%%% The default set of modal commands offers % weights \mdseries and \bfseries, % shapes \upshape, \itshape, \scshape and \slshape % families \rmfamily, \sffamily and \ttfamily. % To form the \textXX commands, the first two letters of the modal % commands are always used. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% FONTS \let\oldphi=\phi \let\phi=\varphi \let\epsilon=\varepsilon % italic uppercase greek \let\Gamma\varGamma \let\Delta\varDelta \let\Theta\varTheta \let\Lambda\varLambda \let\Xi\varXi \let\Pi\varPi \let\Sigma\varSigma \let\Upsilon\varUpsilon \let\Phi\varPhi \let\Psi\varPsi \let\Omega\varOmega %% Definitions utiles: \let\goth=\smathfrak % soft math frak defined in fontsModifier.sty \let\bgoth=\sbmathfrak % soft bold math frak defined in fontsModifier.sty % \let\tmpcal=\EuScript \let\tmpcal=\mathcal %%% exinsting commands: \AA \SS \aa \ss % \AA and \aa are redefined %%% Caracteres Blackboard \renewcommand{\AA}{{\mathbb A}} \newcommand{\BB}{{\mathbb B}} \newcommand{\CC}{{\mathbb C}} \newcommand{\DD}{{\mathbb D}} \newcommand{\EE}{{\mathbb E}} \newcommand{\FF}{{\mathbb F}} \newcommand{\GG}{{\mathbb G}} \newcommand{\HH}{{\mathbb H}} \newcommand{\II}{{\mathbb I}} \newcommand{\JJ}{{\mathbb J}} \newcommand{\KK}{{\mathbb K}} \newcommand{\LL}{{\mathbb L}} \newcommand{\MM}{{\mathbb M}} \newcommand{\NN}{{\mathbb N}} \newcommand{\OO}{{\mathbb O}} \newcommand{\PP}{{\mathbb P}} \newcommand{\QQ}{{\mathbb Q}} \newcommand{\RR}{{\mathbb R}} \newcommand{\Sbb}{{\mathbb S}} \newcommand{\TT}{{\mathbb T}} \newcommand{\UU}{{\mathbb U}} \newcommand{\VV}{{\mathbb V}} \newcommand{\WW}{{\mathbb W}} \newcommand{\XX}{{\mathbb X}} \newcommand{\YY}{{\mathbb Y}} \newcommand{\ZZ}{{\mathbb Z}} %%% Majuscules scriptes \newcommand{\Aa}{{\tmpcal A}} \newcommand{\Bb}{{\tmpcal B}} \newcommand{\Cc}{{\tmpcal C}} \newcommand{\Dd}{{\tmpcal D}} \newcommand{\Ee}{{\tmpcal E}} \newcommand{\Ff}{{\tmpcal F}} \newcommand{\Gg}{{\tmpcal G}} \newcommand{\Hh}{{\tmpcal H}} \newcommand{\Ii}{{\tmpcal I}} \newcommand{\Jj}{{\tmpcal J}} \newcommand{\Kk}{{\tmpcal K}} \newcommand{\Ll}{{\tmpcal L}} \newcommand{\Mm}{{\tmpcal M}} \newcommand{\Nn}{{\tmpcal N}} \newcommand{\Oo}{{\tmpcal O}} \newcommand{\Pp}{{\tmpcal P}} \newcommand{\Qq}{{\tmpcal Q}} \newcommand{\Rr}{{\tmpcal R}} \newcommand{\Ss}{{\tmpcal S}} \newcommand{\Tt}{{\tmpcal T}} \newcommand{\Uu}{{\tmpcal U}} \newcommand{\Vv}{{\tmpcal V}} \newcommand{\Ww}{{\tmpcal W}} \newcommand{\Xx}{{\tmpcal X}} \newcommand{\Yy}{{\tmpcal Y}} \newcommand{\Zz}{{\tmpcal Z}} %%% Lettres gothiques \newcommand{\AAA}{{\goth A}} \newcommand{\aaa}{{\goth a}} \newcommand{\BBB}{{\goth B}} \newcommand{\bbb}{{\goth b}} \newcommand{\CCC}{{\goth C}} \newcommand{\ccc}{{\goth