%                                                          >> ensmath.tex
%
% Formats pour L'Enseignement Mathematique
%
% **************************************************************************
% *  Version du 15 avril 1999       Copyright L'Enseignement Math‚matique  *
% **************************************************************************
%
%
\ifx\ENSEIGN\undefined\let\ENSEIGN=Y\else\endinput \fi
\input amstex
\UseAMSsymbols
%
% Reglages pour l'impression:
%
\topskip=9.0mm  \advance \topskip by -14pt 
% regle la distance entre le titre courant et le texte
% (9mm d'un bas de ligne a l'autre)
\hsize=11.3cm    %% largeur du texte          
\vsize=17.6cm    %% hauteur du texte sans le titre courant
%\hoffset=2.3truecm sans magnification
\hoffset=7.95truecm
\advance\hoffset by -5.65cm
%\voffset=3.0truecm sans magnification
\voffset=11.8truecm
\advance\voffset by -8.8cm
\parindent=.5cm     %% indentation
\def\footnoterule{\kern -3pt\hrule width 1.4cm\kern 4pt}
%
\parskip=.5pt plus.75pt minus.25pt   %% espacement supplementaire
                                     %% entre les alineas
\hfuzz=2pt          %% autorise un debordement horizontal limite
                    %% a l'exterieur du cadre normal
\mathsurround=.1em  %% espace supplementaire autour des
                    %% expressions mathematiques (redefini avec les fontes)
\pretolerance=400   %% qualite de la ligne sans coupures de mots
\tolerance=800      %% qualite de la ligne apres avoir coupe des mots
\binoppenalty=2400  %% decourage les coupures apres une operation binaire
\relpenalty=1200    %% decourage les coupures apres une relation mathematique
\clubpenalty=1000   %% decourage les lignes orphelines
\widowpenalty=1000  %% decourage les lignes veuves
\frenchspacing      %% meme espacement en bout de phrase qu'entre les mots
\newskip\EMskip     %% interligne extensible (redefini avec les fontes)
\EMskip=\normalbaselineskip
\def\EMquad{\hskip 1em plus .02em minus .2em}  %% cadratin compressible
%
% Espace au-dessus et en dessous des formules mathematiques centrees:
%
\abovedisplayskip=7pt plus 3pt minus 4pt
\belowdisplayskip=7pt plus 3pt minus 4pt
\abovedisplayshortskip=0pt plus 3pt
\belowdisplayshortskip=5pt plus 3pt minus 2pt
\predisplaypenalty=0
\def\EMpar{\belowdisplayskip=0pt\belowdisplayshortskip=0pt\par}
%
% Reglage des espacements avant et apres certains signes de ponctuation:
%
\catcode`\@=11
\catcode`\;=\active
\def;{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\kern.1em
\fi\string;\ifhmode\ \ignorespaces\fi}
\catcode`\:=\active
\def:{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\kern.15em
\fi\string:\ifhmode\ \ignorespaces\fi}
\def\deuxpoints{\string:}
\let\colon=\:
\catcode`\!=\active
\def!{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\kern.18em\fi\string!}
\def\exclam{\string!}
\catcode`\?=\active
\def?{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\kern.18em\fi\string?}
\def\interr{\string?}
\def\pnt{\,\ldotp}  %% point en mathematiques
%
% Notes de bas de page:
%
\def\EMraise#1{\leavevmode\raise.78ex\hbox{#1}}
\def\EMtvn{\vrule height 2.9mm depth 0pt width 0pt}
%
\def\EMmark#1{\def\next{#1}\ifx\next\empty\else
\smash{\ninepol\EMraise{\sixpol #1}\kern.12em)}\fi\EMtvn}
%
\long\def\EMtext#1{\pluspetit\ignorespaces #1\par}
%
\long\def\footnote#1#2{\relax
\ifhmode\ifdim\lastskip>\z@\unskip\fi\/\kern.15em%
\bgroup\parindent=.8cm\plainfootnote{\bgroup\EMmark{#1}\egroup}%
{{\EMtext{#2}}\vskip -\baselineskip}\egroup\fi}
%
\newcount\notenumber  \notenumber=1
\long\def\note#1{\footnote{\the\notenumber}{#1}%
{\global\advance\notenumber by 1 }}
%
\footline={\hfil\tenpol\folio\hfil}
%
% Definitions utiles:
%
\let\maj=\uppercase
\let\ced=\c
\let\emptyset=\varnothing
\def\ms{\mathsurround=0pt}
\def\nm{\nomathbreak}
%
\def\smallpenalty{\interlinepenalty=100 }
\def\medpenalty{\interlinepenalty=500 }
\def\bigpenalty{\interlinepenalty=\@M }
