+
+%___________________ PARAGRAPHES ___________________
+
+\let\sx\section
+\let\ssx\subsection
+\let\sssx\subsubsection
+
+%___________________ STYLES __________________________
+
+\let\ts=\textstyle
+\let\ds=\displaystyle
+\let\ssc=\scriptstyle
+\let\sss=\scriptscriptstyle
+
+\let\dl=\displaylines
+
+\let\sou=\underline
+\let\sur=\overline
+
+% \font\large=cmr12
+\font\grand=cmr12
+\font\giga=cmr17
+
+%______ EXPOSANTS, INDICES EN MODE NON MATH _________
+
+\def\up#1{\raisebox{1ex}{{\scriptsize #1}}}
+\def\down#1{\raisebox{-1ex}{{\scriptsize #1}}}
+\def\no{n\up{$\circ$}}
+
+%__________ ENCADREMENTS , TRAITS DIVERS _____________________
+
+\def\entoure#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\x#1{\entoure{4pt}{#1}}
+
+\def\cvirp{\raise 2pt\hbox{,}}
+
+\def\cqfd{\unskip\kern 6pt\penalty 500\raise
+-2pt\hbox{\vrule\vbox to 10pt{\hrule width
+4pt\vfill\hrule}\vrule}\par}
+
+\def\clv{\hbox{\vrule\vbox to 6 pt{\hrule width
+4pt\vfill\hrule}\vrule}}
+
+\def\trait {\hrule height 1pt depth 0pt}
+
+\def\traith {\hrule height 1pt depth 0pt}
+\def\traitb {\hrule height 0pt depth 1pt}
+
+\def\tvi#1#2{\vrule height #1 pt depth #2 pt width 0pt}
+\def\tvii#1{\vrule height #1 pt depth 5pt width 0pt}
+\def\tv{\tvii{12}\vrule}
+\def\ttv{\left\Vert\tvi{12}\right.}
+
+%____________ INF OU EGAL __________________________
+
+\let\infeg\leqslant
+\let\supeg\geqslant
+
+%____________ SUPERPOSITION DE SYMBOLES _____________
+
+\def\superpose#1_#2^#3{\mathrel{\mathop{\kern
+0pt#1}\limits_{#2}^{#3}}}
+
+\def\fr #1#2{\ds {\raise -2pt\hbox{$#1$}\over
+ \raise 2pt\hbox{$#2$}}}
+
+%______ Lignes de titre _________________
+
+\def\ligne#1#2{#1 \hfill #2}
+\def\titre#1{\centerline{\entoure{5pt}{\bf #1}}}
+
+%__________ N, Z, Q, R, C __________
+
+\def\nmat{\hbox{\it I\hskip -2pt N}}
+\def\zmat{\hbox{\it Z\hskip -4pt Z}}
+\def\qmat{\hbox{\it l\hskip -5.5pt Q}}
+\def\rmat{\hbox{\it I\hskip -2pt R}}
+\def\cmat{\hbox{\it l\hskip -5.5pt C\/}}
+
+\def\N{{\mathbb N}}
+\def\Net{{\mathbb N}^*}
+\def\Z{{\mathbb Z}}
+\def\Q{{\mathbb Q}}
+\def\R{{\mathbb R}}
+\def\Ret{{\mathbb R}^*}
+\def\Rpl{{\mathbb R}_+}
+\def\Rplet{{\mathbb R}_+^*}
+\def\Rmn{{\mathbb R}_-}
+\def\Rmnet{{\mathbb R}_-^*}
+\def\C{{\mathbb C}}
+\def\K{{\mathbb K}}
+\def\D{{\mathbb D}}
+
+%__________ FLECHES ET LOGIQUE __________
+
+\let\fc=\longmapsto % pour "x donne f(x)"
+\let\vers=\rightarrow % pour "tend vers"
+\let\flg=\leftarrow % fleche simple courte vers la gauche
+\let\rec=\longleftarrow % symbole d'affectation
+\let\Rec=\Longleftarrow % fleche double longue vers la gauche
+\let\Imp=\Rightarrow % implique (double barre)
+\let\Ssi=\Leftrightarrow % est equivalent a (double barre)
