% -------------------------------------------------------
% -------------------------------------------------------
% -------------------------------------------------------
%%%%%%%%%%%%%%%%%%% caract\`eres sp\'eciaux 
% -------------------------------------------------------
% -------------------------------------------------------
% -------------------------------------------------------
\everymath{\displaystyle}

\def\eclaire{\mathbb}

\def\R{\ensuremath{\eclaire R}}
\def\K{\ensuremath{\eclaire K}}
\def\F{\ensuremath{\eclaire F}}
\def\C{\ensuremath{\eclaire C}}
\def\N{\ensuremath{\eclaire N}}
\def\Z{\ensuremath{\eclaire Z}}
\def\Q{\ensuremath{\eclaire Q}}
\def\rmat{\ensuremath{\eclaire R}}
\def\kmat{\ensuremath{\eclaire K}}
\def\fmat{\ensuremath{\eclaire F}}
\def\cmat{\ensuremath{\eclaire C}}
\def\nmat{\ensuremath{\eclaire N}}
\def\zmat{\ensuremath{\eclaire Z}}
\def\qmat{\ensuremath{\eclaire Q}}

\DeclareMathSymbol{\leqslant}     {\mathrel}{AMSa}{"36}
\DeclareMathSymbol{\geqslant}     {\mathrel}{AMSa}{"3E}
\def\leq{\leqslant}
\def\geq{\geqslant}
\def\le{\leqslant}
\def\ge{\geqslant}


%%%%%%%%%%%%%%%%%%%%% signes et fonctions math\'ematiques

\def\rond#1{\build#1_{}^{\>\circ}}
\def\union{\;\cup\;}
\def\inter{\;\cap\;}
\def\sur{\above .2pt}
\def\rbar{\overline\rmat}
\def\og{\leavevmode\raise.3ex\hbox{$\sst\langle\!\langle$}}
\def\fg{\leavevmode\raise.3ex\hbox{$\sst\,\rangle\!\rangle$}}

\def\vect#1{\kern 2pt\overrightarrow{\kern -2pt#1}}
\def\norme#1{\Vert #1  \Vert}
\def\esp{\mkern -2mu}
\def\tpn{|\esp |\esp |} % triple norme (+ \mkern 1mu)

\def\soul#1{$\underline{\vrule depth 1.8pt width
0pt\hbox{#1}}$}
\def\build#1_#2^#3{\mathrel{\mathop{\kern
0pt#1}\limits_{#2}^{#3}}}
\def\sub#1{\build{#1}_{\mkern -20mu {{}^{\vbox{\hrule height
1.3pt depth 0pt width 5pt}}}}^{}}

\def\re{\mathop{\Re \mskip -0.5\thinmuskip e}\nolimits}
\def\im{\mathop{\Im \mskip -0.5\thinmuskip m}\nolimits}
\let\ReCal=\Re
\let\ImCal=\Im
\def\Re{\mathop{\rm Re}\nolimits}
\def\Im{\mathop{\rm Im}\nolimits}
\def\Arg{\mathop{\rm Arg}\nolimits}

\def\min{\mathop{\rm min}\nolimits}
\def\max{\mathop{\rm max}\nolimits}
\def\Min{\mathop{\rm Min}\nolimits}
\def\Max{\mathop{\rm Max}\nolimits}
\def\inf{\mathop{\rm inf}\nolimits}
\def\sup{\mathop{\rm sup}\nolimits}
\def\Inf{\mathop{\rm Inf}\nolimits}
\def\Sup{\mathop{\rm Sup}\nolimits}
\def\limsup{\mathop{\overline{\rm lim}}}
\def\liminf{\mathop{\underline{\rm lim}}}
\def\Sum{\sum\limits}

\def\id{\hbox{{\rm 1}\kern-.4em\hbox{{\rm 1}}}\! }
\def\dim{\mathop{\rm dim}\nolimits}
\def\codim{\mathop{\rm codim}\nolimits}
\def\rg{\mathop{\rm rg}\nolimits}
\def\Ker{\mathop{\rm Ker}\nolimits}
\def\ker{\mathop{\rm Ker}\nolimits}
\def\Image{\mathop{\rm Im}\nolimits}
\def\Aut{\mathop{\rm Aut}\nolimits}
\def\tr{\mathop{\rm tr}\nolimits}

