%                            MATHs.sty

%\input a4
%
% fontes pour entete et notation R,C,...
%
\catcode`\@=11

\catcode`\;=\active
\def;{\relax\ifhmode\ifdim\lastskip>\z@
\unskip\fi\kern.2em\fi\string;}
\parindent=0mm

%\catcode`\:=\active
%\def:{\relax\ifhmode\ifdim\lastskip>\z@\unskip\fi
%\penalty\@M\ \fi\string:}

\catcode`\!=\active
\def!{\relax\ifhmode\ifdim\lastskip>\z@
\unskip\fi\kern.2em\fi\string!}

%\catcode`\?=\active
%\def?{\relax\ifhmode\ifdim\lastskip>\z@
%\unskip\fi\kern.2em\fi\string?}

\catcode`\é=\active
\def é{\relax\'e}

\catcode`\è=\active
\def è{\relax\`e}

\def\^#1{\if#1i{\accent"5E\i}\else{\accent"5E #1}\fi}
\def\"#1{\if#1i{\accent"7F\i}\else{\accent"7F #1}\fi}

\catcode`\à=\active
\def à{\relax\`a}

\catcode`\ê=\active
\def ê{\relax\^e}

\catcode`\ë=\active
\def ë{\relax\¨e}

\catcode`\â=\active
\def â{\relax\^a}

\catcode`\ä=\active
\def ä{\relax\¨a}

\catcode`\î=\active
\def î{\relax\^i}

\catcode`\ï=\active
\def ï{\relax\"i}

\catcode`\ô=\active
\def ô{\relax\^o}

\catcode`\ö=\active
\def ö{\relax\¨o}

\catcode`\ù=\active
\def ù{\relax\`u}

\catcode`\û=\active
\def û{\relax\^u}

\catcode`\ü=\active
\def ü{\relax\"u}

\catcode`\ç=\active
\def ç{\relax\c c\relax}

\frenchspacing

\catcode`\@=12

%
%pour les tableaux
%
\def\tvi{\vrule height 12 pt depth 5pt width 0pt}
\def\tv{\tvi\vrule}
\def\hfq{\hfill\quad}
\def\cc#1{\hfq#1\hfq}

%
%cadre
%
\def\cadre#1#2{\setbox1=\hbox{\kern#1{#2}\kern#1}%
\dimen1=\ht1 \advance\dimen1 by #1 \dimen2=\dp1 \advance\dimen2 by #1
\setbox1=\hbox{\vrule height\dimen1 depth\dimen2\box1\vrule}%
\setbox1=\vbox{\hrule\box1\hrule}%
\advance\dimen1 by .4pt \ht1=\dimen1
\advance\dimen2 by .4pt \dp1=\dimen2 \box1\relax}

\def\up#1{\raise 1ex\hbox{\sevenrm#1}}
\font\mab=cmsy10
\font\gss=cmss10 scaled\magstep2
\font\gsl=cmsl10 scaled\magstep1
%\font\mab=msbm10 scaled 960

\font\msl=cmsl10

%
%entete avec date ‚ventuelle
%

\def\grostitre#1{\centerline{\gss#1}\bigskip\bigskip}
\def\titrecentre#1{\centerline{\bf\underbar{#1}}\medskip}
\def\titre#1{\medskip\hskip -1truecm{\bf\underbar{#1}}\medskip}

\def\ds#1{\centerline{\gsl
SP\'E M2 \hskip 4truecm \cadre{3pt}{D.S. #1}}\bigskip\medskip}

\def\devoir#1{\centerline{\gsl
SP\'E M2 \hskip 3truecm \cadre{3pt}{DEVOIR #1}}\bigskip\medskip}

\def\corrig‚#1{\centerline{\gsl
SP\'E M2 \hskip 2truecm \cadre{4pt}{DEVOIR #1. \'El\'ements de Corrig\'e}}\bigskip\medskip}

\def\colles{\line{\gsl
SP\'E M2 \hskip 4truecm \cadre{3pt}{COLLES DE MATHS}\hfill}\bigskip}

\def\exo#1{\centerline{\gsl
SP\'E M2 \hskip 2truecm \cadre{3pt}{Fiche d'EXERCICES  #1}}\bigskip\medskip}

\def\td#1{\line{\gsl
SP\'E M2 \hskip 3truecm \cadre{3pt}{EXERCICES}\hfill\msl #1}\bigskip\medskip}

