


\let\et=\wedge
\let\ou=\lor
\def\<<{\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\langle\!\langle$~}}
\def\>>{~\leavevmode\raise.3ex\hbox{$\scriptscriptstyle\rangle\!\rangle$}}
\frenchspacing

\font\sc=cmcsc10 at 12pt
\font\bb=msbm10 at 12pt
\font\fr=eufm10 at 12pt

\font\rom=cmr12 % at 12pt
\font\romm=cmr7



\def\N{\mathbb{N}}
\def\R{\mathbb{R}}
\def\Q{\mathbb{Q}}
\def\Z{\mathbb{Z}}
\def\U{\mathbb{U}}
\def\H{\mathbb{H}}
\def\F{\mathbb{F}}
\def\A{\mathbb{A}}
\def\B{\mathbb{B}}
\def\C{\mathbb{C}}
\def\K{\mathbb{K}}
\def\P{\mathbb{P}}

\def\d{\hskip -1.5mm ---\hskip 1.5mm}


\def\AA{{\cal A}}
\def\BB{{\cal B}}
\def\CC{{\cal C}}
\def\DD{{\cal D}}
\def\EE{{\cal E}}
\def\FF{{\cal F}}
\def\GG{{\cal G}}
\def\HH{{\cal H}}
\def\II{{\cal I}}
\def\KK{{\cal K}}
\def\LL{{\cal L}}
\def\MM{{\cal M}}
\def\PP{{\cal P}}
\def\RR{{\cal R}}
\def\SS{{\cal S}}
\def\TT{{\cal T}}

\def\Cnk{{\rm C}}

\def\e{\textrm{e}}

\def\degre{^\circ}
\def\ti{$\setp{{}^2_1}$
-OT}
\def\te{OT}

\let\dis=\displaystyle
\let\vphi=\varphi
\let\imply=\Rightarrow
\def\implique{\quad\Longrightarrow\quad}
\def\moy#1{\langle #1\rangle}
\def\demo{{\em D\'emonstration:\/\par} }
\def\abs#1{\left|#1\right|}
\def\set#1{\left\{#1\right\}}
\def\setc#1{\left[#1\right]}
\def\setp#1{\left(#1\right)}
\def\flooor#1{\left\lfloor#1\right\rfloor}
\def\norme#1{\left\Vert#1\right\Vert}
\def\suite#1#2{(#1_1,#1_2,\ldots, #1_#2)}
\def\suit#1#2#3{(#1_#2)_{#2\in\inter{#3}}}
\def\inter#1{\set{1,2,\ldots ,#1}}
%\def\encadre#1{\vbox{$$\fbox{\vbox{#1}}$$}}
\newcommand{\encadre}[1]
{\smallskip\begin{center}
\fbox
{\begin{minipage}{405pt}
\smallskip
#1
\smallskip
\end{minipage}}
\end{center}\smallskip}
\let\vect=\overrightarrow
\def\paral{\slash\!\slash}
\let\app=\mapsto
\let\appl=\longrightarrow
\let\lett=\leftarrow
\def\ie{{\it i.e.\/}\ }
\def\cf{{\it cf.\/}\ }
\def\etc{{\it etc.}}
\let\eps=\varepsilon
\def\di{\displaystyle\mathop{\rm diag}}
\def\DO{{\rm\bf DO}}
\def\tr{\displaystyle\mathop{\rm tr}}
\def\rg{\displaystyle\mathop{\rm rg}}
\def\Vect{\displaystyle\mathop{\rm Vect}}
\def\dim{\displaystyle\mathop{\rm dim}}
\def\Pas{\displaystyle\mathop{\rm Pas}}
\def\Mat{\displaystyle\mathop{\rm Mat}}
\def\GL{\mathop{\rm GL}}