%
\def\smallitem#1{\par\vskip 2pt\noindent\hbox to .6cm{\ignorespaces 
#1\hfill}\hangindent=.6cm\hangafter=1 \ignorespaces }
\def\meditem#1{\par\vskip 2pt\noindent\hbox to .7cm{\hfill
\ignorespaces #1\enspace}%
\hangindent=.7cm\hangafter=1 \ignorespaces }
\def\bigitem#1{\par\vskip 2pt\noindent\hbox to .8cm{\hfill
\ignorespaces #1\enspace}%
\hangindent=.8cm\hangafter=1 \ignorespaces }
%
\def\cite#1{[#1]}
%
\let\INDENT=\indent
\def\CASE{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi\fi}
\newif\ifperiod  \periodtrue  \def\noperiod{\global\periodfalse}
%
\newcount\LANGUE
\def\anglais{\LANGUE=0 } \def\francais{\LANGUE=1 } 
    \def\allemand{\LANGUE=2 }  \def\italien{\LANGUE=3 }
\let\english=\anglais  \let\deutsch=\allemand  \let\italiano=\italien
\anglais
%
\def\BY{\ifcase\LANGUE by\or par\or von\or da\else\fi}
\def\AND{\ifcase\LANGUE and\or et\or und\or e\else\fi}
\def\ABSTRACT{\ifcase\LANGUE Abstract\or R\'esum\'e\or 
     Kurzfassung\or Riassunto\else\fi}
\def\DEFINITION{\ifcase\LANGUE Definition\or D\'efinition\or 
     Definition\or Definizione\else\fi}
\def\DEFINITIONS{\ifcase\LANGUE Definitions\or D\'efinitions\or 
     Definitionen\or Definizioni\else\fi}
\def\EXAMPLE{\ifcase\LANGUE Example\or Exemple\or 
     Beispiel\or Esempio\else\fi}
\def\EXAMPLES{\ifcase\LANGUE Examples\or Exemples\or 
     Beispiele\or Esempi\else\fi}
\def\PROOF{\ifcase\LANGUE Proof\or D\'emonstration\or 
     Beweis\or Dimostrazione\else\fi}
%
\def\THEOREM{\ifcase\LANGUE Theorem\or Th\'eor\`eme\or 
     Theorem\or Teorema\else\fi}
\def\LEMMA{\ifcase\LANGUE Lemma\or Lemme\or 
     Hilfssatz\or Lemma\else\fi}
\def\PROPOSITION{\ifcase\LANGUE Proposition\or Proposition\or 
     Satz\or Proposizione\else\fi}
\def\NOTATION{\ifcase\LANGUE Notation\or Notation\or 
     Notation\or Notazione\else\fi}
\def\COROLLARY{\ifcase\LANGUE Corollary\or Corollaire\or 
     Korollar\or Corollario\else\fi}
\def\CONJECTURE{\ifcase\LANGUE Conjecture\or Conjecture\or 
     Vermutung\or Congettura\else\fi}
\def\REMARK{\ifcase\LANGUE Remark\or Remarque\or 
     Bemerkung\or Osservazione\else\fi}
\def\REMARKS{\ifcase\LANGUE Remarks\or Remarques\or 
     Bemerkungen\or Osservazioni\else\fi}
%
% Boite centree (avec notes en bas de page):
% 
\newcount\FIRST
\newbox\EMboxone \newbox\EMboxtwo \newbox\EMboxthree
\newbox\EMboxfour \newbox\EMboxfive
%
\def\raggedcenter{\leftskip=0pt plus 1fill \rightskip=0pt plus 1fill
\parfillskip=0pt\pretolerance=\@M \hyphenpenalty=\@M }
%
\long\def\boitecentree#1{\bgroup\parindent=.8cm
%
\bgroup\global\FIRST=0
\long\def\footnote##1##2{\relax                               %% {begdef
\ifhmode\ifdim\lastskip>\z@\unskip\fi\/\kern.15em\fi%
\global\advance\FIRST by 1
\ifnum\FIRST=1 \global\setbox\EMboxone=\hbox{\EMmark{##1}}%
\gdef\EMtextone{\EMtext{##2}}\copy\EMboxone\fi%
\ifnum\FIRST=2 \global\setbox\EMboxtwo=\hbox{\EMmark{##1}}%
\gdef\EMtexttwo{\EMtext{##2}}\copy\EMboxtwo\fi%
\ifnum\FIRST=3 \global\setbox\EMboxthree=\hbox{\EMmark{##1}}%
\gdef\EMtextthree{\EMtext{##2}}\copy\EMboxthree\fi%
\ifnum\FIRST=4 \global\setbox\EMboxfour=\hbox{\EMmark{##1}}%
\gdef\EMtextfour{\EMtext{##2}}\copy\EMboxfour\fi%
\ifnum\FIRST=5 \global\setbox\EMboxfive=\hbox{\EMmark{##1}}%
\gdef\EMtextfive{\EMtext{##2}}\copy\EMboxfive\fi}%                %% }enddef
%
\vbox{\parindent=0pt\raggedcenter\let\par=\endgraf\let\\=\par
#1\par}\egroup%
%
\ifnum\FIRST>0 \vfootnote{\copy\EMboxone}{{\EMtextone}%
\vskip -\baselineskip}\fi
\ifnum\FIRST>1 \vfootnote{\copy\EMboxtwo}{{\EMtexttwo}%
\vskip -\baselineskip}\fi
\ifnum\FIRST>2 \vfootnote{\copy\EMboxthree}{{\EMtextthree}%
\vskip -\baselineskip}\fi
\ifnum\FIRST>3 \vfootnote{\copy\EMboxfour}{{\EMtextfour}%
\vskip -\baselineskip}\fi
\ifnum\FIRST>4 \vfootnote{\copy\EMboxfive}{{\EMtextfive}%
\vskip -\baselineskip}\fi
\egroup}
% 
% Titre:
%
\newtoks\titrecrt  \titrecrt={\hfil}
%
\long\def\titre#1{\null\vskip 2.5cm plus 1.2cm minus .5cm
