\RequirePackage{calrsfs}
\DeclareSymbolFont{rsfscript}{OMS}{rsfs}{m}{b}
\DeclareSymbolFontAlphabet{\mathrsfs}{rsfscript}

\usepackage{color}
\definecolor{shadecolor}{gray}{0.90}

\def\bfit{\bfseries\itshape}
\def\itbf{\bfseries\itshape}


\input xypic
\xyoption{all}
\xyoption{arc}




\renewcommand\theequation{\thetheorem}
\def\equat{\refstepcounter{theorem}\begin{equation}}
\def\endequat{\end{equation}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                %%%%%%%%%%%%%%%%%%%%          
%%    CARACTERES GOTHIQUES    %%                %%  DOUBLE BARRE  %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                %%%%%%%%%%%%%%%%%%%%

\def\AG{{\mathfrak A}}  \def\aG{{\mathfrak a}}  \def\AM{{\mathbb{A}}}
\def\BG{{\mathfrak B}}  \def\bG{{\mathfrak b}}  \def\BM{{\mathbb{B}}}
\def\CG{{\mathfrak C}}  \def\cG{{\mathfrak c}}  \def\CM{{\mathbb{C}}}
\def\DG{{\mathfrak D}}  \def\dG{{\mathfrak d}}  \def\DM{{\mathbb{D}}}
\def\EG{{\mathfrak E}}  \def\eG{{\mathfrak e}}  \def\EM{{\mathbb{E}}}
\def\FG{{\mathfrak F}}  \def\fG{{\mathfrak f}}  \def\FM{{\mathbb{F}}}
\def\GG{{\mathfrak G}}  \def\gG{{\mathfrak g}}  \def\GM{{\mathbb{G}}}
\def\HG{{\mathfrak H}}  \def\hG{{\mathfrak h}}  \def\HM{{\mathbb{H}}}
\def\IG{{\mathfrak I}}  \def\iG{{\mathfrak i}}  \def\IM{{\mathbb{I}}}
\def\JG{{\mathfrak J}}  \def\jG{{\mathfrak j}}  \def\JM{{\mathbb{J}}}
\def\KG{{\mathfrak K}}  \def\kG{{\mathfrak k}}  \def\KM{{\mathbb{K}}}
\def\LG{{\mathfrak L}}  \def\lG{{\mathfrak l}}  \def\LM{{\mathbb{L}}}
\def\MG{{\mathfrak M}}  \def\mG{{\mathfrak m}}  \def\MM{{\mathbb{M}}}
\def\NG{{\mathfrak N}}  \def\nG{{\mathfrak n}}  \def\NM{{\mathbb{N}}}
\def\OG{{\mathfrak O}}  \def\oG{{\mathfrak o}}  \def\OM{{\mathbb{O}}}
\def\PG{{\mathfrak P}}  \def\pG{{\mathfrak p}}  \def\PM{{\mathbb{P}}}
\def\QG{{\mathfrak Q}}  \def\qG{{\mathfrak q}}  \def\QM{{\mathbb{Q}}}
\def\RG{{\mathfrak R}}  \def\rG{{\mathfrak r}}  \def\RM{{\mathbb{R}}}
\def\SG{{\mathfrak S}}  \def\sG{{\mathfrak s}}  \def\SM{{\mathbb{S}}}
\def\TG{{\mathfrak T}}  \def\tG{{\mathfrak t}}  \def\TM{{\mathbb{T}}}
\def\UG{{\mathfrak U}}  \def\uG{{\mathfrak u}}  \def\UM{{\mathbb{U}}}
\def\VG{{\mathfrak V}}  \def\vG{{\mathfrak v}}  \def\VM{{\mathbb{V}}}
\def\WG{{\mathfrak W}}  \def\wG{{\mathfrak w}}  \def\WM{{\mathbb{W}}}
\def\XG{{\mathfrak X}}  \def\xG{{\mathfrak x}}  \def\XM{{\mathbb{X}}}
\def\YG{{\mathfrak Y}}  \def\yG{{\mathfrak y}}  \def\YM{{\mathbb{Y}}}
\def\ZG{{\mathfrak Z}}  \def\zG{{\mathfrak z}}  \def\ZM{{\mathbb{Z}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES GOTHIQUES GRAS   %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\AGB{{\boldsymbol{\mathfrak A}}}  \def\aGB{{\boldsymbol{\mathfrak a}}}
\def\BGB{{\boldsymbol{\mathfrak B}}}  \def\bGB{{\boldsymbol{\mathfrak b}}}
\def\CGB{{\boldsymbol{\mathfrak C}}}  \def\cGB{{\boldsymbol{\mathfrak c}}}
\def\DGB{{\boldsymbol{\mathfrak D}}}  \def\dGB{{\boldsymbol{\mathfrak d}}}
\def\EGB{{\boldsymbol{\mathfrak E}}}  \def\eGB{{\boldsymbol{\mathfrak e}}}
\def\FGB{{\boldsymbol{\mathfrak F}}}  \def\fGB{{\boldsymbol{\mathfrak f}}}
\def\GGB{{\boldsymbol{\mathfrak G}}}  \def\gGB{{\boldsymbol{\mathfrak g}}}
\def\HGB{{\boldsymbol{\mathfrak H}}}  \def\hGB{{\boldsymbol{\mathfrak h}}}
\def\IGB{{\boldsymbol{\mathfrak I}}}  \def\iGB{{\boldsymbol{\mathfrak i}}}
\def\JGB{{\boldsymbol{\mathfrak J}}}  \def\jGB{{\boldsymbol{\mathfrak j}}}
\def\KGB{{\boldsymbol{\mathfrak K}}}  \def\kGB{{\boldsymbol{\mathfrak k}}}
\def\LGB{{\boldsymbol{\mathfrak L}}}  \def\lGB{{\boldsymbol{\mathfrak l}}}
\def\MGB{{\boldsymbol{\mathfrak M}}}  \def\mGB{{\boldsymbol{\mathfrak m}}}
\def\NGB{{\boldsymbol{\mathfrak N}}}  \def\nGB{{\boldsymbol{\mathfrak n}}}
\def\OGB{{\boldsymbol{\mathfrak O}}}  \def\oGB{{\boldsymbol{\mathfrak o}}}
\def\PGB{{\boldsymbol{\mathfrak P}}}  \def\pGB{{\boldsymbol{\mathfrak p}}}
\def\QGB{{\boldsymbol{\mathfrak Q}}}  \def\qGB{{\boldsymbol{\mathfrak q}}}
\def\RGB{{\boldsymbol{\mathfrak R}}}  \def\rGB{{\boldsymbol{\mathfrak r}}}
\def\SGB{{\boldsymbol{\mathfrak S}}}  \def\sGB{{\boldsymbol{\mathfrak s}}}
\def\TGB{{\boldsymbol{\mathfrak T}}}  \def\tGB{{\boldsymbol{\mathfrak t}}}
\def\UGB{{\boldsymbol{\mathfrak U}}}  \def\uGB{{\boldsymbol{\mathfrak u}}}
\def\VGB{{\boldsymbol{\mathfrak V}}}  \def\vGB{{\boldsymbol{\mathfrak v}}}
\def\WGB{{\boldsymbol{\mathfrak W}}}  \def\wGB{{\boldsymbol{\mathfrak w}}}
\def\XGB{{\boldsymbol{\mathfrak X}}}  \def\xGB{{\boldsymbol{\mathfrak x}}}
\def\YGB{{\boldsymbol{\mathfrak Y}}}  \def\yGB{{\boldsymbol{\mathfrak y}}}
\def\ZGB{{\boldsymbol{\mathfrak Z}}}  \def\zGB{{\boldsymbol{\mathfrak z}}}