\def\cof{\mathop{\rm cof}\nolimits}
\def\deg{\mathop{\rm deg}\nolimits}
\def\proj{\mathop{\rm proj}\nolimits}
\def\Supp{\mathop{\rm Supp}\nolimits}
\def\ord{\mathop{\rm ord}\nolimits}
\def\mod{\mathop{\rm mod}\nolimits}
\def\rad{\mathop{\rm rad}\nolimits}
\def\resp{\mathop{\rm resp}\nolimits}
\def\res{\mathop{\rm res}\nolimits}
\def\det{\mathop{\rm det}\nolimits}
\def\sgn{\mathop{\rm sgn}\nolimits}
\def\ln{\mathop{\rm ln}\nolimits}
\def\ord{\mathop{\rm ord}\nolimits}
\def\Frac{\mathop{\rm Frac}\nolimits}
\def\Card{\mathop{\rm Card}\nolimits}
\def\pgcd{\mathop{\rm pgcd}\nolimits}
\def\ppcm{\mathop{\rm ppcm}\nolimits}
\def\res{\mathop{\rm res}\nolimits}
\def\Res{\mathop{\rm Res}\nolimits}
\def\dbar{\overline\partial}
\def\zbar{\overline z}
\def\iint{\int\!\!\!\int}
\def\ep#1{\smallbreak\indent\e{#1}}
\def\drp#1#2{{\partial#1\over\partial#2}}
\def\ronde#1{\buildrel\circ\over#1}
\def\bul{{\scriptstyle\,\bullet\,}}

\def\vers{\;\longmapsto\;}
\def\lto{\;\longrightarrow\;}
\def\nameto#1{\buildrel#1\over\rightarrow}
\def\namelto#1{\;\buildrel#1\over\longrightarrow\;}
\def\isom{\;\buildrel \sim\over\longrightarrow\;}
\def\into{\hookrightarrow}
\def\linto{\lhook\joinrel\longrightarrow}
\def\midbarre{\mathrel{\mid\kern-2.2mm/}}
\def\fle{\longrightarrow}
\def\mapright#1{\smash{\mathop{\longrightarrow}\limits^{#1}}}

\def\flechelongue#1{\mathop{\hbox{\rightarrowfill}}
\limits^{\quad #1\quad}}

\def\cc{{\cal C}} \def\cd{{\cal D}} \def\ce{{\cal E}}
\def\cf{{\cal F}} \def\cg{{\cal G}} \def\ch{{\cal H}}
\def\cl{{\cal L}} \def\cm{{\cal M}} \def\co{{\cal O}}
\def\cp{{\cal P}} \def\ct{{\cal T}} \def\cu{{\cal U}}
\def\cv{{\cal V}} \def\cx{{\cal X}}

\def\eps{\varepsilon}
\def\ph{\varphi}

\def\vide{\emptyset}
\def\dans{\longrightarrow}
\def\implique{\Longrightarrow}
\def\ssi{\Longleftrightarrow}
\def\d{\,\mathop{{\rm d}\kern -2pt}\nolimits}

\def\argsh{\mathop{\rm Argsh}\nolimits}
\def\argch{\mathop{\rm Argch}\nolimits}
\def\argth{\mathop{\rm Argth}\nolimits}
\def\argcoth{\mathop{\rm Argcoth}\nolimits}
\def\coth{\mathop{\rm coth}\nolimits}
\def\cotan{\mathop{\rm cotan}\nolimits}
\def\rac#1{\displaystyle\sqrt{#1}}

%________image_______
\def\im{\mathop{\rm Im}\nolimits}
%________determinant_______
\def\det{\mathop{\rm det}\nolimits}  % MONASSE
%________rang_______
\def\rg{\mathop{\rm rg}\nolimits}
%________vect_______
\def\Vect{\mathop{\rm Vect}\nolimits}
%________id_______
\def\id{\mathop{\rm id}\nolimits}
\def\tr{\mathop{\rm tr}\nolimits}
\def\Id{\mathop{\rm Id}\nolimits}
\def\card{\mathop{\rm card}\nolimits}
\def\grad{\mathop{\rm grad}\nolimits}

%________GL_______
\def\GL{\mathop{\rm GL}\nolimits}
\def\SL{\mathop{\rm SL}\nolimits}
\def\GLR#1{{\rm GL}_{#1}(\rmat)}  % MONASSE
\def\GLC#1{{\rm GL}_{#1}(\rmat)}  % MONASSE
\def\GLK#1#2{{\rm GL}_{#1}(#2)}  % MONASSE
\renewcommand{\L}{\mathcal{L}}

%________spectre_______
\newcommand{\Sp}{\mathop{\rm Sp}\nolimits}
\newcommand{\spec}{\mathop{\rm sp}\nolimits}