c}} \newcommand{\DDD}{{\goth D}} \newcommand{\ddd}{{\goth d}} \newcommand{\EEE}{{\goth E}} \newcommand{\eee}{{\goth e}} \newcommand{\FFF}{{\goth F}} \newcommand{\fff}{{\goth f}} \newcommand{\GGG}{{\goth G}} \def\ggg{\goth g} \newcommand{\HHH}{{\goth H}} \newcommand{\hhh}{{\goth h}} \newcommand{\III}{{\goth I}} \newcommand{\iii}{{\goth i}} \newcommand{\JJJ}{{\goth J}} \newcommand{\jjj}{{\goth j}} \newcommand{\KKK}{{\goth K}} \newcommand{\kkk}{{\goth k}} \newcommand{\LLL}{{\goth L}} \def\lll{\goth l} \newcommand{\MMM}{{\goth M}} \newcommand{\mmm}{{\goth m}} \newcommand{\NNN}{{\goth N}} \newcommand{\nnn}{{\goth n}} \newcommand{\OOO}{{\goth O}} \newcommand{\ooo}{{\goth o}} \newcommand{\PPP}{{\goth P}} \newcommand{\ppp}{{\goth p}} \newcommand{\QQQ}{{\goth Q}} \newcommand{\qqq}{{\goth q}} \newcommand{\RRR}{{\goth R}} \newcommand{\rrr}{{\goth r}} \newcommand{\SSS}{{\goth S}} \newcommand{\sss}{{\goth s}} \newcommand{\TTT}{{\goth T}} \newcommand{\ttt}{{\goth t}} \newcommand{\UUU}{{\goth U}} \newcommand{\uuu}{{\goth u}} \newcommand{\VVV}{{\goth V}} \newcommand{\vvv}{{\goth v}} \newcommand{\WWW}{{\goth W}} \newcommand{\www}{{\goth w}} \newcommand{\XXX}{{\goth X}} \newcommand{\xxx}{{\goth x}} \newcommand{\YYY}{{\goth Y}} \newcommand{\yyy}{{\goth y}} \newcommand{\ZZZ}{{\goth Z}} \newcommand{\zzz}{{\goth z}} % Lettres surmontees d'une barre \newcommand{\Abar}{{\hspace{1pt}\overline{\hspace{-1pt}A}}} \newcommand{\abar}{{\hspace{1pt}\overline{\hspace{-1pt}a}}} \newcommand{\Bbar}{{\hspace{1pt}\overline{\hspace{-1pt}B}}} \newcommand{\bbar}{{\hspace{1pt}\overline{\hspace{-1pt}b}}} \newcommand{\Cbar}{{\hspace{1pt}\overline{\hspace{-1pt}C}}} \newcommand{\cbar}{{\hspace{1pt}\overline{\hspace{-1pt}c}}} \newcommand{\Dbar}{{\hspace{1pt}\overline{\hspace{-1pt}D}}} \newcommand{\dbar}{{\hspace{1pt}\overline{\hspace{-1pt}d}}} \newcommand{\Ebar}{{\hspace{1pt}\overline{\hspace{-1pt}E}}} \newcommand{\ebar}{{\hspace{1pt}\overline{\hspace{-1pt}e}}} \newcommand{\Fbar}{{\hspace{1pt}\overline{\hspace{-1pt}F}}} \newcommand{\fbar}{{\hspace{1pt}\overline{\hspace{-1pt}f}}} \newcommand{\Gbar}{{\hspace{1pt}\overline{\hspace{-1pt}G}}} \newcommand{\gbar}{{\hspace{1pt}\overline{\hspace{-1pt}g}}} \newcommand{\Hbar}{{\hspace{1pt}\overline{\hspace{-1pt}H}}} \def\hhbar{{\,\hbar}} \renewcommand{\hbar}{{\hspace{1pt}\overline{\hspace{-1pt}h}}} \newcommand{\Ibar}{{\hspace{1pt}\overline{\hspace{-1pt}I}}} \newcommand{\ibar}{{\hspace{1pt}\overline{\hspace{-1pt}i}}} \newcommand{\Jbar}{{\hspace{1pt}\overline{\hspace{-1pt}J}}} \newcommand{\jbar}{{\hspace{1pt}\overline{\hspace{-1pt}j}}} \newcommand{\Kbar}{{\hspace{1pt}\overline{\hspace{-1pt}K}}} \newcommand{\kbar}{{\hspace{1pt}\overline{\hspace{-1pt}k}}} \newcommand{\Lbar}{{\hspace{1