%%%%%%%%%%%%%%%%%%%%%%                      %%%%%%%%%%%%%%%%%%%%          
%%  CARACTERES GRAS %%                      %%  CALLIGRAHPIES %%
%%%%%%%%%%%%%%%%%%%%%%                      %%%%%%%%%%%%%%%%%%%%

\def\Ab{{\mathbf A}}  \def\ab{{\mathbf a}}  \def\AC{{\mathcal{A}}}
\def\Bb{{\mathbf B}}  \def\bb{{\mathbf b}}  \def\BC{{\mathcal{B}}}
\def\Cb{{\mathbf C}}  \def\cb{{\mathbf c}}  \def\CC{{\mathcal{C}}}
\def\Db{{\mathbf D}}  \def\db{{\mathbf d}}  \def\DC{{\mathcal{D}}}
\def\Eb{{\mathbf E}}  \def\eb{{\mathbf e}}  \def\EC{{\mathcal{E}}}
\def\Fb{{\mathbf F}}  \def\fb{{\mathbf f}}  \def\FC{{\mathcal{F}}}
\def\Gb{{\mathbf G}}  \def\gb{{\mathbf g}}  \def\GC{{\mathcal{G}}}
\def\Hb{{\mathbf H}}  \def\hb{{\mathbf h}}  \def\HC{{\mathcal{H}}}
\def\Ib{{\mathbf I}}  \def\ib{{\mathbf i}}  \def\IC{{\mathcal{I}}}
\def\Jb{{\mathbf J}}  \def\jb{{\mathbf j}}  \def\JC{{\mathcal{J}}}
\def\Kb{{\mathbf K}}  \def\kb{{\mathbf k}}  \def\KC{{\mathcal{K}}}
\def\Lb{{\mathbf L}}  \def\lb{{\mathbf l}}  \def\LC{{\mathcal{L}}}
\def\Mb{{\mathbf M}}  \def\mb{{\mathbf m}}  \def\MC{{\mathcal{M}}}
\def\Nb{{\mathbf N}}  \def\nb{{\mathbf n}}  \def\NC{{\mathcal{N}}}
\def\Ob{{\mathbf O}}  \def\ob{{\mathbf o}}  \def\OC{{\mathcal{O}}}
\def\Pb{{\mathbf P}}  \def\pb{{\mathbf p}}  \def\PC{{\mathcal{P}}}
\def\Qb{{\mathbf Q}}  \def\qb{{\mathbf q}}  \def\QC{{\mathcal{Q}}}
\def\Rb{{\mathbf R}}  \def\rb{{\mathbf r}}  \def\RC{{\mathcal{R}}}
\def\Sb{{\mathbf S}}  \def\sb{{\mathbf s}}  \def\SC{{\mathcal{S}}}
\def\Tb{{\mathbf T}}  \def\tb{{\mathbf t}}  \def\TC{{\mathcal{T}}}
\def\Ub{{\mathbf U}}  \def\ub{{\mathbf u}}  \def\UC{{\mathcal{U}}}
\def\Vb{{\mathbf V}}  \def\vb{{\mathbf v}}  \def\VC{{\mathcal{V}}}
\def\Wb{{\mathbf W}}  \def\wb{{\mathbf w}}  \def\WC{{\mathcal{W}}}
\def\Xb{{\mathbf X}}  \def\xb{{\mathbf x}}  \def\XC{{\mathcal{X}}}
\def\Yb{{\mathbf Y}}  \def\yb{{\mathbf y}}  \def\YC{{\mathcal{Y}}}
\def\Zb{{\mathbf Z}}  \def\zb{{\mathbf z}}  \def\ZC{{\mathcal{Z}}}