\boitecentree{\let\desserre=\desserreplus\normal\baselineskip=5mm #1}%
\ifx\TITREBREF\undefined\titrecrt={%
\def\\{\CASE\space\ignorespaces }\let\par=\\%
#1}\fi\vskip 1cm}
%
\def\titrebref#1{\let\TITREBREF=Y\titrecrt={#1}}
%
% Auteur:
%
\newtoks\auteurcrt  \auteurcrt={\hfil}
%
\long\def\auteur#1{\vskip -.6cm
\def\sn##1{\bgroup\smc ##1\egroup}%
\boitecentree{\normal\BY\ {#1}}%
\ifx\AUTEURBREF\undefined\auteurcrt={%
\long\def\footnote##1##2{\relax}\def\sn##1{##1}%
\def\\{\CASE\space\ignorespaces }\let\par=\\%
\maj{#1}}\fi\vskip 1cm}
% 
\def\auteurbref#1{\let\AUTEURBREF=Y\auteurcrt={\maj{#1}}}
% 
% Resume: 
%
\long\def\EMabstract#1#2{\goodbreak\bgroup\petit\INDENT
\def\next{#1}\ifx\next\empty\else{\smc {\ignorespaces #1\CASE}.\EMquad}\fi
\rm\ignorespaces #2\EMpar\egroup\vskip .25cm}
% 
\long\def\abstract#1{\EMabstract{\ABSTRACT}{#1}}
\long\def\resume#1{\EMabstract{R\'esum\'e}{#1}}
\long\def\summary#1{\EMabstract{Summary}{#1}}
%
% Paragraphes:
%
\long\def\sec#1#2{\removelastskip\goodbreak\vskip 10mm plus 6mm minus 3mm
\normal\goodbreak\boitecentree{\let\it=\sl
\smc\def\next{#1}\ifx\next\empty\ignorespaces #2\else
\def\\##1/{\labchap{##1}.}%
\ignorespaces #1\EMquad\ignorespaces #2\fi}
\nobreak\vskip\baselineskip}
%
\long\def\subsec#1#2{\removelastskip\penalty-200 \vskip\EMskip
\penalty-200 \noindent{\let\it=\sl
\smc\def\next{#1}\noindent\ifx\next\empty\ignorespaces #2\else
\def\\##1/{\labsec{##1}}%
\setbox0=\hbox{\ignorespaces #1\EMquad}%
\dimen1=\wd0\box0\hangindent=\dimen1\hangafter=1 
\def\\{\CASE\break\ignorespaces}%
\ignorespaces #2\fi\par}\par\nobreak\vskip.35\baselineskip}
% 
\long\def\parag#1{\removelastskip\penalty-100 \vskip\EMskip\INDENT
\leavevmode\null\def\next{#1}\ifx\next\empty\else{%
\def\\##1/{\labsec{##1}}%
\smc {\ignorespaces #1\CASE}\ifperiod.\else
\global\periodtrue\fi\kern.8em}\fi\ignorespaces }
%
% Enonces:
%
% Cas general:
%
\long\def\proclaim#1#2{\ifvmode\removelastskip\goodbreak\vskip\EMskip
\INDENT\fi\def\next{#1}\ifx\next\empty\else{%
\def\\##1/{\labtheo{##1}}%
\smc {\ignorespaces
#1\CASE}\ifperiod.\else\global\periodtrue\fi\EMquad
}\fi{\interlinepenalty=\@M \clubpenalty=5000
\widowpenalty=\@M \predisplaypenalty=\@M
\it\ignorespaces #2\EMpar}\vskip\EMskip}
%
% Cas particuliers:
%
% Conjecture:
\long\def\conjecture#1#2{\proclaim{\CONJECTURE~\rm\ignorespaces #1}{#2}}
% Corollaire:
\long\def\corollary#1#2{\proclaim{\COROLLARY~\rm\ignorespaces #1}{#2}}
\let\corollaire=\corollary  
% Definition(s):
\long\def\definition#1#2{\proclaim{\DEFINITION~\rm\ignorespaces #1}{\rm 
\ignorespaces #2}}
\long\def\definitions#1{\proclaim{\DEFINITIONS}{\medpenalty\rm
\ignorespaces #1}}
% Exemple(s):
\long\def\example#1#2{\proclaim{\EXAMPLE~\rm\ignorespaces #1}{\smallpenalty
\rm\ignorespaces #2}}
\long\def\examples#1{\proclaim{\EXAMPLES}{\medpenalty\rm\ignorespaces #1}}
\let\exemple=\example  \let\exemples=\examples
% Lemme:
\long\def\lemma#1#2{\proclaim{\LEMMA~\rm\ignorespaces #1}{#2}}
\let\lemme=\lemma
% Notation:
\long\def\notation#1#2{\proclaim{\NOTATION~\rm\ignorespaces #1}{\rm
\ignorespaces #2}}
% Proposition:
\long\def\proposition#1#2{\proclaim{\PROPOSITION~\rm\ignorespaces #1}{#2}}
% Remarque(s):
\long\def\remark#1#2{\proclaim{\REMARK~\rm\ignorespaces 
#1}{\smallpenalty\rm\ignorespaces #2}}
\long\def\remarks#1{\proclaim{\REMARKS}{\medpenalty\rm\ignorespaces #1}}
\let\remarque=\remark   \let\remarques=\remarks
% Theoreme:
\long\def\theorem#1#2{\proclaim{\THEOREM~\rm\ignorespaces #1}{#2}}
\let\theoreme=\theorem
%
% Demonstration:
%
\long\def\EMdemo#1#2{\removelastskip\vskip.6\baselineskip
\INDENT\def\next{#1}\ifx\next\empty\else{\it {\ignorespaces 
#1\CASE}\ifperiod.\else\global\periodtrue\fi\EMquad}\fi{\clubpenalty=5000
\rm\ignorespaces #2\EMpar}\penalty-150\vskip\EMskip}
%
\long\def\preuve#1{\EMdemo{Preuve}{#1}}
\long\def\proof#1{\EMdemo{\PROOF}{#1}}
\long\def\sketch#1{\EMdemo{Sketch of proof}{#1}}