pt}\overline{\hspace{-1pt}L}}} \newcommand{\lbar}{{\hspace{1pt}\overline{\hspace{-1pt}l}}} \newcommand{\Mbar}{{\hspace{1pt}\overline{\hspace{-1pt}M}}} \newcommand{\mbar}{{\hspace{1pt}\overline{\hspace{-1pt}m}}} \newcommand{\Nbar}{{\hspace{1pt}\overline{\hspace{-1pt}N}}} \newcommand{\nbar}{{\hspace{1pt}\overline{\hspace{-1pt}n}}} \newcommand{\Obar}{{\hspace{1pt}\overline{\hspace{-1pt}O}}} \newcommand{\obar}{{\hspace{1pt}\overline{\hspace{-1pt}o}}} \newcommand{\Pbar}{{\hspace{1pt}\overline{\hspace{-1pt}P}}} \newcommand{\pbar}{{\hspace{1pt}\overline{\hspace{-1pt}p}}} \newcommand{\Qbar}{{\hspace{1pt}\overline{\hspace{-1pt}Q}}} \newcommand{\qbar}{{\hspace{1pt}\overline{\hspace{-1pt}q}}} \newcommand{\Rbar}{{\hspace{1pt}\overline{\hspace{-1pt}R}}} \newcommand{\rbar}{{\hspace{1pt}\overline{\hspace{-1pt}r}}} \newcommand{\Sbar}{{\hspace{1pt}\overline{\hspace{-1pt}S}}} \newcommand{\sbar}{{\hspace{1pt}\overline{\hspace{-1pt}s}}} \newcommand{\Tbar}{{\hspace{1pt}\overline{\hspace{-1pt}T}}} \newcommand{\tbar}{{\hspace{1pt}\overline{\hspace{-1pt}t}}} \newcommand{\Ubar}{{\hspace{1pt}\overline{\hspace{-1pt}U}}} \newcommand{\ubar}{{\hspace{1pt}\overline{\hspace{-1pt}u}}} \newcommand{\Vbar}{{\hspace{1pt}\overline{\hspace{-1pt}V}}} \newcommand{\vbar}{{\hspace{1pt}\overline{\hspace{-1pt}v}}} \newcommand{\Wbar}{{\hspace{1pt}\overline{\hspace{-1pt}W}}} \newcommand{\wbar}{{\hspace{1pt}\overline{\hspace{-1pt}w}}} \newcommand{\Xbar}{{\hspace{1pt}\overline{\hspace{-1pt}X}}} \newcommand{\xbar}{{\hspace{1pt}\overline{\hspace{-1pt}x}}} \newcommand{\Ybar}{{\,\overline{Y}}} \newcommand{\ybar}{{\hspace{1pt}\overline{\hspace{-1pt}y}}} \newcommand{\Zbar}{{\hspace{1pt}\overline{\hspace{-1pt}Z}}} \newcommand{\zbar}{{\hspace{1pt}\overline{\hspace{-1pt}z}}} \newcommand{\alphabar}{\operatorname{\overline{\alpha}}} \newcommand{\betabar}{\operatorname{\overline{\beta}}} \newcommand{\gammabar}{\operatorname{\overline{\gamma}}} \newcommand{\Gammabar}{\operatorname{\overline{\Gamma}}} \newcommand{\deltabar}{\operatorname{\overline{\delta}}} \newcommand{\Deltabar}{\operatorname{\overline{\Delta}}} \newcommand{\epsilonbar}{\operatorname{\overline{\epsilon}}} \newcommand{\zetabar}{\operatorname{\overline{\zeta}}} \newcommand{\etabar}{\operatorname{\overline{\eta}}} \newcommand{\thetabar}{\operatorname{\overline{\theta}}} \newcommand{\Thetabar}{\operatorname{\overline{\Theta}}} \newcommand{\iotabar}{\operatorname{\overline{\iota}}} \newcommand{\kappabar}{\operatorname{\overline{\kappa}}} \newcommand{\lambdabar}{\operatorname{\overline{\lambda}}} \newcommand{\Lambdabar}{\operatorname{\overline{\Lambda}}} \newcommand{\mubar}{\operatorname{\overline{\mu}}} \newcommand{\nubar}{\operatorname{\overline{\nu}}} \newcommand