%%%%%%%%%%%%%%%%%%%%%%%                         %%%%%%%%%%%%%%%%%%%%%%%%%%          
%% CARACTERES DROITS %%                         %%  CALLIGRAPHIES GRAS  %%
%%%%%%%%%%%%%%%%%%%%%%%                         %%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Arm{{\mathrm{A}}}  \def\arm{{\mathrm{a}}}  \def\ACB{{\boldsymbol{\mathcal{A}}}}
\def\Brm{{\mathrm{B}}}  \def\brm{{\mathrm{b}}}  \def\BCB{{\boldsymbol{\mathcal{B}}}}
\def\Crm{{\mathrm{C}}}  \def\crm{{\mathrm{c}}}  \def\CCB{{\boldsymbol{\mathcal{C}}}}
\def\Drm{{\mathrm{D}}}  \def\drm{{\mathrm{d}}}  \def\DCB{{\boldsymbol{\mathcal{D}}}}
\def\Erm{{\mathrm{E}}}  \def\erm{{\mathrm{e}}}  \def\ECB{{\boldsymbol{\mathcal{E}}}}
\def\Frm{{\mathrm{F}}}  \def\frm{{\mathrm{f}}}  \def\FCB{{\boldsymbol{\mathcal{F}}}}
\def\Grm{{\mathrm{G}}}  \def\grm{{\mathrm{g}}}  \def\GCB{{\boldsymbol{\mathcal{G}}}}
\def\Hrm{{\mathrm{H}}}  \def\hrm{{\mathrm{h}}}  \def\HCB{{\boldsymbol{\mathcal{H}}}}
\def\Irm{{\mathrm{I}}}  \def\irm{{\mathrm{i}}}  \def\ICB{{\boldsymbol{\mathcal{I}}}}
\def\Jrm{{\mathrm{J}}}  \def\jrm{{\mathrm{j}}}  \def\JCB{{\boldsymbol{\mathcal{J}}}}
\def\Krm{{\mathrm{K}}}  \def\krm{{\mathrm{k}}}  \def\KCB{{\boldsymbol{\mathcal{K}}}}
\def\Lrm{{\mathrm{L}}}  \def\lrm{{\mathrm{l}}}  \def\LCB{{\boldsymbol{\mathcal{L}}}}
\def\Mrm{{\mathrm{M}}}  \def\mrm{{\mathrm{m}}}  \def\MCB{{\boldsymbol{\mathcal{M}}}}
\def\Nrm{{\mathrm{N}}}  \def\nrm{{\mathrm{n}}}  \def\NCB{{\boldsymbol{\mathcal{N}}}}
\def\Orm{{\mathrm{O}}}  \def\orm{{\mathrm{o}}}  \def\OCB{{\boldsymbol{\mathcal{O}}}}
\def\Prm{{\mathrm{P}}}  \def\prm{{\mathrm{p}}}  \def\PCB{{\boldsymbol{\mathcal{P}}}}
\def\Qrm{{\mathrm{Q}}}  \def\qrm{{\mathrm{q}}}  \def\QCB{{\boldsymbol{\mathcal{Q}}}}
\def\Rrm{{\mathrm{R}}}  \def\rrm{{\mathrm{r}}}  \def\RCB{{\boldsymbol{\mathcal{R}}}}
\def\Srm{{\mathrm{S}}}  \def\srm{{\mathrm{s}}}  \def\SCB{{\boldsymbol{\mathcal{S}}}}
\def\Trm{{\mathrm{T}}}  \def\trm{{\mathrm{t}}}  \def\TCB{{\boldsymbol{\mathcal{T}}}}
\def\Urm{{\mathrm{U}}}  \def\urm{{\mathrm{u}}}  \def\UCB{{\boldsymbol{\mathcal{U}}}}
\def\Vrm{{\mathrm{V}}}  \def\vrm{{\mathrm{v}}}  \def\VCB{{\boldsymbol{\mathcal{V}}}}
\def\Wrm{{\mathrm{W}}}  \def\wrm{{\mathrm{w}}}  \def\WCB{{\boldsymbol{\mathcal{W}}}}
\def\Xrm{{\mathrm{X}}}  \def\xrm{{\mathrm{x}}}  \def\XCB{{\boldsymbol{\mathcal{X}}}}
\def\Yrm{{\mathrm{Y}}}  \def\yrm{{\mathrm{y}}}  \def\YCB{{\boldsymbol{\mathcal{Y}}}}
\def\Zrm{{\mathrm{Z}}}  \def\zrm{{\mathrm{z}}}  \def\ZCB{{\boldsymbol{\mathcal{Z}}}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                 %%%%%%%%%%%%%%%%%%%%%%%%%%%
%% CARACTERES AVEC TILDE   %%                 %%  CALLIGRAPHIES TILDE  %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%                 %%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Ati{{\tilde{A}}}  \def\ati{{\tilde{a}}}  \def\ACt{{\tilde{\mathcal{A}}}}
\def\Bti{{\tilde{B}}}  \def\bti{{\tilde{b}}}  \def\BCt{{\tilde{\mathcal{B}}}}
\def\Cti{{\tilde{C}}}  \def\cti{{\tilde{c}}}  \def\CCt{{\tilde{\mathcal{C}}}}
\def\Dti{{\tilde{D}}}  \def\dti{{\tilde{d}}}  \def\DCt{{\tilde{\mathcal{D}}}}
\def\Eti{{\tilde{E}}}  \def\eti{{\tilde{e}}}  \def\ECt{{\tilde{\mathcal{E}}}}
\def\Fti{{\tilde{F}}}  \def\fti{{\tilde{f}}}  \def\FCt{{\tilde{\mathcal{F}}}}
\def\Gti{{\tilde{G}}}  \def\gti{{\tilde{g}}}  \def\GCt{{\tilde{\mathcal{G}}}}
\def\Hti{{\tilde{H}}}  \def\hti{{\tilde{h}}}  \def\HCt{{\tilde{\mathcal{H}}}}
\def\Iti{{\tilde{I}}}  \def\iti{{\tilde{i}}}  \def\ICt{{\tilde{\mathcal{I}}}}
\def\Jti{{\tilde{J}}}  \def\jti{{\tilde{j}}}  \def\JCt{{\tilde{\mathcal{J}}}}
\def\Kti{{\tilde{K}}}  \def\kti{{\tilde{k}}}  \def\KCt{{\tilde{\mathcal{K}}}}
\def\Lti{{\tilde{L}}}  \def\lti{{\tilde{l}}}  \def\LCt{{\tilde{\mathcal{L}}}}
\def\Mti{{\tilde{M}}}  \def\mti{{\tilde{m}}}  \def\MCt{{\tilde{\mathcal{M}}}}
\def\Nti{{\tilde{N}}}  \def\nti{{\tilde{n}}}  \def\NCt{{\tilde{\mathcal{N}}}}
\def\Oti{{\tilde{O}}}  \def\oti{{\tilde{o}}}  \def\OCt{{\tilde{\mathcal{O}}}}
\def\Pti{{\tilde{P}}}  \def\pti{{\tilde{p}}}  \def\PCt{{\tilde{\mathcal{P}}}}
\def\Qti{{\tilde{Q}}}  \def\qti{{\tilde{q}}}  \def\QCt{{\tilde{\mathcal{Q}}}}
\def\Rti{{\tilde{R}}}  \def\rti{{\tilde{r}}}  \def\RCt{{\tilde{\mathcal{R}}}}
\def\Sti{{\tilde{S}}}  \def\sti{{\tilde{s}}}  \def\SCt{{\tilde{\mathcal{S}}}}
\def\Tti{{\tilde{T}}}  \def\tti{{\tilde{t}}}  \def\TCt{{\tilde{\mathcal{T}}}}
\def\Uti{{\tilde{U}}}  \def\uti{{\tilde{u}}}  \def\UCt{{\tilde{\mathcal{U}}}}
\def\Vti{{\tilde{V}}}  \def\vti{{\tilde{v}}}  \def\VCt{{\tilde{\mathcal{V}}}}
\def\Wti{{\tilde{W}}}  \def\wti{{\tilde{w}}}  \def\WCt{{\tilde{\mathcal{W}}}}
\def\Xti{{\tilde{X}}}  \def\xti{{\tilde{x}}}  \def\XCt{{\tilde{\mathcal{X}}}}
\def\Yti{{\tilde{Y}}}  \def\yti{{\tilde{y}}}  \def\YCt{{\tilde{\mathcal{Y}}}}
\def\Zti{{\tilde{Z}}}  \def\zti{{\tilde{z}}}  \def\ZCt{{\tilde{\mathcal{Z}}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%                 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% CARACTERES AVEC BARRE %%                 %%  CALLIGRAPHIES CHAPEAU  %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%                 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Ahat{{\hat{A}}}  \def\ahat{{\hat{a}}}  \def\ACh{{\hat{\mathcal{A}}}}
\def\Bhat{{\hat{B}}}  \def\bhat{{\hat{b}}}  \def\BCh{{\hat{\mathcal{B}}}}
\def\Chat{{\hat{C}}}  \def\chat{{\hat{c}}}  \def\CCh{{\hat{\mathcal{C}}}}
\def\Dhat{{\hat{D}}}  \def\dhat{{\hat{d}}}  \def\DCh{{\hat{\mathcal{D}}}}
\def\Ehat{{\hat{E}}}  \def\ehat{{\hat{e}}}  \def\ECh{{\hat{\mathcal{E}}}}