\newtheorem{coro}{\sc Corollaire}
\newtheorem{theo}{\sc Th\'eor\`eme}
\newtheorem{exo}{\sc Exercice}
\newtheorem{exple}{\sc Exemple}
\newtheorem{fait}{\sc Fait}
\newtheorem{lemma}{\sc Lemme}
\newtheorem{propo}{\sc Proposition}
{\theoremstyle{break}
\newtheorem{theo-l}[theo]{\sc Th\'eor\`eme}
\newtheorem{exo-l}[exo]{\sc Exercice}
\newtheorem{lemma-l}[lemma]{\sc Lemme}
\newtheorem{propos}[propo]{\sc Proposition}
\newtheorem{coros}[coro]{\sc Corollaire}
\newtheorem{exples}[exple]{\sc Exemples}}
{\theorembodyfont{\rmfamily}\newtheorem{exem}{\sc Exemple}[section]
\newtheorem{rema}{\sc Remarque}
\newtheorem{exo-f}{\sc Exercice}
\theoremstyle{break}
\newtheorem{rques}[rema]{\sc Remarques}
\newtheorem{DM}{\sc Devoir \`a la maison}
\newtheorem{defi}{\sc D\'efinition}
\newtheorem{exo-f-l}[exo-f]{\sc Exercice}
\newtheorem{solu-f}{\sc Exercice}}
%\newtheorem{solu-f-l}[solu-f]{\sc Exercice}


\newcommand{\cqfd}
{\mbox{}
\nolinebreak
\hfill
\rule{2mm}{2mm}
\medbreak
\par}
\newenvironment{proof}{{\sc Preuve :}\begin{rm}}{\end{rm}\cqfd}
\newenvironment{solut}{{\sc Solution :}\begin{rm}}{\end{rm}}
\newenvironment{rappel}{{\sc Rappel :}\begin{rm}}{\end{rm}}
\newenvironment{item-bul}{%
\renewcommand{\labelitemi}{$\bullet$}%
\begin{itemize}}{\end{itemize}}



%\pagestyle{headings}

\def\[{[\![}
\def\]{]\!]}
\let\phi=\varphi
\let\vect=\overrightarrow
\let\app=\rightarrow
\let\appl=\mapsto
\let\imply=\Rightarrow
\let\ssi=\Longleftrightarrow
\def\det{\mbox{\rom det\,}}
\def\pgcd{\mbox{\rom pgcd\,}}
\def\tr{\mbox{\rom tr\,}}
%\def\dim{\mbox{\rom dim\,}}

\def\sup{\mathop{\textup{Sup}}\limits}
\def\inf{\mathop{\textup{Inf}}\limits}
\def\max{\mathop{\textup{Max}}\limits}
\def\min{\mathop{\textup{Min}}\limits}
\def\={\mathop{=}\limits}
\def\simlim{\mathop{\sim}\limits}

\def\pa#1{\left({#1}\right)}
\def\set#1{\left\{{#1}\right\}}
\def\suit#1{\left({#1}\right)}
\def\suitn#1#2{\left({#1_{#2}}\right)_{#2}}
\def\norme#1{\left\|{#1}\right\|}
\def\abs#1{\left|{#1}\right|}
\def\mod#1{\mbox{\  \rom(mod $#1$)\  }}
\def\des{\mbox{\rom DES\,}}
\def\card{\mbox{\rom card\,}}
\def\Id{\mbox{\rom Id}}
\def\endo{\mbox{\rom End}}
\def\l{{\cal L}}
\def\m{{\cal M}}
\def\gl{\mbox{\rom GL}}
\def\sp{\mbox{\rom Sp\,}}
\def\diag{\mbox{diag}}
\def\im{\mbox{\rom im\,}}
\def\car{\mbox{\rom car\,}}
\def\vec{\mbox{\rom vect\,}}
\def\t#1{{}^{\mbox{\romm t}}#1}
\def\lleq{<\!\!<}
\def\decrois{\searrow}
\def\decroisstrict{\searrow\!\!\!\searrow}
\def\crois{\nearrow}
\def\croisstrict{\nearrow\!\!\!\nearrow}
\def\un{{\bf 1}}