\def\htrait
{\medskip\hskip -1.1truecm\hbox{\vrule height 1pt width 19truecm}\smallskip}

\def\collenum#1#2
{\hskip -1truecm\cadre{3pt}{COLLE n\up{o}#1}
\hskip 4.5 truecm {\bf\underbar{Semaine #2}\bigskip}}

\def\dst{\displaystyle}

\def\og{\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\langle\!\langle$}}
\def\fg{\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\,
\rangle\!\rangle$\ }}
%
% Num‚rotation des parties, questions ...
%

\newcount\pno\pno=0
\newcount\qno\qno=0
\newcount\sqno\sqno=96

\def\partie
{\qno=0\sqno=96\advance\pno by1\penalty-200\vskip\bigskipamount
\noindent{\hskip -1.1truecm\bf\underbar {Partie\
\ifcase\pno\or I \or II \or III \or IV \or V \or VI \or VII \or VIII \or IX
\fi}}
\nobreak\bigskip}

\def\partietitre#1
{\qno=0\sqno=96\advance\pno by1\penalty-200\vskip\bigskipamount
\noindent{\hskip -1.1truecm\bf\underbar {Partie\
\ifcase\pno\or I \or II \or III \or IV \or V \or VI \or VII \or VIII \or IX
\fi\ :\ #1}}
\nobreak\bigskip}


\def\question
{\sqno=96\advance\qno by1\medbreak
\noindent{\hskip -9truemm\bf \the\qno \raisebox{5pt}{\rm \footnotesize  o})
\ \ }\nobreak}

\def\questiontitre#1
{\sqno=96\advance\qno by1\medbreak
\noindent{\hskip -9truemm\bf \the\qno \raisebox{5pt}{\rm \footnotesize  o})
\ \ #1}\par\nobreak}

\def\sousquestion
{\advance\sqno by1\smallbreak\hangafter=1\hangindent.5cm\noindent
{\bf\char\sqno{\rm )}}\hskip5pt}

\def\fin{\bigskip\centerline{- FIN -}}



%
% quelques ensembles
%
\def\barre{\vbox{\hrule height 2mm depth -0.3mm width .1mm}}
\def\Barre{\vbox{\offinterlineskip
  \hsize .7mm\hrule height .1mm width .6mm
  \hbox{\hskip .3mm\vrule height 2.2mm width .2mm}
  \hrule  height .1mm width .6mm}}

\def\R{{\mathbb R}}
\def\N{{\mathbb N }}
\def\C{{\mathbb C }}
\def\Q{{\mathbb Q }}
\def\Z{{\mathbb Z }}
\def\U{{\mathbb U }}
\def\K{{\mathbb K }}
%\def\NN{\Barre\hskip -.1mm{\rm N}}
%\def\RR{\Barre\hskip -.2mm{\rm R}}
%\def\KK{\Barre\hskip -.1mm{\rm K}}
%\def\CC{{\rm C}\hskip -1.5mm\barre\hskip 1.4mm}
%\def\QQ{{\rm Q}\hskip -1.7mm\barre\hskip 1.6mm}

%
% quelques macros
%
\def\dpar#1#2{\dst{\drond{#1} \over \drond{#2}}}
\def\suite#1#2{({#1}_0,{#1}_1,\ldots,{#1}_{#2})}
\def\uplet#1#2{({#1}_1,{#1}_2,\ldots,{#1}_{#2})}
\def\PS#1#2{<\!#1,#2\!>}
\def\Vec#1{\overrightarrow{#1}}
%
% quelques op‚rateurs
%