\def\Fhat{{\hat{F}}}  \def\fhat{{\hat{f}}}  \def\FCh{{\hat{\mathcal{F}}}}
\def\Ghat{{\hat{G}}}  \def\ghat{{\hat{g}}}  \def\GCh{{\hat{\mathcal{G}}}}
\def\Hhat{{\hat{H}}}  \def\hhat{{\hat{h}}}  \def\HCh{{\hat{\mathcal{H}}}}
\def\Ihat{{\hat{I}}}  \def\ihat{{\hat{i}}}  \def\ICh{{\hat{\mathcal{I}}}}
\def\Jhat{{\hat{J}}}  \def\jhat{{\hat{j}}}  \def\JCh{{\hat{\mathcal{J}}}}
\def\Khat{{\hat{K}}}  \def\khat{{\hat{k}}}  \def\KCh{{\hat{\mathcal{K}}}}
\def\Lhat{{\hat{L}}}  \def\lhat{{\hat{l}}}  \def\LCh{{\hat{\mathcal{L}}}}
\def\Mhat{{\hat{M}}}  \def\mhat{{\hat{m}}}  \def\MCh{{\hat{\mathcal{M}}}}
\def\Nhat{{\hat{N}}}  \def\nhat{{\hat{n}}}  \def\NCh{{\hat{\mathcal{N}}}}
\def\Ohat{{\hat{O}}}  \def\ohat{{\hat{o}}}  \def\OCh{{\hat{\mathcal{O}}}}
\def\Phat{{\hat{P}}}  \def\phat{{\hat{p}}}  \def\PCh{{\hat{\mathcal{P}}}}
\def\Qhat{{\hat{Q}}}  \def\qhat{{\hat{q}}}  \def\QCh{{\hat{\mathcal{Q}}}}
\def\Rhat{{\hat{R}}}  \def\rhat{{\hat{r}}}  \def\RCh{{\hat{\mathcal{R}}}}
\def\Shat{{\hat{S}}}  \def\shat{{\hat{s}}}  \def\SCh{{\hat{\mathcal{S}}}}
\def\That{{\hat{T}}}  \def\that{{\hat{t}}}  \def\TCh{{\hat{\mathcal{T}}}}
\def\Uhat{{\hat{U}}}  \def\uhat{{\hat{u}}}  \def\UCh{{\hat{\mathcal{U}}}}
\def\Vhat{{\hat{V}}}  \def\vhat{{\hat{v}}}  \def\VCh{{\hat{\mathcal{V}}}}
\def\What{{\hat{W}}}  \def\what{{\hat{w}}}  \def\WCh{{\hat{\mathcal{W}}}}
\def\Xhat{{\hat{X}}}  \def\xhat{{\hat{x}}}  \def\XCh{{\hat{\mathcal{X}}}}
\def\Yhat{{\hat{Y}}}  \def\yhat{{\hat{y}}}  \def\YCh{{\hat{\mathcal{Y}}}}
\def\Zhat{{\hat{Z}}}  \def\zhat{{\hat{z}}}  \def\ZCh{{\hat{\mathcal{Z}}}}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES AVEC POINT   %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Ado{{\dot{A}}}          \def\ado{{\dot{a}}}
\def\Bdo{{\dot{B}}}          \def\bdo{{\dot{b}}}
\def\Cdo{{\dot{C}}}          \def\cdo{{\dot{c}}}
\def\Ddo{{\dot{D}}}          \def\ddo{{\dot{d}}}
\def\Edo{{\dot{E}}}          \def\edo{{\dot{e}}}
\def\Fdo{{\dot{F}}}          \def\fdo{{\dot{f}}}
\def\Gdo{{\dot{G}}}          \def\gdo{{\dot{g}}}
\def\Hdo{{\dot{H}}}          \def\hdo{{\dot{h}}}
\def\Ido{{\dot{I}}}          \def\ido{{\dot{i}}}
\def\Jdo{{\dot{J}}}          \def\jdo{{\dot{j}}}
\def\Kdo{{\dot{K}}}          \def\kdo{{\dot{k}}}
\def\Ldo{{\dot{L}}}          \def\ldo{{\dot{l}}}
\def\Mdo{{\dot{M}}}          \def\mdo{{\dot{m}}}
\def\Ndo{{\dot{N}}}          \def\ndo{{\dot{n}}}
\def\Odo{{\dot{O}}}          \def\odo{{\dot{o}}}
\def\Pdo{{\dot{P}}}          \def\pdo{{\dot{p}}}
\def\Qdo{{\dot{Q}}}          \def\qdo{{\dot{q}}}
\def\Rdo{{\dot{R}}}          \def\rdo{{\dot{r}}}
\def\Sdo{{\dot{S}}}          \def\sdo{{\dot{s}}}
\def\Tdo{{\dot{T}}}          \def\tdo{{\dot{t}}}
\def\Udo{{\dot{U}}}          \def\udo{{\dot{u}}}
\def\Vdo{{\dot{V}}}          \def\vdo{{\dot{v}}}
\def\Wdo{{\dot{W}}}          \def\wdo{{\dot{w}}}
\def\Xdo{{\dot{X}}}          \def\xdo{{\dot{x}}}
\def\Ydo{{\dot{Y}}}          \def\ydo{{\dot{y}}}
\def\Zdo{{\dot{Z}}}          \def\zdo{{\dot{z}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES AVEC BARRE   %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Aba{{\bar{A}}}          \def\aba{{\bar{a}}}
\def\Bba{{\bar{B}}}          \def\bba{{\bar{b}}}
\def\Cba{{\bar{C}}}          \def\cba{{\bar{c}}}
\def\Dba{{\bar{D}}}          \def\dba{{\bar{d}}}
\def\Eba{{\bar{E}}}          \def\eba{{\bar{e}}}
\def\Fba{{\bar{F}}}          \def\fba{{\bar{f}}}
\def\Gba{{\bar{G}}}          \def\gba{{\bar{g}}}
\def\Hba{{\bar{H}}}          \def\hba{{\bar{h}}}
\def\Iba{{\bar{I}}}          \def\iba{{\bar{i}}}
\def\Jba{{\bar{J}}}          \def\jba{{\bar{j}}}
\def\Kba{{\bar{K}}}          \def\kba{{\bar{k}}}
\def\Lba{{\bar{L}}}          \def\lba{{\bar{l}}}
\def\Mba{{\bar{M}}}          \def\mba{{\bar{m}}}
\def\Nba{{\bar{N}}}          \def\nba{{\bar{n}}}
\def\Oba{{\bar{O}}}          \def\oba{{\bar{o}}}
\def\Pba{{\bar{P}}}          \def\pba{{\bar{p}}}
\def\Qba{{\bar{Q}}}          \def\qba{{\bar{q}}}
\def\Rba{{\bar{R}}}          \def\rba{{\bar{r}}}
\def\Sba{{\bar{S}}}          \def\sba{{\bar{s}}}
\def\Tba{{\bar{T}}}          \def\tba{{\bar{t}}}
\def\Uba{{\bar{U}}}          \def\uba{{\bar{u}}}
\def\Vba{{\bar{V}}}          \def\vba{{\bar{v}}}
\def\Wba{{\bar{W}}}          \def\wba{{\bar{w}}}
\def\Xba{{\bar{X}}}          \def\xba{{\bar{x}}}
\def\Yba{{\bar{Y}}}          \def\yba{{\bar{y}}}
\def\Zba{{\bar{Z}}}          \def\zba{{\bar{z}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES SURLIGNES   %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Aov{{\overline{A}}}          \def\aov{{\overline{a}}}
\def\Bov{{\overline{B}}}          \def\bov{{\overline{b}}}
\def\Cov{{\overline{C}}}          \def\cov{{\overline{c}}}
\def\Dov{{\overline{D}}}          \def\dov{{\overline{d}}}
\def\Eov{{\overline{E}}}          \def\eov{{\overline{e}}}
\def\Fov{{\overline{F}}}          \def\fov{{\overline{f}}}
\def\Gov{{\overline{G}}}          \def\gov{{\overline{g}}}
\def\Hov{{\overline{H}}}          \def\hov{{\overline{h}}}
\def\Iov{{\overline{I}}}          \def\iov{{\overline{i}}}
\def\Jov{{\overline{J}}}          \def\jov{{\overline{j}}}
\def\Kov{{\overline{K}}}          \def\kov{{\overline{k}}}
\def\Lov{{\overline{L}}}          \def\lov{{\overline{l}}}
\def\Mov{{\overline{M}}}          \def\mov{{\overline{m}}}
\def\Nov{{\overline{N}}}          \def\nov{{\overline{n}}}
\def\Oov{{\overline{O}}}          \def\oov{{\overline{o}}}
\def\Pov{{\overline{P}}}          \def\pov{{\overline{p}}}
\def\Qov{{\overline{Q}}}          \def\qov{{\overline{q}}}