{\xibar}{\operatorname{\overline{\xi}}} \newcommand{\Xibar}{\operatorname{\overline{\Xi}}} \newcommand{\pibar}{\operatorname{\overline{\pi}}} \newcommand{\Pibar}{\operatorname{\overline{\Pi}}} \newcommand{\rhobar}{\operatorname{\overline{\rho}}} \newcommand{\sigmabar}{\operatorname{\overline{\sigma}}} \newcommand{\Sigmabar}{\operatorname{\overline{\Sigma}}} \newcommand{\taubar}{\operatorname{\overline{\tau}}} \newcommand{\phibar}{\operatorname{\overline{\phi}}} \newcommand{\Phibar}{\operatorname{\overline{\Phi}}} \newcommand{\chibar}{\operatorname{\overline{\chi}}} \newcommand{\psibar}{\operatorname{\overline{\psi}}} \newcommand{\Psibar}{\operatorname{\overline{\Psi}}} \newcommand{\omegabar}{\operatorname{\overline{\omega}}} \newcommand{\Omegabar}{\operatorname{\overline{\Omega}}} \newcommand{\xxbar}{{\,\overline{\xx}}} \newcommand{\yybar}{{\,\overline{\yy}}} \newcommand{\zzbar}{{\,\overline{\zz}}} \newcommand{\partialbar}{\operatorname{\;\overline{\!\partial}}} %%% Lettres surmontees d'un tilde \newcommand{\Atilde}{{\,\widetilde{\!A}}} \newcommand{\atilde}{{\,\widetilde{\!a}}} \newcommand{\Btilde}{{\,\widetilde{\!B}}} \newcommand{\btilde}{{\,\widetilde{\!b}}} \newcommand{\Ctilde}{{\,\widetilde{\!C}}} \newcommand{\ctilde}{{\,\widetilde{\!c}}} \newcommand{\Dtilde}{{\,\widetilde{\!D}}} \newcommand{\dtilde}{{\,\widetilde{\!d}}} \newcommand{\Etilde}{{\,\widetilde{\!E}}} \newcommand{\etilde}{{\,\widetilde{\!e}}} \newcommand{\Ftilde}{{\,\widetilde{\!F}}} \newcommand{\ftilde}{{\,\widetilde{\!f}}} \newcommand{\Gtilde}{{\,\widetilde{\!G}}} \newcommand{\gtilde}{{\,\widetilde{\!g}}} \newcommand{\Htilde}{{\,\widetilde{\!H}}} \newcommand{\htilde}{{\,\widetilde{\!h}}} \newcommand{\Itilde}{{\,\widetilde{\!I}}} \newcommand{\itilde}{{\,\widetilde{\!i}}} \newcommand{\Jtilde}{{\,\widetilde{\!J}}} \newcommand{\jtilde}{{\,\widetilde{\!j}}} \newcommand{\Ktilde}{{\,\widetilde{\!K}}} \newcommand{\ktilde}{{\,\widetilde{\!k}}} \newcommand{\Ltilde}{{\,\widetilde{\!L}}} \newcommand{\ltilde}{{\,\widetilde{\!l}}} \newcommand{\Mtilde}{{\,\widetilde{\!M}}} \newcommand{\mtilde}{{\,\widetilde{\!m}}} \newcommand{\Ntilde}{{\,\widetilde{\!N}}} \newcommand{\ntilde}{{\,\widetilde{\!n}}} \newcommand{\Otilde}{{\,\widetilde{\!O}}} \newcommand{\otilde}{{\,\widetilde{\!o}}} \newcommand{\Ptilde}{{\,\widetilde{\!P}}} \newcommand{\ptilde}{{\,\widetilde{\!p}}} \newcommand{\Qtilde}{{\,\widetilde{\!Q}}} \newcommand{\qtilde}{{\,\widetilde{\!q}}} \newcommand{\Rtilde}{{\,\widetilde{\!R}}} \newcommand{\rtilde}{{\,\widetilde{\!r}}} \newcommand{\Stilde}{{\,\widetilde{\!S}}} \newcommand{\stilde}{{\,\widetilde{\!s}}} \newcommand{\Ttilde}{{\,\widetilde{\!T}}} \newcommand{\ttilde}{{\,\widetilde{\!t}}} \newcommand{\Utilde}{{