%
% Carre blanc:
%
\newbox\sqwh    %% boite redefinie avec les fontes dans la taille correcte
%
\def\makesqwh{\def\EMtraiv{\vrule height 1.5ex depth .03ex width .03em}%
\def\EMtraih{\hrule height .03em depth 0pt}%
\setbox\sqwh=\vbox{\EMtraih\hbox{\EMtraiv\kern 1.53ex\EMtraiv}\EMtraih}%
\dimen1=1.5ex  \advance\dimen1 by .03em  \ht\sqwh=\dimen1   
\dimen2=.03ex  \advance\dimen2 by .03em  \dp\sqwh=\dimen2 \relax}
%
\makesqwh
% ecarte de 6mm:
\def\qed{\ifmmode\hskip 6mm plus 1mm minus 3mm\copy\sqwh\else\CASE
\hglue 6mm plus 1mm minus 3mm{\copy\sqwh\finalhyphendemerits=0\EMpar}\fi}
% en bout de ligne:
\def\cqfd{\ifmmode\hskip 6mm plus 1mm minus 3mm\copy\sqwh\else\CASE
\nobreak\hfil\penalty50\hskip1em\null\nobreak\hfil
{\copy\sqwh\parfillskip=0pt\finalhyphendemerits=0\let\par=\endgraf\EMpar}\fi}
%
% Format dans le style "LaTeX":
%
\newcount\EMchap  \EMchap=0
\newcount\EMsec   \EMsec=0
\newcount\EMequa  \EMequa=0
\newcount\EMtheo  \EMtheo=0
\newread\infile   \newwrite\outfile
%
\def\latex{\openin\infile=\jobname.aux
\ifeof\infile\else\input\jobname.aux\fi
\immediate\openout\outfile=\jobname.aux}
%
\def\labchap#1{\global\EMsec=0  \global\EMequa=0 \global\EMtheo=0 
       \global\advance\EMchap by 1 {\the\EMchap}%
       \def\next{#1}{\ifx\next\empty\else\immediate\write\outfile%
       {\def\expandafter\noexpand\csname emEMeM#1\endcsname%
       {\the\EMchap}}\fi}}
\def\labsec#1{\global\advance\EMsec by 1 {\the\EMchap.\the\EMsec}%
       \def\next{#1}{\ifx\next\empty\else\immediate\write\outfile%
       {\def\expandafter\noexpand\csname emEMeM#1\endcsname%
       {\the\EMchap.\the\EMsec}}\fi}}
\def\labequa#1 {\global\advance\EMequa by 1 {\the\EMchap.\the\EMequa}%
       \def\next{#1}{\ifx\next\empty\else\immediate\write\outfile%
       {\def\expandafter\noexpand\csname emEMeM#1\endcsname%
       {\the\EMchap.\the\EMequa}}\fi}}
\def\labtheo#1{\global\advance\EMtheo by 1 {\the\EMchap.\the\EMtheo}%
       \def\next{#1}{\ifx\next\empty\else\immediate\write\outfile%
       {\def\expandafter\noexpand\csname emEMeM#1\endcsname%
       {\the\EMchap.\the\EMtheo}}\fi}}
\def\ref#1{{\csname emEMeM#1\endcsname}}
\let\?=\labequa
%
% References bibliographiques
%
\def\EMdash{\hbox to 7.5mm{\vrule height .63ex depth -.59ex 
width 5.4mm\hfill}}
\newdimen\hangbiblio  \newcount\EMrefno  \EMrefno=1
%
\def\EMbegref#1#2{\removelastskip\goodbreak
\par\bgroup\EMrefno=1 \parindent=#2\petit\let\sl=\it
\vskip 10mm plus 6mm minus 3mm\goodbreak
\centerline{\maj{#1}}\nobreak\vskip\baselineskip\nobreak
\hangbiblio=\parindent \advance\hangbiblio by 7.5mm}
%
\def\EMrefa{\par\ifnum\EMrefno<3 \nobreak\else\goodbreak\fi
\vskip 1pt\noindent}
%
\def\EMrefb{\advance\EMrefno by 1 
\hangindent=\hangbiblio\hangafter=1 \ignorespaces }
%
% References libres:
%
\def\begref#1{\EMbegref{#1}{0mm}\def\ref{\EMrefa\EMrefb}}
%
% References numerotees:
%
\def\begrefnum#1{\EMbegref{#1}{10.5mm}\def\ref{\EMrefa
\hbox to\parindent{\hphantom{\,[00]}\llap{[\the\EMrefno]}\hfill}\EMrefb}%
\def\refsp##1.##2 {\EMrefa
\hbox to\parindent{\hphantom{\,[00}\llap{[##1}##2]\hfill}\EMrefb}}
%
% References avec etiquette:
%
\def\begreflab#1#2{\EMbegref{#1}{#2}\def\ref##1 {\EMrefa
\hbox to\parindent{[##1]\hfill}\EMrefb}}
%
\def\endref{\par\egroup}
%
% Adresse:
%
\long\def\adresse#1{\removelastskip\nobreak\vskip\baselineskip\noindent
\vbox\bgroup\def\\{\vskip 1.0mm\parindent=.75cm\relax}\petit
\parindent=0pt\obeylines {#1}}
\def\email#1{{\it e-mail:\/} #1}
\def\endadresse{\egroup}
%
% Table des matieres:
%
\def\begmat{\bgroup\parindent=6mm\rightskip=12.95mm\let\par=\endgraf
\def\s##1{\nobreak\item{##1}}%
\def\ss##1{\nobreak\itemitem{##1}}}
%
\def\art{\par\noindent\hangindent=\parindent\hangafter=1 \ignorespaces }
%
\def\pp#1 {\CASE\leaders\hbox to 2mm{\hfil.}\hfill
\rlap{\hbox to 12.95mm{\hfill #1}}\par}
%
% Attention: \parindent doit etre un multiple entier
% de l'espace entre les points!