\def\Rov{{\overline{R}}}          \def\rov{{\overline{r}}}
\def\Sov{{\overline{S}}}          \def\sov{{\overline{s}}}
\def\Tov{{\overline{T}}}          \def\tov{{\overline{t}}}
\def\Uov{{\overline{U}}}          \def\uov{{\overline{u}}}
\def\Vov{{\overline{V}}}          \def\vov{{\overline{v}}}
\def\Wov{{\overline{W}}}          \def\wov{{\overline{w}}}
\def\Xov{{\overline{X}}}          \def\xov{{\overline{x}}}
\def\Yov{{\overline{Y}}}          \def\yov{{\overline{y}}}
\def\Zov{{\overline{Z}}}          \def\zov{{\overline{z}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES GRAS AVEC TILDE    %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\Abt{{\tilde{\Ab}}}          \def\abt{{\tilde{\ab}}}
\def\Bbt{{\tilde{\Bb}}}          \def\bbt{{\tilde{\bb}}}
\def\Cbt{{\tilde{\Cb}}}          \def\cbt{{\tilde{\cb}}}
\def\Dbt{{\tilde{\Db}}}          \def\dbt{{\tilde{\db}}}
\def\Ebt{{\tilde{\Eb}}}          \def\ebt{{\tilde{\eb}}}
\def\Fbt{{\tilde{\Fb}}}          \def\fbt{{\tilde{\fb}}}
\def\Gbt{{\tilde{\Gb}}}          \def\gbt{{\tilde{\gb}}}
\def\Hbt{{\widetilde{\Hb}}}          \def\hbt{{\tilde{\hb}}}
\def\Ibt{{\tilde{\Ib}}}          \def\ibt{{\tilde{\ib}}}
\def\Jbt{{\tilde{\Jb}}}          \def\jbt{{\tilde{\jb}}}
\def\Kbt{{\tilde{\Kb}}}          \def\kbt{{\tilde{\kb}}}
\def\Lbt{{\tilde{\Lb}}}          \def\lbt{{\tilde{\lb}}}
\def\Mbt{{\tilde{\Mb}}}          \def\mbt{{\tilde{\mb}}}
\def\Nbt{{\tilde{\Nb}}}          \def\nbt{{\tilde{\nb}}}
\def\Obt{{\tilde{\Ob}}}          \def\obt{{\tilde{\ob}}}
\def\Pbt{{\tilde{\Pb}}}          \def\pbt{{\tilde{\pb}}}
\def\Qbt{{\tilde{\Qb}}}          \def\qbt{{\tilde{\qb}}}
\def\Rbt{{\tilde{\Rb}}}          \def\rbt{{\tilde{\rb}}}
\def\Sbt{{\tilde{\Sb}}}          \def\sbt{{\tilde{\sb}}}
\def\Tbt{{\tilde{\Tb}}}          \def\tbt{{\tilde{\tb}}}
\def\Ubt{{\tilde{\Ub}}}          \def\ubt{{\tilde{\ub}}}
\def\Vbt{{\tilde{\Vb}}}          \def\vbt{{\tilde{\vb}}}
\def\Wbt{{\tilde{\Wb}}}          \def\wbt{{\tilde{\wb}}}
\def\Xbt{{\tilde{\Xb}}}          \def\xbt{{\tilde{\xb}}}
\def\Ybt{{\tilde{\Yb}}}          \def\ybt{{\tilde{\yb}}}
\def\Zbt{{\tilde{\Zb}}}          \def\zbt{{\tilde{\zb}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES GRAS AVEC CHAPEAU    %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\abh{{\hat{\ab}}}          \def\Abh{{\hat{\Ab}}}
\def\bbh{{\hat{\bb}}}          \def\Bbh{{\hat{\Bb}}}
\def\cbh{{\hat{\cb}}}          \def\Cbh{{\hat{\Cb}}}
\def\dbh{{\hat{\db}}}          \def\Dbh{{\hat{\Db}}}
\def\ebh{{\hat{\eb}}}          \def\Ebh{{\hat{\Eb}}}
\def\fbh{{\hat{\fb}}}          \def\Fbh{{\hat{\Fb}}}
\def\gbh{{\hat{\gb}}}          \def\Gbh{{\hat{\Gb}}}
\def\hbh{{\hat{\hb}}}          \def\Hbh{{\hat{\Hb}}}
\def\ibh{{\hat{\ib}}}          \def\Ibh{{\hat{\Ib}}}
\def\jbh{{\hat{\jb}}}          \def\Jbh{{\hat{\Jb}}}
\def\kbh{{\hat{\kb}}}          \def\Kbh{{\hat{\Kb}}}
\def\lbh{{\hat{\lb}}}          \def\Lbh{{\hat{\Lb}}}
\def\mbh{{\hat{\mb}}}          \def\Mbh{{\hat{\Mb}}}
\def\nbh{{\hat{\nb}}}          \def\Nbh{{\hat{\Nb}}}
\def\obh{{\hat{\ob}}}          \def\Obh{{\hat{\Ob}}}
\def\pbh{{\hat{\pb}}}          \def\Pbh{{\hat{\Pb}}}
\def\qbh{{\hat{\qb}}}          \def\Qbh{{\hat{\Qb}}}
\def\rbh{{\hat{\rb}}}          \def\Rbh{{\hat{\Rb}}}
\def\sbh{{\hat{\sb}}}          \def\Sbh{{\hat{\Sb}}}
\def\tbh{{\hat{\tb}}}          \def\Tbh{{\hat{\Tb}}}
\def\ubh{{\hat{\ub}}}          \def\Ubh{{\hat{\Ub}}}
\def\vbh{{\hat{\vb}}}          \def\Vbh{{\hat{\Vb}}}
\def\wbh{{\hat{\wb}}}          \def\Wbh{{\hat{\Wb}}}
\def\xbh{{\hat{\xb}}}          \def\Xbh{{\hat{\Xb}}}
\def\ybh{{\hat{\yb}}}          \def\Ybh{{\hat{\Yb}}}
\def\zbh{{\hat{\zb}}}          \def\Zbh{{\hat{\Zb}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%    CARACTERES GRAS AVEC BARRE    %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\abo{{\overline{\ab}}}          \def\Abo{{\overline{\Ab}}}
\def\bbo{{\overline{\bb}}}          \def\Bbo{{\overline{\Bb}}}
\def\cbo{{\overline{\cb}}}          \def\Cbo{{\overline{\Cb}}}
\def\dbo{{\overline{\db}}}          \def\Dbo{{\overline{\Db}}}
\def\ebo{{\overline{\eb}}}          \def\Ebo{{\overline{\Eb}}}
\def\fbo{{\overline{\fb}}}          \def\Fbo{{\overline{\Fb}}}
\def\gbo{{\overline{\gb}}}          \def\Gbo{{\overline{\Gb}}}
\def\hbo{{\overline{\hb}}}          \def\Hbo{{\overline{\Hb}}}
\def\ibo{{\overline{\ib}}}          \def\Ibo{{\overline{\Ib}}}
\def\jbo{{\overline{\jb}}}          \def\Jbo{{\overline{\Jb}}}
\def\kbo{{\overline{\kb}}}          \def\Kbo{{\overline{\Kb}}}
\def\lbo{{\overline{\lb}}}          \def\Lbo{{\overline{\Lb}}}
\def\mbo{{\overline{\mb}}}          \def\Mbo{{\overline{\Mb}}}
\def\nbo{{\overline{\nb}}}          \def\Nbo{{\overline{\Nb}}}
\def\obo{{\overline{\ob}}}          \def\Obo{{\overline{\Ob}}}
\def\pbo{{\overline{\pb}}}          \def\Pbo{{\overline{\Pb}}}
\def\qbo{{\overline{\qb}}}          \def\Qbo{{\overline{\Qb}}}
\def\rbo{{\overline{\rb}}}          \def\Rbo{{\overline{\Rb}}}
\def\sbo{{\overline{\sb}}}          \def\Sbo{{\overline{\Sb}}}
\def\tbo{{\overline{\tb}}}          \def\Tbo{{\overline{\Tb}}}
\def\ubo{{\overline{\ub}}}          \def\Ubo{{\overline{\Ub}}}
\def\vbo{{\overline{\vb}}}          \def\Vbo{{\overline{\Vb}}}
\def\wbo{{\overline{\wb}}}          \def\Wbo{{\overline{\Wb}}}
\def\xbo{{\overline{\xb}}}          \def\Xbo{{\overline{\Xb}}}
\def\ybo{{\overline{\yb}}}          \def\Ybo{{\overline{\Yb}}}
\def\zbo{{\overline{\zb}}}          \def\Zbo{{\overline{\Zb}}}

