mathcal Bor}\nolimits}%
\def\Dom{\mathop{\rm Dom}\nolimits}%
\def\Id{\mathop{\rm Id}\nolimits}%
\def\sgn{\mathop{\rm sgn}\nolimits}%
\def\card{\mathop{\rm Card}\nolimits}\let\Card=\card
\ifx\complement\undefined\def\complement{c}\fi
\mathchardef\D="7064% d differentiel
\mathchardef\E="7065% e exponentiel
\mathchardef\I="7069% i imaginaire
\DefineOption{isolatin}{%
	\def\@tmp##1{\ifx##1\undefined\let\@next=\relax
		\else\catcode`##1=\active\fi\@next}%
	\let\@next=\@tmp
	\@tmp�����������������������
	�����������������ܾ����\undefined}%
{\option@isolatin
	\gdef�{``}\gdef�{''}%
	\gdef�{\'a}\gdef�{\`a}\gdef�{\^a}\gdef�{\"a}%
	\gdef�{\c c}%
	\gdef�{\'e}\gdef�{\`e}\gdef�{\^e}\gdef�{\"e}%
	\gdef�{\`\i}\gdef�{\^\i}\gdef�{\"\i}%
	\gdef�{\~n}%
	\gdef�{\'o}\gdef�{\`o}\gdef�{\^o}\gdef�{\"o}%
	\gdef�{\`u}\gdef�{\^u}\gdef�{\"u}%
	\gdef�{\"y}%
	\gdef�{\`A}\gdef�{\^A}\gdef�{\"A}%
	\gdef�{\c C}%
	\gdef�{\'E}\gdef�{\`E}\gdef�{\^E}\gdef�{\"E}%
	\gdef�{\`I}\gdef�{\^I}\gdef�{\"I}%
	\gdef�{\~N}%
	\gdef�{\`O}\gdef�{\^O}\gdef�{\"O}%
	\gdef�{\`U}\gdef�{\^U}\gdef�{\"U}%
	\gdef�{\"Y}\gdef�{\ifmmode^\circ\else$^\circ$\fi}%
	\gdef�{\smash{\hbox to 0.5em{\hss\vrule height\ht\strutbox
	depth\dp\strutbox width 0.4pt\hss}}}%
	\gdef�{\hbox{\dimen@=-0.5ex\advance\dimen@ by 0.4pt
	\vrule width0.5em height0.5ex depth\dimen@}}%
	\gdef�{\smash{\rlap{�}�}}}%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% THAT'S ALL, FOLKS!
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\outer\def\bye{\extra@end\par\vfill\supereject\stop}%
\let\document=\relax
\let\enddocument=\bye
\let\\=\endgraf
\def\newpage{\par\vfil\eject}%
%
% initialization of \jobname.aux
%
\immediate\openin\aux@out=\jobname.aux
\ifeof\aux@out\immediate\closein\aux@out
\else\immediate\closein\aux@out\init@aux
\fi
%
\catcode`\@=12
%
\UseOptions{english,article,defaultsectioning,openright}%
\tenpoint
\parindent=1.333em
\itemindent=\parindent
\endinput