%
\newcount\EMaaa  \newcount\EMbbb
\def\ssec#1#2{\removelastskip\goodbreak
\setbox0=\hbox{\smc\ignorespaces #1\CASE~}%
\dimen1=\wd0  \EMaaa=\dimen1  \dimen2=2mm  \EMbbb=\dimen2
\divide\EMaaa by \EMbbb  \advance\EMaaa by 1
\multiply\dimen2 by \EMaaa  \wd0=\dimen2
\medskip\noindent\hangindent=\dimen2\hangafter=1
\box0\ignorespaces #2}
%
\def\endmat{\par\egroup}
%
% Espace reserve pour une figure:
%
\def\begfig#1{\midinsert\kern #1}   %% donner la hauteur precise du dessin
\def\endfig{\endinsert}
%
\newdimen\largeurfig  \largeurfig=\hsize
\newskip\deplacefig   \deplacefig=0mm      %% deplacement horizontal
\newskip\montefig     \montefig=0mm        %% pour remonter le dessin
\newskip\EMpush
%
% Insertion d'une figure Postscript:
%
\def\figinsert#1{%
\EMpush=\hsize  \advance\EMpush by -\largeurfig
\divide\EMpush by 2  \advance\EMpush by \deplacefig
\par\nobreak\vskip-\montefig
\noindent\null\hskip\EMpush
%\special{psfile=#1}%            %% PC - Sun
\special{postscriptfile #1}%     %% TeXtures
\vskip\montefig
}
%
% Legende:
%
\def\figure#1#2{\par\nobreak\vskip 5.0mm
\boitecentree{\pluspetit{\smc Figure}~\ignorespaces #1\CASE\par
\def\next{#2}\ifx\next\empty\else\nobreak\vskip 1.2mm 
\ignorespaces #2\CASE\fi}%
\vskip 1.2mm}
%
% Cas de deux figures cote a cote:
%
\def\doublefig#1#2#3{\bgroup\begfig{#1}\let\par=\endgraf
\line{\vtop{\hsize=.45\hsize #2}\hfill\vtop{\hsize=.45\hsize #3}}
\endfig\egroup}
%
\catcode`\@=\active
%
\newif\ifpremierepage  \premierepagetrue
\newtoks\headpremierepage  \headpremierepage={\hfil}
%
\newtoks\leftheadline  \newtoks\rightheadline  
%
\leftheadline={\tenpol\folio\hfil\bgroup\trespetit
\the\auteurcrt\egroup\hfil\hphantom{\folio}}
%
\rightheadline={\tenpol\hphantom{\folio}\hfil\bgroup\trespetit
\the\titrecrt\egroup\hfil\folio}
%
\headline={\ifpremierepage\rightheadline=\headpremierepage
\leftheadline=\headpremierepage\fi%
\ifodd\pageno\the\rightheadline%
\else\the\leftheadline\fi}
%
\footline={\ifpremierepage\global\premierepagefalse\fi%
\hfil\quad\hfil}
%
% Appel des fontes CM  (attention: elles sont necessaires meme si l'on
%          travaille seulement en Times ! (points de suspension,+,=, etc.)
%
% Definition des fontes:
%
\font \tenrm                  = cmr10           %fam0
\font \ninerm                 = cmr9
\font \eightrm                = cmr8
\font \sevenrm                = cmr7
\font \sixrm                  = cmr6
\font \fiverm                 = cmr5
%
\font \teni                   = cmmi10          %fam1
\font \ninei                  = cmmi9
\font \eighti                 = cmmi8
\font \seveni                 = cmmi7
\font \sixi                   = cmmi6
\font \fivei                  = cmmi5
%
\font \tensy                  = cmsy10          %fam2
\font \ninesy                 = cmsy9
\font \eightsy                = cmsy8
\font \sevensy                = cmsy7
\font \sixsy                  = cmsy6
\font \fivesy                 = cmsy5
%
\font \tenex                  = cmex10          %fam3
\font \nineex                 = cmex10 at 9pt
\font \eightex                = cmex10 at 8pt
\font \sevenex                = cmex10 at 7pt
\font \sixex                  = cmex10 at 6pt
\font \fiveex                 = cmex10 at 5pt
%
\font \tenit                  = cmti10          %fam4
\font \nineit                 = cmti9
\font \eightit                = cmti8
\font \sevenit                = cmti7
\font \sixit                  = cmti7 at 6pt
\font \fiveit                 = cmti7 at 5pt
%
\font \tensl                  = cmsl10          %fam5
\font \ninesl                 = cmsl9
\font \eightsl                = cmsl8
\font \sevensl                = cmsl8 at 7pt
\font \sixsl                  = cmsl8 at 6pt
\font \fivesl                 = cmsl8 at 5pt
%
\font \tenbf                  = cmbx10          %fam6
\font \ninebf                 = cmbx9
\font \eightbf                = cmbx8
\font \sevenbf                = cmbx7
\font \sixbf                  = cmbx6
\font \fivebf                 = cmbx5
%
\font \tentt                  = cmtt10          %fam7
\font \ninett                 = cmtt9
\font \eighttt                = cmtt8
%
% Fontes definies par AMS-TeX:
%
\font \tenmsa                 = msam10          %fam8
\font \ninemsa                = msam9
\font \eightmsa               = msam8