%%%%%%%%%%%%%%%
%% GRECQUES  %%
%%%%%%%%%%%%%%%

\def\a{\alpha}
\def\b{\beta}
\def\g{\gamma}
\def\G{\Gamma}
\def\d{\delta}
\def\D{\Delta}
\def\e{\varepsilon}
\def\ph{\varphi}
\def\l{\lambda}
\def\L{\Lambda}
\def\m{\mu}
\def\o{\omega}
\def\O{\Omega}
\def\r{\rho}
\def\s{\sigma}
\def\Sig{\Sigma}
\def\th{\theta}
\def\Th{\Theta}
\def\t{\tau}
\def\x{\xi}
\def\z{\zeta}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  CARACTERES GRECS GRAS  %%            %%    CARACTERES GRECS AVEC TILDE    %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%            %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\alpb{{\boldsymbol{\alpha}}}        \def\alpt{{\tilde{\alpha}}}
\def\betb{{\boldsymbol{\beta}}}         \def\bett{{\tilde{\beta}}}
\def\gamb{{\boldsymbol{\gamma}}}        \def\gamt{{\tilde{\gamma}}}
\def\Gamb{{\boldsymbol{\Gamma}}}        \def\Gamt{{\tilde{\Gamma}}}
\def\delb{{\boldsymbol{\delta}}}        \def\delt{{\tilde{\delta}}}
\def\Delb{{\boldsymbol{\Delta}}}        \def\Delt{{\tilde{\Delta}}}
\def\epsb{{\boldsymbol{\varepsilon}}}   \def\epst{{\tilde{\varepsilon}}}
\def\phb{{\boldsymbol{\varphi}}}        \def\pht{{\tilde{\varphi}}}
\def\phib{{\boldsymbol{\phi}}}          \def\phit{{\tilde{\phi}}}
\def\Phib{{\boldsymbol{\Phi}}}          \def\Phit{{\tilde{\Phi}}}
\def\psib{{\boldsymbol{\psi}}}          \def\psit{{\tilde{\psi}}}
\def\Psib{{\boldsymbol{\Psi}}}          \def\Psit{{\tilde{\Psi}}}
\def\chib{{\boldsymbol{\chi}}}          \def\chit{{\tilde{\chi}}}
\def\lamb{{\boldsymbol{\lambda}}}       \def\lamt{{\tilde{\lambda}}}
\def\Lamb{{\boldsymbol{\Lambda}}}       \def\Lamt{{\tilde{\Lambda}}}
\def\mub{{\boldsymbol{\mu}}}            \def\mut{{\tilde{\mu}}}
\def\nub{{\boldsymbol{\nu}}}            \def\nut{{\tilde{\nu}}}
\def\omeb{{\boldsymbol{\omega}}}        \def\omet{{\tilde{\omega}}}
\def\Omeb{{\boldsymbol{\Omega}}}        \def\Omet{{\tilde{\Omega}}}
\def\pib{{\boldsymbol{\pi}}}            \def\pit{{\tilde{\pi}}}
\def\Pib{{\boldsymbol{^}}}            \def\Pit{{\tilde{\Pi}}}
\def\rhob{{\boldsymbol{\rho}}}          \def\rhot{{\tilde{\rho}}}
\def\sigb{{\boldsymbol{\sigma}}}        \def\sigt{{\tilde{\s}}}
\def\Sigb{{\boldsymbol{\Sigma}}}        \def\Sigt{{\tilde{\S}}}
\def\theb{{\boldsymbol{\theta}}}        \def\thet{{\tilde{\th}}}
\def\Theb{{\boldsymbol{\Theta}}}        \def\Thet{{\tilde{\Theta}}}
\def\taub{{\boldsymbol{\tau}}}          \def\taut{{\tilde{\t}}}
\def\xib{{\boldsymbol{\xi}}}            \def\xit{{\tilde{\xi}}}
\def\Xib{{\boldsymbol{\Xi}}}            \def\Xit{{\tilde{\Xi}}}
\def\zetb{{\boldsymbol{\zeta}}}         \def\zett{{\tilde{\zeta}}}
\def\etab{{\boldsymbol{\eta}}}          \def\etat{{\tilde{\eta}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  CARACTERES GRECS AVEC BARRE  %%  %%  CARACTERES GRECS AVEC BARRE %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\alpba{{\bar{\alpha}}}           \def\alph{{\hat{\alpha}}}
\def\betba{{\bar{\beta}}}            \def\beth{{\hat{\beta}}}
\def\gamba{{\bar{\gamma}}}           \def\gamh{{\hat{\gamma}}}
\def\Gamba{{\bar{\Gamma}}}           \def\Gamh{{\hat{\Gamma}}}
\def\delba{{\bar{\delta}}}           \def\delh{{\hat{\delta}}}
\def\Delba{{\bar{\Delta}}}           \def\Delh{{\hat{\Delta}}}
\def\epsba{{\bar{\varepsilon}}}      \def\epsh{{\hat{\varepsilon}}}
\def\phba{{\bar{\varphi}}}           \def\phh{{\hat{\varphi}}}
\def\phiba{{\bar{\phi}}}             \def\phih{{\hat{\phi}}}
\def\Phiba{{\bar{\Phi}}}             \def\Phih{{\hat{\Phi}}}
\def\psiba{{\bar{\psi}}}             \def\psih{{\hat{\psi}}}
\def\Psiba{{\bar{\Psi}}}             \def\Psih{{\hat{\Psi}}}
\def\chiba{{\bar{\chi}}}             \def\chih{{\hat{\chi}}}
\def\lamba{{\bar{\lambda}}}          \def\lamh{{\hat{\lambda}}}
\def\Lamba{{\bar{\Lambda}}}          \def\Lamh{{\hat{\Lambda}}}
\def\muba{{\bar{\mu}}}               \def\muh{{\hat{\mu}}}
\def\nuba{{\bar{\nu}}}               \def\nuh{{\hat{\nu}}}
\def\omeba{{\bar{\omega}}}           \def\omeh{{\hat{\omega}}}
\def\Omeba{{\bar{\Omega}}}           \def\Omeh{{\hat{\Omega}}}
\def\piba{{\bar{\pi}}}               \def\pih{{\hat{\pi}}}
\def\Piba{{\bar{\Pi}}}               \def\Pih{{\hat{\Pi}}}
\def\rhoba{{\bar{\rho}}}             \def\rhoh{{\hat{\rho}}}
\def\sigba{{\bar{\s}}}               \def\sigh{{\hat{\s}}}
\def\Sigba{{\bar{\S}}}               \def\Sigh{{\hat{\S}}}
\def\tauba{{\bar{\t}}}               \def\tauh{{\hat{\t}}}
\def\theba{{\bar{\theta}}}           \def\theh{{\hat{\theta}}}
\def\Theba{{\bar{\Theta}}}           \def\Theh{{\hat{\Theta}}}
\def\xiba{{\bar{\xi}}}               \def\xih{{\hat{\xi}}}
\def\Xiba{{\bar{\Xi}}}               \def\Xih{{\hat{\Xi}}}
\def\zetba{{\bar{\zeta}}}            \def\zeth{{\hat{\zeta}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  CARACTERES GRECS GRAS AVEC TILDE  %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\alpbt{{\tilde{\boldsymbol{\alpha}}}}
\def\betbt{{\tilde{\boldsymbol{\beta}}}}
\def\gambt{{\tilde{\boldsymbol{\gamma}}}}
\def\Gambt{{\tilde{\boldsymbol{\Gamma}}}}
\def\delbt{{\tilde{\boldsymbol{\delta}}}}
\def\Delbt{{\tilde{\boldsymbol{\Delta}}}}
\def\epsbt{{\tilde{\boldsymbol{\varepsilon}}}}
\def\phbt{{\tilde{\boldsymbol{\varphi}}}}
\def\phibt{{\tilde{\boldsymbol{\phi}}}}
\def\Phibt{{\tilde{\boldsymbol{\Phi}}}}
\def\psibt{{\tilde{\boldsymbol{\psi}}}}
\def\Psibt{{\tilde{\boldsymbol{\Psi}}}}
\def\pibt{{\tilde{\boldsymbol{\pi}}}}
\def\Pibt{{\tilde{\boldsymbol{\Pi}}}}
\def\chibt{{\tilde{\boldsymbol{\chi}}}}
\def\lambt{{\tilde{\boldsymbol{\lambda}}}}
\def\Lambt{{\tilde{\boldsymbol{\Lambda}}}}
\def\mubt{{\tilde{\boldsymbol{\mu}}}}
\def\nubt{{\tilde{\boldsymbol{\nu}}}}
\def\omebt{{\tilde{\boldsymbol{\omega}}}}
\def\Omebt{{\tilde{\boldsymbol{\Omega}}}}
\def\rhobt{{\tilde{\boldsymbol{\rho}}}}
\def\sigbt{{\tilde{\boldsymbol{\sig}}}}
\def\Sigbt{{\tilde{\boldsymbol{\Sig}}}}
\def\thebt{{\tilde{\boldsymbol{\theta}}}}
\def\Thebt{{\tilde{\boldsymbol{\Theta}}}}
\def\taubt{{\tilde{\boldsymbol{\tau}}}}
\def\xibt{{\tilde{\boldsymbol{\xi}}}}
\def\Xibt{{\tilde{\boldsymbol{\Xi}}}}
\def\zetbt{{\tilde{\boldsymbol{\zeta}}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  CARACTERES GRECS GRAS AVEC CHAPEAU  %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\alpbh{{\hat{\boldsymbol{\alpha}}}}
\def\betbh{{\hat{\boldsymbol{\beta}}}}
\def\gambh{{\hat{\boldsymbol{\gamma}}}}
\def\Gambh{{\hat{\boldsymbol{\Gamma}}}}
\def\delbh{{\hat{\boldsymbol{\delta}}}}
\def\Delbh{{\hat{\boldsymbol{\Delta}}}}
\def\epsbh{{\hat{\boldsymbol{\varepsilon}}}}
\def\phbh{{\hat{\boldsymbol{\varphi}}}}
\def\phibh{{\hat{\boldsymbol{\phi}}}}
\def\Phibh{{\hat{\boldsymbol{\Phi}}}}
\def\psibh{{\hat{\boldsymbol{\psi}}}}
\def\Psibh{{\hat{\boldsymbol{\Psi}}}}
\def\pibh{{\hat{\boldsymbol{\pi}}}}
\def\Pibh{{\hat{\boldsymbol{\Pi}}}}
\def\chibh{{\hat{\boldsymbol{\chi}}}}
\def\lambh{{\hat{\boldsymbol{\lambda}}}}
\def\Lambh{{\hat{\boldsymbol{\Lambda}}}}
\def\mubh{{\hat{\boldsymbol{\mu}}}}
\def\nubh{{\hat{\boldsymbol{\nu}}}}
\def\omebh{{\hat{\boldsymbol{\omega}}}}
\def\Omebh{{\hat{\boldsymbol{\Omega}}}}
\def\rhobh{{\hat{\boldsymbol{\rho}}}}
\def\sigbh{{\hat{\boldsymbol{\sig}}}}
\def\Sigbh{{\hat{\boldsymbol{\Sig}}}}
\def\thebh{{\hat{\boldsymbol{\theta}}}}
\def\Thebh{{\hat{\boldsymbol{\Theta}}}}
\def\taubh{{\hat{\boldsymbol{\tau}}}}
\def\xibh{{\hat{\boldsymbol{\xi}}}}
\def\Xibh{{\hat{\boldsymbol{\Xi}}}}
\def\zetbh{{\hat{\boldsymbol{\zeta}}}}