+
+\let\ou=\vee % disjonction logique
+\let\et=\wedge % conjonction logique
+\let\non=\neg % negation logique
+\let\imp=\Rightarrow % implication logique
+\let\ssi=\Longleftrightarrow % equivalence logique
+\let\eqv=\Longleftrightarrow
+
+\let\qqs=\forall % quantificateur universel
+\let\exi=\exists % quantificateur existentiel
+
+\let\theor=\vdash % déduction
+\let\tauto=\models % conséquence logique
+\def\vrai{\textit{vrai}} % vrai
+\def\faux{\textit{faux}} % faux
+
+
+
+%___________ COMBINATOIRE ET ENSEMBLES ______________
+
+\def\cnp{\mathop{\raise -1pt\hbox{\large C}}\nolimits}
+\def\card{\mathop{\rm Card}\nolimits}
+
+\let\vide=\emptyset
+\def\void{\not{\kern -1.55pt\rm o}}
+
+\let\union=\cup
+\let\inter=\cap
+\let\moins=\setminus
+\let\sse=\subset
+
+\def\enspart#1{{\cal P}(#1)}
+
+\def\rest#1#2{{#1}_{\left|\mathstrut #2\right.}}
+\def\idl#1{{\goth #1}}
+
+%__________ TOPO ____________________________
+
+\def\min{\mathop{\rm Min}\limits}
+\def\max{\mathop{\rm Max}\limits}
+\def\sup{\mathop{\rm Sup}\limits}
+\def\inf{\mathop{\rm Inf}\limits}
+
+\let\nor=\Vert % norme
+\def\nme#1{\nor #1\nor}
+\def\trnme#1{|||#1|||} % "triple" norme
+\def\nmex#1{\left|\!\left|#1\right|\!\right|}
+ % norme extensible
+
+\let\Inf=\infty % infini
+\def\plinf{{+\infty}} % plus l'infini
+\def\moinf{{-\infty}} % moins l'infini
+
+\def\Rpl{\R_{\sss +}} % double R plus
+\def\Rmo{\R_{\sss -}} % double R moins
+
+\def\intr#1{\,\buildrel{\kern 2pt\circ}\over{#1}} % int�rieur
+
+%_____________________ FONCTIONS _______________________
+
+\def\tg{\mathop{\rm tg}\nolimits}
+\def\arcsin{\mathop{\rm Arcsin}\nolimits}
+\def\arccos{\mathop{\rm Arccos}\nolimits}
+\def\arctg{\mathop{\rm Arctg}\nolimits}
+\def\ch{\mathop{\rm ch}\nolimits}
+\def\sh{\mathop{\rm sh}\nolimits}
+\def\th{\mathop{\rm th}\nolimits}
+\def\argsh{\mathop{\rm Argsh}\nolimits}
+\def\argch{\mathop{\rm Argch}\nolimits}
+\def\argth{\mathop{\rm Argth}\nolimits}
+\def\log{\mathop{\rm ln}\nolimits}
+\def\Log{\mathop{\rm Log}\nolimits}
+\def\E{\mathop{\rm E}\nolimits} % partie entiere
+\def\e{\mathop{\rm e}\nolimits} % exponentielle
+
+%______________ ANALYSE _______________
+
+\def\cl{{\cal C}} % classe d'une fonction
+
+\def\intint{\int\!\!\!\!\int} % int. double
+\def\intintint{\int\!\!\!\!\int\!\!\!\!\int} % int. triple
+
+\let\dep=\partial % d rond
+\def\ddr{{\rm d\,}} % d droit
+\def\dpar#1#2{\fr{\partial#1}{\partial#2}} % d rond #1 sur d rond #2
+\def\dtot#1#2{\fr{{\rm d}#1}{{\rm d}#2}} % d droit #1 sur d droit #2
+
+\def\ste#1#2#3{\left(#1_#2\right)_{#2\in #3}}
+\def\sten#1#2{\ste{#1}{#2}\N}
+\def\stenet#1#2{\ste{#1}{#2}{\N^*}}
+\def\stenn#1{\sten{#1}n}