\def\adh#1{\overline{\!#1}}
\def\rond#1{\buildrel\;\circ\over #1}

\def\re{{\rm Re}}
\def\im{{\rm Im}}

%
%
%
\def\floor#1{\lfloor#1\rfloor}
\def\ceil#1{\lceil#1\rceil}
\def \vabs#1{\left|#1\right|}
\def \scal#1#2{<\!\!#1|#2\!\!>}
\def \scalvide{<\!\!\cdot|\cdot\!\!>}
\def \norme#1{\Vert #1 \Vert}
\def \Norme#1{\vert\vert\vert #1 \vert\vert \vert}
\def\[{[\![}
\def\]{]\!]}
\def\Frac#1#2{\dis{#1\over#2}}
\def\frac#1#2{{\scriptstyle#1\over\scriptstyle#2}}
\def\Der#1#2{\Frac{\hbox{d}#1}{\hbox{d}#2}} % Ex:\Der{y}{x}
\def\Derr#1#2{\Frac{\hbox{d}^2#1}{\hbox{d}#2^2}}
\def\Dron#1#2{\Frac{\partial#1}{\partial#2}}
\def\dron#1#2{\frac{\partial#1}{\partial#2}}
%\def\vect#1{\overrightarrow{#1}} % vecteur\def\e{{\rm e}}
\def\ch{\mathop{\rm ch}\nolimits}
\def\sh{\mathop{\rm sh}\nolimits}
\def\th{\mathop{\rm th}\nolimits}
\def\argch{\mathop{\rm argch}\nolimits}
\def\argsh{\mathop{\rm argsh}\nolimits}
\def\argth{\mathop{\rm argth}\nolimits}
\def\arccos{\mathop{\rm arccos}\nolimits}
\def\arcsin{\mathop{\rm arcsin}\nolimits}
\def\arctan{\mathop{\rm arctan}\nolimits}
\def\cotan{\mathop{\rm cotan}\nolimits}

\def\Ker{{\rm Ker\,}}
\def\Im{{\rm Im\,}}


\def\tend#1{\displaystyle\mathop{\longrightarrow}_{#1}}
\def\limenn{\mathop{\longrightarrow}\limits_{n\rightarrow\infty}}
\def\Tend#1#2{\mathop{\longrightarrow}\limits_{#1\rightarrow#2}}
\def\Lim#1#2{\dis\lim_{#1\to#2}}
\def\lim{\mathop{{\rm lim}}\limits}


\def\rond#1{\buildrel\;\circ\over #1}
\def\adh#1{\overline{\!#1}}
\def\conj#1{\overline{#1}}
\def\limInf{\underline{\lim}}
\def\limSup{\overline{\lim}}



% %% define the macintosh "option" generated characters

% \catcode`\�=\active\def�{{\aa}}       % option a
% \catcode`\�=\active\def�{\int}        % option b (math mode) 
% \catcode`\�=\active\def�{\c c}        % option c
% \catcode`\�=\active\def�{\partial}    % option d (math mode)
% \catcode`\�=\active\def�{\oint}       % option f (math mode) ?
% \catcode`\�=\active\def�{\triangle}   % option j (math mode)
% \catcode`\�=\active\def�{\neg}        % option l (math mode)
% \catcode`\�=\active\def�{\mu}         % option m (math mode)
% \catcode`\�=\active\def�{{\o}}        % option o
% \catcode`\�=\active\def�{\pi}         % option p (math mode w/ arg.)
% \catcode`\�=\active\def�{{\oe}}       % option q 
% \catcode`\�=\active\def�{{\ss}}       % option s 
% \catcode`\�=\active\def�{\dagger}     % option t  (math mode)
% \catcode`\�=\active\def�{\sqrt}       % option v (math mode w/ arg.)
% \catcode`\�=\active\def�{\sum}      % option w (math mode)
% \catcode`\�=\active\def�{\approx}     % option x (math mode)
% \catcode`\�=\active\def�{\Omega}      % option z (math mode)
% \catcode`\�=\active\def�{{\it\$}}     % option 3 ($ from italic font)
% \catcode`\�=\active\def�{\infty}      % option 5 (math mode)
% %\catcode`\�=\active\def�{{\S}}        % option 6 
% \catcode`\�=\active\def�{{\P}}        % option 7
% \catcode`\�=\active\def�{\bullet}     % option 8 
% \catcode`\�=\active\def�{\leavevmode\raise.585ex\hbox{\b a}}      % option 9
% \catcode`\�=\active\def�{\leavevmode\raise.6ex\hbox{\b o}}        % option 0
% \catcode`\�=\active\def�{\not=}       % option = (math mode)
% \catcode`\�=\active\def�{\leq}        % option , (math mode)
% \catcode`\�=\active\def�{\geq}        % option . (math mode)
% \catcode`\�=\active\def�{\div}        % option / (math mode)
% \catcode`\�=\active\def�{{\dots}}     % option ; 
% \catcode`\�=\active\def�{{\ae}}       % option '
% \catcode`\�=\active\def�{\ll}         % option \ (math mode)
% \catcode`\�=\active\def�{``}          % option [
% \catcode`\�=\active\def�{!`}          % option !
% \catcode`\�=\active\def�{\rlap/c}     % option 4