%%%%%%%%%%%%%%%%%
%%  FONCTEURS  %%
%%%%%%%%%%%%%%%%%

\DeclareMathOperator{\ad}{{\mathrm{ad}}}
\DeclareMathOperator{\Ad}{{\mathrm{Ad}}}
\DeclareMathOperator{\ann}{{\mathrm{ann}}}
\DeclareMathOperator{\Ann}{{\mathrm{Ann}}}
\DeclareMathOperator{\Arccos}{{\mathrm{Arccos}}}
\DeclareMathOperator{\Arcsin}{{\mathrm{Arcsin}}}
\DeclareMathOperator{\Arctan}{{\mathrm{Arctan}}}
\DeclareMathOperator{\Aut}{{\mathrm{Aut}}}
\DeclareMathOperator{\aut}{{\mathrm{Aut}}}
\DeclareMathOperator{\Bip}{{\mathrm{Bip}}}
\DeclareMathOperator{\Cent}{{\mathrm{Cent}}}
\DeclareMathOperator{\Class}{{\mathrm{Class}}}
\DeclareMathOperator{\card}{{\mathrm{card}}}
\DeclareMathOperator{\Card}{{\mathrm{Card}}}
\DeclareMathOperator{\Cl}{{\mathrm{Cl}}}
\DeclareMathOperator{\cl}{{\mathrm{Cl}}}
\DeclareMathOperator{\Coker}{{\mathrm{Coker}}}
\DeclareMathOperator{\Conj}{{\mathrm{Conj}}}
\DeclareMathOperator{\cus}{{\mathrm{cus}}}
\DeclareMathOperator{\Cus}{{\mathrm{Cus}}}
\DeclareMathOperator{\Diag}{{\mathrm{Diag}}}
\DeclareMathOperator{\End}{{\mathrm{End}}}
\DeclareMathOperator{\Ext}{{\mathrm{Ext}}}
\DeclareMathOperator{\Gal}{{\mathrm{Gal}}}
\DeclareMathOperator{\Hom}{{\mathrm{Hom}}}
\DeclareMathOperator{\htp}{{\mathrm{Htp}}}
\DeclareMathOperator{\Id}{{\mathrm{Id}}}
\DeclareMathOperator{\im}{{\mathrm{Im}}}
\DeclareMathOperator{\ind}{{\mathrm{ind}}}
\DeclareMathOperator{\Ind}{{\mathrm{Ind}}}
\DeclareMathOperator{\Inf}{{\mathrm{Inf}}}
\DeclareMathOperator{\Int}{{\mathrm{Int}}}
\DeclareMathOperator{\INT}{{\mathrm{int}}}
\DeclareMathOperator{\Irr}{{\mathrm{Irr}}}
\DeclareMathOperator{\Ker}{{\mathrm{Ker}}}
\DeclareMathOperator{\Log}{{\mathrm{Log}}}
\DeclareMathOperator{\Max}{{\mathrm{Max}}}
\DeclareMathOperator{\Mat}{{\mathrm{Mat}}}
\DeclareMathOperator{\orb}{{\mathrm{orb}}}
\DeclareMathOperator{\Out}{{\mathrm{Out}}}
\DeclareMathOperator{\Oplus}{{\oplus}}
\DeclareMathOperator{\Part}{{\mathrm{Part}}}
\DeclareMathOperator{\Proj}{{\mathrm{Proj}}}
\DeclareMathOperator{\rad}{{\mathrm{rad}}}
\DeclareMathOperator{\Rad}{{\mathrm{Rad}}}
\DeclareMathOperator{\reg}{{\mathrm{reg}}}
\DeclareMathOperator{\Reg}{{\mathrm{Reg}}}
\DeclareMathOperator{\res}{{\mathrm{res}}}
\DeclareMathOperator{\Res}{{\mathrm{Res}}}
\DeclareMathOperator{\rg}{{\mathrm{rg}}}
\DeclareMathOperator{\Sem}{{\mathrm{Sem}}}
\DeclareMathOperator{\sgn}{{\mathrm{sgn}}}
\DeclareMathOperator{\Sh}{{\mathrm{Sh}}}
\DeclareMathOperator{\Spec}{{\mathrm{Spec}}}
\DeclareMathOperator{\Specmax}{{\mathrm{Specmax}}}
\DeclareMathOperator{\St}{{\mathrm{St}}}
\DeclareMathOperator{\stab}{{\mathrm{st}}}
\DeclareMathOperator{\Stab}{{\mathrm{Stab}}}
\DeclareMathOperator{\supp}{{\mathrm{supp}}}
\DeclareMathOperator{\Supp}{{\mathrm{Supp}}}
\DeclareMathOperator{\syl}{{\mathrm{Syl}}}
\DeclareMathOperator{\Syl}{{\mathrm{Syl}}}
\DeclareMathOperator{\Tor}{{\mathrm{Tor}}}
\DeclareMathOperator{\Trace}{{\mathrm{Trace}}}
\DeclareMathOperator{\uni}{{\mathrm{uni}}}
\DeclareMathOperator{\val}{{\mathrm{val}}}
\DeclareMathOperator{\disc}{{\mathrm{disc}}}
\DeclareMathOperator{\classe}{{\mathrm{Cl}}}
\DeclareMathOperator{\longueur}{{\mathrm{Length}}}