\font \sevenmsa               = msam7
\font \sixmsa                 = msam6
\font \fivemsa                = msam5
%
\font \tenmsb                 = msbm10          %fam9
\font \ninemsb                = msbm9
\font \eightmsb               = msbm8
\font \sevenmsb               = msbm7
\font \sixmsb                 = msbm6
\font \fivemsb                = msbm5
%
% Familles supplementaires:
%
\newfam\eufmfam                                 %fam10
\newfam\sansfam                                 %fam11
%
\font \teneufm                = eufm10
\font \nineeufm               = eufm9
\font \eighteufm              = eufm8
\font \seveneufm              = eufm7
\font \sixeufm                = eufm6
\font \fiveeufm               = eufm5
%
\font \tensans                = cmss10            
\font \ninesans               = cmss9
\font \eightsans              = cmss8
\font \sevensans              = cmss8 at 7pt
\font \sixsans                = cmss8 at 6pt
\font \fivesans               = cmss8 at 5pt
%
\font \tensmc                 = cmcsc10
\font \ninesmc                = cmcsc9
\font \eightsmc               = cmcsc8
\font \sevensmc               = cmcsc8 at 7pt
\font \sixsmc                 = cmcsc8 at 6pt
\font \fivesmc                = cmcsc8 at 5pt
%
\font \tenbfsl                = cmbxsl10           
\font \ninebfsl               = cmbxsl10 at 9pt
\font \eightbfsl              = cmbxsl10 at 8pt
\font \sevenbfsl              = cmbxsl10 at 7pt
\font \sixbfsl                = cmbxsl10 at 6pt
\font \fivebfsl               = cmbxsl10 at 5pt
%
\skewchar\ninei='177 \skewchar\eighti='177 \skewchar\sixi='177
\skewchar\ninesy='60 \skewchar\eightsy='60 \skewchar\sixsy='60
\hyphenchar\ninett=-1
%
\def\loadeuex{\Loadmathfont{euex}\let\EUEX=Y}
\def\loadeurm{\Loadmathfont{eurm}\let\EURM=Y}
\def\loadeusm{\Loadmathfont{eusm}\def\scr##1{{\eusm ##1}}\let\EUSM=Y}
\def\loadeufb{\Loadmathfont{eufb}\let\EUFB=Y}
\def\loadeurb{\Loadmathfont{eurb}\let\EURB=Y}
\def\loadeusb{\Loadmathfont{eusb}\let\EUSB=Y}
%
\catcode`\@=11
\def\Loadmathfont#1{% 
   \expandafter\font\csname ten#1\endcsname=#110
   \expandafter\font\csname nine#1\endcsname=#19
   \expandafter\font\csname eight#1\endcsname=#18
   \expandafter\font\csname seven#1\endcsname=#17
   \expandafter\font\csname six#1\endcsname=#16
   \expandafter\font\csname five#1\endcsname=#15
%   
   \edef\next{\noexpand\alloc@@8\fam\chardef\sixt@@n
     \expandafter\noexpand\csname#1fam\endcsname}%
   \next
%   
   \textfont\csname#1fam\endcsname \csname ten#1\endcsname
   \scriptfont\csname#1fam\endcsname \csname seven#1\endcsname
   \scriptscriptfont\csname#1fam\endcsname \csname five#1\endcsname
%   
   \expandafter\def\csname #1\expandafter\endcsname\expandafter{%
      \expandafter\fam\csname#1fam\endcsname
      \csname ten#1\endcsname}%
   \expandafter\gdef\csname load#1\endcsname{}%
}%
\catcode`\@=\active
%
\def\famsupp{%
\ifx\EUEX\undefined\else\textfont\euexfam=\teneuex 
\scriptfont\euexfam=\seveneuex \scriptscriptfont\euexfam=\fiveeuex 
\def\euex{\fam\euexfam\teneuex}\fi
%
\ifx\EURM\undefined\else\textfont\eurmfam=\teneurm 
\scriptfont\eurmfam=\seveneurm \scriptscriptfont\eurmfam=\fiveeurm 
\def\eurm{\fam\eurmfam\teneurm}\fi
%
\ifx\EUSM\undefined\else\textfont\eusmfam=\teneusm 
\scriptfont\eusmfam=\seveneusm \scriptscriptfont\eusmfam=\fiveeusm 
\def\eusm{\fam\eusmfam\teneusm}\fi
%
\ifx\EUFB\undefined\else\textfont\eufbfam=\teneufb 
\scriptfont\eufbfam=\seveneufb \scriptscriptfont\eufbfam=\fiveeufb 
\def\eufb{\fam\eufbfam\teneufb}\fi
%
\ifx\EURB\undefined\else\textfont\eurbfam=\teneurb 
\scriptfont\eurbfam=\seveneurb \scriptscriptfont\eurbfam=\fiveeurb 
\def\eurb{\fam\eurbfam\teneurb}\fi
%
\ifx\EUSB\undefined\else\textfont\eusbfam=\teneusb 
\scriptfont\eusbfam=\seveneusb \scriptscriptfont\eusbfam=\fiveeusb 
\def\eusb{\fam\eusbfam\teneusb}\fi}
%
\def\famsupppetit{%
\ifx\EUEX\undefined\else\textfont\euexfam=\nineeuex 
\scriptfont\euexfam=\sixeuex \scriptscriptfont\euexfam=\fiveeuex 
\def\euex{\fam\euexfam\nineeuex}\fi
%
\ifx\EURM\undefined\else\textfont\eurmfam=\nineeurm 
\scriptfont\eurmfam=\sixeurm \scriptscriptfont\eurmfam=\fiveeurm 
\def\eurm{\fam\eurmfam\nineeurm}\fi
%
\ifx\EUSM\undefined\else\textfont\eusmfam=\nineeusm 
\scriptfont\eusmfam=\sixeusm \scriptscriptfont\eusmfam=\fiveeusm 