+\def\stennet#1{\stenet{#1}n}
+
+%______________ ALGEBRE Complexe _______________
+\renewcommand{\Re}{\mathop{\mathrm{Re}}}
+\renewcommand{\Im}{\mathop{\mathrm{Im}}}
+
+
+%_______________ ALGEBRE LINEAIRE ______________________
+
+\def\com{\mathop{\rm Com}\nolimits}
+\def\det{\mathop{\rm D\acute e t}\nolimits}
+\def\dim{\mathop{\rm dim}\nolimits}
+\def\ker{\mathop{\rm Ker}\nolimits}
+\def\id{\mathop{\rm id}\nolimits}
+\def\tr{\mathop{\rm Tr}\limits}
+\def\vect{\mathop{\rm Vect}\nolimits}
+\def\rang{\mathop{\rm rang}\nolimits}
+\def\diag{\mathop{\rm diag}\nolimits}
+\def\sp{\mathop{\rm Sp}\nolimits}
+\def\GL#1#2{{\cal GL}_{#1}(#2)}
+\def\gl#1{{\cal GL}(#1)}
+\def\mat#1#2{{\rm Mat}\,\left(#1\vir#2\right)}
+\def\matb#1#2#3{{\rm Mat}\left(#1\vir#2\vir#3\right)}
+\def\matbb#1{{\rm Mat}_{\cal B}\left(#1\right)}
+\def\matcar#1#2{{\cal M}_{#1}\left(#2\right)}
+\def\mn#1{\matcar n{#1}}
+\def\matrect#1#2#3{{\cal M}_{#1,#2}\left(#3\right)}
+\def\apl#1#2{{\cal L}\left(#1,#2\right)}
+\def\aplr#1#2{{\cal L}\left(\R^#1,\R^#2\right)}
+\def\endo#1{{\cal L}\left(#1\right)}
+\def\endor#1{{\cal L}\left(\R^#1\right)}
+\def\nul#1{0_{#1}}
+\def\endonul#1{O_{{\cal L}(#1)}}
+\def\evnul#1{\left\{\nul#1\right\}}
+\def\fami#1#2{({#2}_1\,,\,{#2}_2\,,\,\ldots\,,\,{#2}_{#1})}
+\def\famn#1{\fami{n}{#1}}
+
+%_____ POUR MATRICES, points parall�les � diag 2 _____
+
+\def\adots{\mathinner{\mkern2mu\raise1pt\hbox{.}
+\mkern3mu\raise4pt\hbox{.}\mkern1mu\raise7pt\hbox{.}}}
+
+%__________ GEOMETRIE _______________________________
+
+\def\grad{\mathop{\rm grad}\nolimits}
+\def\so{\mathop{\cal SO}\nolimits}
+\def\og#1{{\cal O}(#1)}
+\let\vc=\overrightarrow
+
+\def\arc#1{\buildrel\frown\over{#1}}
+\def\arcfl#1{\buildrel{\ds\bb y}\over{#1}}
+
+\def\pscal#1#2{\langle #1\vir #2\rangle}
+
+%__________ ARITHMETIQUE _______________________________
+
+\def\mod{\mathop{\rm mod}\nolimits}
+\def\dv{\mathop{\rm div}\nolimits}
+
+%__________ Programmes _______________
+
+\def\prol{\parindent=1cm\obeylines\tt }
+\def\dec {\advance\parindent by 1cm}
+
+\def\prog#1{\advance\parindent by #1 cm\obeylines\tt}
+\def\ind#1{\advance\parindent by #1 cm}
+
+%__________ en-dessus, au-dessous d'un symbole __________
+
+\def\build#1_#2^#3{\mathrel{
+\mathop{\kern 0pt#1}\limits_{#2}^{#3}}}
+
+%____________________ DIVERS ____________________________
+
+\def\bs{\char"5C} % le backslash !!!
+
+\def\vir{\,,\,} \def\cdotv{\raise 2pt\hbox{,}}
+
+\def\jbar{\sur{\mathstrut\,j\,}}
+
+\def\psaut{\vskip 2pt}
+\def\saut{\vskip 5pt}
+\def\gsaut{\vskip 8pt}
+\def\Saut{\vskip 8pt}
+
+\def\fin{\gsaut\centerline{\hbox to 3cm{\hrulefill}}}
+
+\def\nopagenumbers{\def\folio{\hfil}}
+