\def\tan{\mathop{\rm tan}\nolimits}
\def\arctan{\mathop{\rm Arctan}\nolimits}
\def\arccotan{\mathop{\rm Arccotan}\nolimits}
\def\arccos{\mathop{\rm Arccos}\nolimits}
\def\arcsin{\mathop{\rm Arcsin}\nolimits}
\def\argth{\mathop{\rm Argth}\nolimits}
\def\argcoth{\mathop{\rm Argcoth}\nolimits}
\def\argch{\mathop{\rm Argch}\nolimits}
\def\argsh{\mathop{\rm Argsh}\nolimits}
\def\ln{\mathop{\rm ln}\nolimits}
\def\sh{\mathop{\rm sh}\nolimits}
\def\ch{\mathop{\rm ch}\nolimits}
\def\th{\mathop{\rm th}\nolimits}
\def\im{\mathop{\rm Im}\nolimits}
\def\ker{\mathop{\rm Ker}\nolimits}
\def\rg{\mathop{\rm rg}\nolimits}
\def\E{\mathop{\rm E}\nolimits}      % partie entiŠre
\def\re{\mathop{\rm Re}\nolimits}
\def\inf{\mathop{\rm Inf}\limits}
\def\sup{\mathop{\rm Sup}\limits}
\def\min{\mathop{\rm Min}\limits}
\def\max{\mathop{\rm Max}\limits}
\def\Sum{\displaystyle\sum}
\def\Prod{\displaystyle\prod}
\def\Lim{\displaystyle\lim}
\def\Inf{\displaystyle\inf}
\def\Sup{\displaystyle\sup}
\def\Min{\displaystyle\min}
\def\Max{\displaystyle\max}
\def\Somdir{\displaystyle\bigoplus}
\def\Inter{\displaystyle\bigcap}
\def\Reun{\displaystyle\bigcup}
%\def\iint{\int\!\!\!\int}
%\def\iiint{\int\!\!\!\int\!\!\!\int}
\def\Int{\displaystyle\int}
\def\Oint{\displaystyle\oint}
\def\Iint{\displaystyle\iint}
\def\Iiint{\displaystyle\iiint}

%
% Nom des ensembles de matrices
%
\def\MnR{{\cal M}_n(\R)}
\def\MnC{{\cal M}_n(\C)}
\def\MnK{{\cal M}_n(\K)}
\def\mat#1#2#3{{\cal {#1}}_{#2}({\bf #3})}

%
% abr‚viations
%
\def\MQ{Montrer que }
\def\DQ{D\'emontrer que }
\def\PQ{Prouver que }
\def\VQ{V\'erifier que }
\def\JQ{Justifier que }
\def\EQ{Etablir que }
\def\ED{En d\'eduire }
\def\EDQ{En d\'eduire que }
\def\virg{,\quad}
\def\tq{\ \big/ \ }
\def\qqsoit{\forall\,}
\def\existe{\exists\,}
\def\ssi{si et seulement si }
\def\ens{ensemble }
\def\enss{ensembles}
\def\elt{\'el\'ement }
\def\elts{\'el\'ements }
\def\ev{espace vectoriel }
\def\evs{espaces vectoriels }
\def\ssev{sous-espace vectoriel }
\def\ssevs{sous-espaces vectoriels }
\def\pol{polyn\^ome }
\def\pols{polyn\^omes }
\def\polcar{polyn\^ome caract\'eristique }
\def\fct{fonction }
\def\fcts{fonctions }
\def\fcont{fonction continue }
\def\fconts{fonctions continues }
\def\appl{application }
\def\appls{applications }
\def\applin{application lin\'eaire }
\def\applins{applications lin\'eaires }
\def\dimf{dimension finie }
\def\cns{condition n\'ecessaire et suffisante }
\def\cn{condition n\'ecessaire }
\def\cs{condition suffisante }
\def\endo{endomorphisme }
\def\endos{endomorphismes }
\def\Equ{\Longleftrightarrow}
\def\equ{\Leftrightarrow}
\def\impl{\Rightarrow}
\def\Impl{\Longrightarrow}
\def\fld{\rightarrow}
\def\Fld{\longrightarrow}
\def\flg{\leftarrow}
\def\Flg{\longleftarrow}
\def\donne{\mapsto}
\def\Donne{\,\longmapsto\,}
\def\dst{\displaystyle}
\def\tst{\textstyle}
\def\sst{\scriptstyle}
\def\vide{\emptyset}
\def\inclus{\subset}
\def\moins{\setminus}
\def\drond{\partial}
\def\ep{\wp}
\def\infini{\infty}
\def\mult{\times}
%\def\Cap{\bigcap}
%\def\Cup{\bigcup}
\def\Oplus{\bigoplus}
\def\ve{\vee}
\def\Ve{\bigvee}
\def\vect{\wedge}
\def\Vect{\bigwedge}
\def\DL{d\'eveloppement limit\'e }
\def\DLA{d\'eveloppement limit\'e asymptotique }
\def\valp{valeur propre }
\def\valps{valeurs propres }
\def\vectp{vecteur propre }
\def\vectps{vecteurs propres }
\def\ssep{sous-espace propre }
\def\sseps{sous-espaces propres }
\def\equadiff{\'equation diff\'erentielle }
\def\ps{produit scalaire }