% %% macintosh "shift-option" generated characters

% \catcode`\�=\active\def�{{\AA}}       % shift-option A
% \catcode`\�=\active\def�{\c C}        % shift-option C
% \catcode`\�=\active\def�{{\O}}        % shift-option O
% \catcode`\�=\active\def�{\Pi}         % shift-option P (math mode)
% \catcode`\�=\active\def�{{\OE}}       % shift-option Q
% \catcode`\�=\active\def�{{\AE}}       % shift-option '
% \catcode`\�=\active\def�{\diamond}    % shift-option V (math mode)
% \catcode`\�=\active\def�{\accent'27}  % shift-option 8
% \catcode`\�=\active\def�{''}          % shift-option [
% \catcode`\�=\active\def�{\pm}         % shift-option = (math mode)
% \catcode`\�=\active\def�{\gg}         % shift-option \ (math mode)
% \catcode`\�=\active\def�{?`}          % shift-option / 
% \catcode`\�=\active\def�{--}          % option - (en-dash)
% \catcode`\�=\active\def�{---}         % shift-option - (em-dash)

% %% define the macintosh "composite" characters

% \catcode`\�=\active\def�{\"a}        % option u, then  a
% \catcode`\�=\active\def�{\"e}        % option u, then  e
% \catcode`\�=\active\def�{\"{\i}}     % option u, then  i
% \catcode`\�=\active\def�{\"o}        % option u, then  o
% \catcode`\�=\active\def�{\"u}        % option u, then  u
% \catcode`\�=\active\def�{\"y}        % option u, then  y
% \catcode`\�=\active\def�{\"A}        % option u, then  A
% \catcode`\�=\active\def�{\"O}        % option u, then  O
% \catcode`\�=\active\def�{\"U}        % option u, then  U
% \catcode`\�=\active\def�{\'a}        % option e, then  a
% \catcode`\�=\active\def�{\'e}        % option e, then  e
% \catcode`\�=\active\def�{\'{\i}}     % option e, then  i
% \catcode`\�=\active\def�{\'o}        % option e, then  o
% \catcode`\�=\active\def�{\'u}        % option e, then  u
% \catcode`\�=\active\def�{\'E}        % option e, then  E
% \catcode`\�=\active\def�{\`a}        % option `, then  a
% \catcode`\�=\active\def�{\`e}        % option `, then  e
% \catcode`\�=\active\def�{\`{\i}}     % option `, then  i
% \catcode`\�=\active\def�{\`o}        % option `, then  o
% \catcode`\�=\active\def�{\`u}        % option `, then  u
% \catcode`\�=\active\def�{\`A}        % option `, then  A
% \catcode`\�=\active\def�{\~a}        % option n, then  a
% \catcode`\�=\active\def�{\~n}        % option n, then  n
% \catcode`\�=\active\def�{\~o}        % option n, then  o
% \catcode`\�=\active\def�{\~A}        % option n, then  A
% \catcode`\�=\active\def�{\~N}        % option n, then  N
% \catcode`\�=\active\def�{\~O}        % option n, then  O
% \catcode`\�=\active\def�{\^a}        % option i, then  a
% \catcode`\�=\active\def�{\^e}        % option i, then  e
% \catcode`\�=\active\def�{\^{\i}}     % option i, then  i
% \catcode`\�=\active\def�{\^o}        % option i, then  o
% \catcode`\�=\active\def�{\^u}        % option i, then  u