\DeclareMathOperator{\Core}{{\mathrm{Core}}}



%%  FLECHES  %%


\def\to{\rightarrow}
\def\longto{\longrightarrow}
\def\injto{\hookrightarrow}

\def\longtrait#1{\hspace{0.3em}{~ \SS{#1} ~ \over ~}\hspace{0.3em}}
\def\longmapdown#1{\Big\downarrow
     \rlap{$\vcenter{\hbox{$\scriptstyle#1$}}$}}

\def\fonction#1#2#3#4#5{\begin{array}{rccc}
{#1} : & {#2} & \longto & {#3}  \\
& {#4} & \longmapsto & {#5} 
\end{array}}
\def\fonctionl#1#2#3#4#5{\begin{array}{rccl}
{#1} : & {#2} & \longto & {#3} \\
& {#4} & \longmapsto & {#5} 
\end{array}}
\def\fonctio#1#2#3#4{\begin{array}{ccc}
{#1} & \longto & {#2} \\
{#3} & \longmapsto & {#4} 
\end{array}}
\def\fonctiol#1#2#3#4{\begin{array}{ccl}
{#1} & \longto & {#2} \\
{#3} & \longmapsto & {#4} 
\end{array}}
\def\bijection#1#2#3#4#5{\begin{array}{rccc}
{#1} : & {#2} & \stackrel{\sim}{\longto} & {#3} \\
& {#4} & \longmapsto & {#5} 
\end{array}}
\def\bijectio#1#2#3#4{\begin{array}{ccc}
{#1} & \stackrel{\sim}{\longto} & {#2} \\
{#3} & \longmapsto & {#4} 
\end{array}}

%%%%%%%%%%%%%%%%%%%%%%%%
%%                    %%
%%      DIVERS        %%
%%                    %%
%%%%%%%%%%%%%%%%%%%%%%%%


\def\vide{\varnothing}
\def\DS{\displaystyle}
\def\SS{\scriptstyle}
\def\SSS{\scriptscriptstyle}

\def\fin{~$\SS \blacksquare$}
\def\finl{~$\blacksquare$}

\def\infspe{\hspace{0.1em}\mathop{\preccurlyeq}\nolimits\hspace{0.1em}}
\def\supspe{\hspace{0.1em}\mathop{\succurlyeq}\nolimits\hspace{0.1em}}
\def\notinfspe{\hspace{0.1em}\mathop{\not\preccurlyeq}\nolimits\hspace{0.1em}}
\def\notsupspe{\hspace{0.1em}\mathop{\not\succurlyeq}\nolimits\hspace{0.1em}}

% \def\determinant#1{\left|\begin{array}{ccccccccccccccccccc}#1\end{array}\right|}

\def\lexp#1#2{\kern\scriptspace\vphantom{#2}^{#1}\kern-\scriptspace#2}
\def\le{\hspace{0.1em}\mathop{\leqslant}\nolimits\hspace{0.1em}}
\def\ge{\hspace{0.1em}\mathop{\geqslant}\nolimits\hspace{0.1em}}
\def\notle{\hspace{0.1em}\mathop{\not\leqslant}\nolimits\hspace{0.1em}}
\def\notge{\hspace{0.1em}\mathop{\not\geqslant}\nolimits\hspace{0.1em}}

\mathchardef\inferieur="321E
\mathchardef\superieur="321F
\def\arobas{\char'100}

\def\eqna{\begin{eqnarray*}}
\def\endeqna{\end{eqnarray*}}

\def\na{\nabla}

\def\maxi{{\mathrm{max}}}
\def\tors{{\mathrm{tors}}}
\def\mini{{\mathrm{min}}}
\def\itemth#1{\item[${\mathrm{(#1)}}$]}

\def\gfp{{\FM_{\! p}}}
\def\gfq{{\FM_{\! q}}}
\def\gfpr#1{{\FM_{\! p^#1}}}
\def\gfqr#1{{\FM_{\! q^#1}}}
\def\qlb{{\overline{\QM}_{\! \ell}}}
\def\ql{{\QM}_{\! \ell}}


\def\rigolo{$\stackrel{\stackrel{\bullet~\bullet}{\SSS{\blacktriangle}}}{{\boldsymbol{\smile}}}$}





\DeclareMathOperator{\Ref}{Ref}

\def\boitegrise#1#2{\begin{centerline}{\fcolorbox{black}{shadecolor}{~
    \begin{minipage}[t]{#2}{\vphantom{~}#1\vphantom{$A_{\DS{A_A}}$}}
            \end{minipage}~}}\end{centerline}\medskip}

\def\ve{{\SSS{\vee}}}
\def\cow{{\mathrm{co}(W)}}
\def\surto{\twoheadrightarrow}
\def\module{{\text{-}}{\mathrm{mod}}}
\def\grmodule{{\mathrm{-grmod}}}


\def\Frac{{\mathrm{Frac}}}



\def\petitespace{\vphantom{$\DS{\frac{\DS{A^A}}{\DS{A_A}}}$}}
\def\trespetitespace{\vphantom{$\DS{\frac{\DS{A}}{\DS{A}}}$}}



\makeatletter
\def\hlinewd#1{%
\noalign{\ifnum0=`}\fi\hrule \@height #1 %
\futurelet\reserved@a\@xhline}
\makeatother

\newlength\epaisLigne
\newcommand\clinewd[2]{\noalign{\global\epaisLigne\arrayrulewidth\global\arrayrulewidth #1}%
\cline{#2} \noalign{\global\arrayrulewidth\epaisLigne}}



\def\dotcup{\hskip1mm\dot{\cup}\hskip1mm}

\def\copie{{\mathrm{cop}}}
\def\iso{{\mathrm{iso}}_0}

\newcommand{\longiso}{\stackrel{\sim}{\longrightarrow}}
\newcommand{\longbij}{\stackrel{\sim}{\leftrightarrow}}


\def\modules{\operatorname{\!-mod}\nolimits}
\def\bimodules{\operatorname{\!-bimod}\nolimits}
\def\Rees{\operatorname{Rees}\nolimits}
\def\codim{\operatorname{codim}\nolimits}



\newcommand{\longinjto}{\lhook\joinrel\longrightarrow}
\newcommand{\longsurto}{\relbar\joinrel\twoheadrightarrow}

\def\sing{{\mathrm{sing}}}
\def\irr{{\mathrm{irr}}}