%_________ transpos\'ee ________
%\def\t{\raise .2em\hbox{${}^{\hbox{\seveni t}}\!$}}
\def\t{\,{}^t\!\!}

%_______M gothL_______
\def\MR#1{M_{#1}(\rmat)}  % MONASSE
\def\MC#1{M_{#1}(\cmat)}  % MONASSE
\def\MK#1#2{M_{#1}(#2)}  % MONASSE

%_______cal L_______
%\def\L{{\euler L}}

%%%%%%%%%%%%%%%%%%%%%%%%% fonctions classiques %%%%%%%%%%%%%%%%%%%%%%
%________cotg_______
\def\cotan{\mathop{\rm cotan}\nolimits}
\def\cotg{\mathop{\rm cotg}\nolimits}
\def\tg{\mathop{\rm tg}\nolimits}
%________th_______
\def\tanh{\mathop{\rm th}\nolimits}
\def\th{\mathop{\rm th}\nolimits}
%________sh_______
\def\sinh{\mathop{\rm sh}\nolimits}
\def\sh{\mathop{\rm sh}\nolimits}
%________ch_______
\def\cosh{\mathop{\rm ch}\nolimits}
\def\ch{\mathop{\rm ch}\nolimits}
%________log_______
\def\log{\mathop{\rm log}\nolimits}

\def\Arcsin{\mathop{\rm Arcsin}\nolimits}   % CLENET
\def\Arccos{\mathop{\rm Arccos}\nolimits}   % CLENET
\def\Arctan{\mathop{\rm Arctan}\nolimits}   % CLENET
\def\Argsh{\mathop{\rm Argsh}\nolimits}     % CLENET
\def\Argch{\mathop{\rm Argch}\nolimits}     % CLENET
\def\Argth{\mathop{\rm Argth}\nolimits}     % CLENET
\def\ve#1{\kern 2pt\overrightarrow{\kern -2pt#1}}
\def\d{\mathop{{\rm d}\kern -2pt}\nolimits}
\def\Arccotan{\mathop{\rm Arccotan}\nolimits}
\def\coth{\mathop{\rm coth}\nolimits}
\def\Argcoth{\mathop{\rm Argcoth}\nolimits}
\def\sgn{\mathop{\rm sgn}\nolimits}
\def\oo{\mathop{o}\nolimits}
\def\build#1_#2^#3{\mathrel{\mathop{\kern 0pt#1}\limits_{#2}^{#3}}} %CLENET

%____________suites et s\'eries_____________________
\def\suiteN #1#2{(#1 _#2)_{#2\in\, \pN }}  % MONASSE
\def\suite #1#2#3{(#1 _#2)_{#2\ge#3 }}  % MONASSE
\def\serieN #1#2{\sum_{#2\in\, \pN } #1_#2}  % MONASSE
\def\serie #1#2#3{\sum_{#2\ge #3} #1_#2}  % MONASSE

%___________norme_________________________
\def\norme#1{\|{#1}\|}  % MONASSE
\def\bignorme#1{\left|\hskip-0.9pt\left|{#1}\right|\hskip-0.9pt\right|}

% des environnements ˆ la AMSmath

\newenvironment{Cases}{%
  \left\lbrace
  \def\arraystretch{1.2}%
  \array{@{}l@{\quad}l@{}}
}{%
  \endarray\right.%
}

\newcount\c@@MaxMatrixCols \c@@MaxMatrixCols=10

\newenvironment{Matrix}{%
  \hskip -\arraycolsep
  \array{*\c@@MaxMatrixCols c}
}{%
  \endarray \hskip -\arraycolsep
}

\newenvironment{Pmatrix}{%
  \left(%
  \Matrix
}{
  \endMatrix\right)%
}

% - les theoremes
\newtheorem{definition}{D\'efinition}
\newtheorem{theoreme}{Th\'eor\`eme}
\newtheorem{proposition}{Proposition}
\newtheorem{lemme}{Lemme}
\newtheorem{corollaire}{Corollaire}
\newtheorem{propriete}{Propri\'et\'e}
\newtheorem{axiome}{Axiome}
\newcommand{\initialisecompteurs}{
       \setcounter{definition}{0}%
       \setcounter{theoreme}{0}%
       \setcounter{proposition}{0}%
       \setcounter{lemme}{0}%
       \setcounter{corollaire}{0}%
       \setcounter{propriete}{0}%
       \setcounter{axiome}{0}%
       \setcounter{section}{0}%
       \setcounter{subsection}{0}%
       \setcounter{subsubsection}{0}%
}