\def\eusm{\fam\eusmfam\nineeusm}\fi
%
\ifx\EUFB\undefined\else\textfont\eufbfam=\nineeufb 
\scriptfont\eufbfam=\sixeufb \scriptscriptfont\eufbfam=\fiveeufb 
\def\eufb{\fam\eufbfam\nineeufb}\fi
%
\ifx\EURB\undefined\else\textfont\eurbfam=\nineeurb 
\scriptfont\eurbfam=\sixeurb \scriptscriptfont\eurbfam=\fiveeurb 
\def\eurb{\fam\eurbfam\nineeurb}\fi
%
\ifx\EUSB\undefined\else\textfont\eusbfam=\nineeusb 
\scriptfont\eusbfam=\sixeusb \scriptscriptfont\eusbfam=\fiveeusb 
\def\eusb{\fam\eusbfam\nineeusb}\fi}
%
\def\famsupppluspetit{%
\ifx\EUEX\undefined\else\textfont\euexfam=\eighteuex 
\scriptfont\euexfam=\sixeuex \scriptscriptfont\euexfam=\fiveeuex 
\def\euex{\fam\euexfam\eighteuex}\fi
%
\ifx\EURM\undefined\else\textfont\eurmfam=\eighteurm 
\scriptfont\eurmfam=\sixeurm \scriptscriptfont\eurmfam=\fiveeurm 
\def\eurm{\fam\eurmfam\eighteurm}\fi
%
\ifx\EUSM\undefined\else\textfont\eusmfam=\eighteusm 
\scriptfont\eusmfam=\sixeusm \scriptscriptfont\eusmfam=\fiveeusm 
\def\eusm{\fam\eusmfam\eighteusm}\fi
%
\ifx\EUFB\undefined\else\textfont\eufbfam=\eighteufb 
\scriptfont\eufbfam=\sixeufb \scriptscriptfont\eufbfam=\fiveeufb 
\def\eufb{\fam\eufbfam\eighteufb}\fi
%
\ifx\EURB\undefined\else\textfont\eurbfam=\eighteurb 
\scriptfont\eurbfam=\sixeurb \scriptscriptfont\eurbfam=\fiveeurb 
\def\eurb{\fam\eurbfam\eighteurb}\fi
%
\ifx\EUSB\undefined\else\textfont\eusbfam=\eighteusb 
\scriptfont\eusbfam=\sixeusb \scriptscriptfont\eusbfam=\fiveeusb 
\def\eusb{\fam\eusbfam\eighteusb}\fi}
%
% Tailles particulieres (sont redefinies en Times):
%
\font \bigb                   = cmbx12
\font \bigbi                  = cmbxsl10 at 12pt
\font \bigbb                  = cmbx12   at 14pt
\font \bigbbi                 = cmbxsl10 at 14pt
\font \bigbbb                 = cmbx12   at 17pt
\font \bigbbbi                = cmbxsl10 at 17pt
%
% Definitions supplementaires pour assurer la compatibilite:
%
\def\endash{--}
\def\emdash{---}
\def\desserre{\mathsurround=.1em \relax}
\def\desserremoins{\mathsurround=.085em \relax}
\def\desserreplus{\mathsurround=.115em \relax}
%
\font \tenpol                 = cmr10
\font \ninepol                = cmr9
\font \eightpol               = cmr8
\font \sevenpol               = cmr7
\font \sixpol                 = cmr6
%
\font \tenpolit               = cmti10
\font \ninepolit              = cmti9
\font \eightpolit             = cmti8
\font \sevenpolit             = cmti7
%
\font \tenpolsmc              = cmcsc10
\font \ninepolsmc             = cmcsc9
\font \eightpolsmc            = cmcsc8
%
% Declaration des tailles pour chaque style:
%
\catcode`\@=11
\def\normal{%
\textfont0=\tenrm \scriptfont0=\sevenrm \scriptscriptfont0=\fiverm
\def\rm{\fam0\tenrm}%
%
\textfont1=\teni \scriptfont1=\seveni \scriptscriptfont1=\fivei
\def\oldstyle{\fam1\teni}%
\textfont2=\tensy \scriptfont2=\sevensy \scriptscriptfont2=\fivesy
\textfont3=\tenex \scriptfont3=\sevenex \scriptscriptfont3=\fiveex
%
\textfont\itfam=\tenit \scriptfont\itfam=\sevenit
\scriptscriptfont\itfam=\fiveit \def\it{\fam\itfam\tenit}%
%
\textfont\slfam=\tensl \scriptfont\slfam=\sevensl
\scriptscriptfont\slfam=\fivesl \def\sl{\fam\slfam\tensl}%
%
\textfont\bffam=\tenbf \scriptfont\bffam=\sevenbf
\scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\tenbf}%
%
\textfont\ttfam=\tentt \def\tt{\fam\ttfam\tentt}%
%
\textfont\msafam=\tenmsa \scriptfont\msafam=\sevenmsa
\scriptscriptfont\msafam=\fivemsa
%
\textfont\msbfam=\tenmsb \scriptfont\msbfam=\sevenmsb
\scriptscriptfont\msbfam=\fivemsb
%
\textfont\eufmfam=\teneufm \scriptfont\eufmfam=\seveneufm
\scriptscriptfont\eufmfam=\fiveeufm \def\goth{\fam\eufmfam\teneufm}%
%
\textfont\sansfam=\tensans \scriptfont\sansfam=\sevensans
\scriptscriptfont\sansfam=\fivesans \def\sans{\fam\sansfam\tensans}%
%
\famsupp
\def\smc{\tensmc}%
\def\bfsl{\tenbfsl}%
%
\normalbaselineskip=4.5mm plus .02mm minus .01mm
\EMskip=\normalbaselineskip  \advance\EMskip by 0mm plus .5mm minus .1mm
\setbox\strutbox=\hbox{\vrule height3.2mm depth1.3mm width0pt}%
\def\big##1{{\hbox{$\left##1\vbox to8.5\p@{}\right.\n@space$}}}%
\def\Big##1{{\hbox{$\left##1\vbox to11.5\p@{}\right.\n@space$}}}%
\def\bigg##1{{\hbox{$\left##1\vbox to14.5\p@{}\right.\n@space$}}}%
\def\Bigg##1{{\hbox{$\left##1\vbox to17.5\p@{}\right.\n@space$}}}%
\normalbaselines\rm\makesqwh
}%
%
\def\petit{%
\textfont0=\ninerm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm
\def\rm{\fam0\ninerm}%
%
\textfont1=\ninei \scriptfont1=\sixi \scriptscriptfont1=\fivei
\def\oldstyle{\fam1\ninei}%
\textfont2=\ninesy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy
\textfont3=\nineex \scriptfont3=\sixex \scriptscriptfont3=\fiveex
%
\textfont\itfam=\nineit \scriptfont\itfam=\sixit
\scriptscriptfont\itfam=\fiveit \def\it{\fam\itfam\nineit}%
%
\textfont\slfam=\ninesl \scriptfont\slfam=\sixsl
\scriptscriptfont\slfam=\fivesl \def\sl{\fam\slfam\ninesl}%
%
\textfont\bffam=\ninebf \scriptfont\bffam=\sixbf
\scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\ninebf}%
%
\textfont\ttfam=\ninett \def\tt{\fam\ttfam\ninett}%
%
\textfont\msafam=\ninemsa \scriptfont\msafam=\sixmsa
\scriptscriptfont\msafam=\fivemsa
%
\textfont\msbfam=\ninemsb \scriptfont\msbfam=\sixmsb
\scriptscriptfont\msbfam=\fivemsb
%
\textfont\eufmfam=\nineeufm \scriptfont\eufmfam=\sixeufm
\scriptscriptfont\eufmfam=\fiveeufm \def\goth{\fam\eufmfam\nineeufm}%
%
\textfont\sansfam=\ninesans\scriptfont\sansfam=\sixsans
\scriptscriptfont\sansfam=\fivesans \def\sans{\fam\sansfam\ninesans}%
%
\famsupppetit
\def\smc{\ninesmc}%
\def\bfsl{\ninebfsl}%
%
\normalbaselineskip=3.5mm plus .015mm
\EMskip=\normalbaselineskip  \advance\EMskip by 0mm plus .4mm
\setbox\strutbox=\hbox{\vrule height2.5mm depth1.0mm width0pt}%
\def\big##1{{\hbox{$\left##1\vbox to7.65\p@{}\right.\n@space$}}}%
\def\Big##1{{\hbox{$\left##1\vbox to10.35\p@{}\right.\n@space$}}}%
\def\bigg##1{{\hbox{$\left##1\vbox to13.05\p@{}\right.\n@space$}}}%
\def\Bigg##1{{\hbox{$\left##1\vbox to15.75\p@{}\right.\n@space$}}}%
\normalbaselines\rm\makesqwh
}%
%
\def\pluspetit{%
\textfont0=\eightrm \scriptfont0=\sixrm \scriptscriptfont0=\fiverm
\def\rm{\fam0\eightrm}%
%
\textfont1=\eighti \scriptfont1=\sixi \scriptscriptfont1=\fivei
\def\oldstyle{\fam1\eighti}%
\textfont2=\eightsy \scriptfont2=\sixsy \scriptscriptfont2=\fivesy
\textfont3=\eightex \scriptfont3=\sixex \scriptscriptfont3=\fiveex
%
\textfont\itfam=\eightit \scriptfont\itfam=\sixit
\scriptscriptfont\itfam=\fiveit \def\it{\fam\itfam\eightit}%
%
\textfont\slfam=\eightsl \scriptfont\slfam=\sixsl
\scriptscriptfont\slfam=\fivesl \def\sl{\fam\slfam\eightsl}%
%
\textfont\bffam=\eightbf \scriptfont\bffam=\sixbf
\scriptscriptfont\bffam=\fivebf \def\bf{\fam\bffam\eightbf}%
%
\textfont\ttfam=\eighttt \def\tt{\fam\ttfam\eighttt}%
%
\textfont\msafam=\eightmsa \scriptfont\msafam=\sixmsa
\scriptscriptfont\msafam=\fivemsa
%
\textfont\msbfam=\eightmsb \scriptfont\msbfam=\sixmsb
\scriptscriptfont\msbfam=\fivemsb
%
\textfont\eufmfam=\eighteufm \scriptfont\eufmfam=\sixeufm
\scriptscriptfont\eufmfam=\fiveeufm \def\goth{\fam\eufmfam\eighteufm}%
%
\textfont\sansfam=\eightsans\scriptfont\sansfam=\sixsans
\scriptscriptfont\sansfam=\fivesans \def\sans{\fam\sansfam\eightsans}%
%
\famsupppluspetit
\def\smc{\eightsmc}%
\def\bfsl{\eightbfsl}%
%
\normalbaselineskip=3mm plus .01mm
\EMskip=\normalbaselineskip  \advance\EMskip by 0mm plus .3mm
\setbox\strutbox=\hbox{\vrule height2.1mm depth.9mm width0pt}%
\def\big##1{{\hbox{$\left##1\vbox to6.8\p@{}\right.\n@space$}}}%
\def\Big##1{{\hbox{$\left##1\vbox to9.2\p@{}\right.\n@space$}}}%
\def\bigg##1{{\hbox{$\left##1\vbox to11.6\p@{}\right.\n@space$}}}%
\def\Bigg##1{{\hbox{$\left##1\vbox to14.0\p@{}\right.\n@space$}}}%
\normalbaselines\rm\makesqwh
}%
%
\def\trespetit{\pluspetit}%
%
% caracteres gothiques en mathematiques
%
\def\frak{\relaxnext@\ifmmode\let\next\frak@\else
 \def\next{\Err@{Use \string\frak\space only in math mode}}\fi\next}
\def\frak@#1{{\frak@@{#1}}}
\def\frak@@#1{\noaccents@\fam\eufmfam#1}
\catcode`\@=\active
%
% Definitions complementaires:
%
\def\gbp{{\it \$\/}}              % livre sterling
\def\TIL{{$\sim$}}                % tilde sur la ligne
\def\pourmille{\%o}               % %o
\def\aoben{$^{\text{a}}$}         % ^a 
\def\ooben{$^{\text{o}}$}         % ^o
\let\EMsavS=\S
\def\S{\leavevmode\unkern\EMsavS\kern.1em\ignorespaces}
\def\og{\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\langle\!\langle$}}
\def\fg{\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\rangle\!\rangle$}}
\let\cedpol=\ced
%
\normal
%
% Macros utilitaires:
%
\input macutil
%