\,\widetilde{\!U}}} \newcommand{\utilde}{{\,\widetilde{\!u}}} \newcommand{\Vtilde}{{\,\widetilde{\!V}}} \newcommand{\vtilde}{{\,\widetilde{\!v}}} \newcommand{\Wtilde}{{\,\widetilde{\!W}}} \newcommand{\wtilde}{{\,\widetilde{\!w}}} \newcommand{\Xtilde}{{\,\widetilde{\!X}}} \newcommand{\xtilde}{{\,\widetilde{\!x}}} \newcommand{\Ytilde}{{\,\widetilde{\!Y}}} \newcommand{\ytilde}{{\,\widetilde{\!y}}} \newcommand{\Ztilde}{{\,\widetilde{\!Z}}} \newcommand{\ztilde}{{\,\widetilde{\!z}}} \newcommand{\alphatilde}{\operatorname{\;\widetilde{\!\alpha}}} \newcommand{\betatilde}{\operatorname{\;\widetilde{\!\beta}}} \newcommand{\gammatilde}{\operatorname{\;\widetilde{\!\gamma}}} \newcommand{\Gammatilde}{\operatorname{\;\widetilde{\!\Gamma}}} \newcommand{\deltatilde}{\operatorname{\;\widetilde{\!\delta}}} \newcommand{\Deltatilde}{\operatorname{\;\widetilde{\!\Delta}}} \newcommand{\epsilontilde}{\operatorname{\;\widetilde{\!\epsilon}}} \newcommand{\zetatilde}{\operatorname{\;\widetilde{\!\zeta}}} \newcommand{\etatilde}{\operatorname{\;\widetilde{\!\eta}}} \newcommand{\thetatilde}{\operatorname{\;\widetilde{\!\theta}}} \newcommand{\Thetatilde}{\operatorname{\;\widetilde{\!\Theta}}} \newcommand{\iotatilde}{\operatorname{\;\widetilde{\!\iota}}} \newcommand{\kappatilde}{\operatorname{\;\widetilde{\!\kappa}}} \newcommand{\lambdatilde}{\operatorname{\;\widetilde{\!\lambda}}} \newcommand{\Lambdatilde}{\operatorname{\;\widetilde{\!\Lambda}}} \newcommand{\mutilde}{\operatorname{\;\widetilde{\!\mu}}} \newcommand{\nutilde}{\operatorname{\;\widetilde{\!\nu}}} \newcommand{\xitilde}{\operatorname{\;\widetilde{\!\xi}}} \newcommand{\Xitilde}{\operatorname{\;\widetilde{\!\Xi}}} \newcommand{\pitilde}{\operatorname{\;\widetilde{\!\pi}}} \newcommand{\rhotilde}{\operatorname{\;\widetilde{\!\rho}}} \newcommand{\sigmatilde}{\operatorname{\;\widetilde{\!\sigma}}} \newcommand{\Sigmatilde}{\operatorname{\;\widetilde{\!\Sigma}}} \newcommand{\tautilde}{\operatorname{\;\widetilde{\!\tau}}} \newcommand{\phitilde}{\operatorname{\;\widetilde{\!\phi}}} \newcommand{\Phitilde}{\operatorname{\;\widetilde{\!\Phi}}} \newcommand{\chitilde}{\operatorname{\;\widetilde{\!\chi}}} \newcommand{\psitilde}{\operatorname{\;\widetilde{\!\psi}}} \newcommand{\Psitilde}{\operatorname{\;\widetilde{\!\Psi}}} \newcommand{\omegatilde}{\operatorname{\;\widetilde{\!\omega}}} \newcommand{\Omegatilde}{\operatorname{\;\widetilde{\!\Omega}}} \newcommand{\Rrtilde}{{\,\widetilde{\!\Rr}}} %%% Lettres surmontees d'un chapeau \newcommand{\Ahat}{{\,\widehat{\!A}}} \newcommand{\ahat}{{\,\widehat{\!a}}} \newcommand{\Bhat}{{\,\widehat{\!B}}} \newcommand{\bhat}{{\,\widehat{\!b}}} \newcommand{\Chat}{{\,\widehat{\!C}}} \newcommand{\chat}{{\,\widehat{\!c}}} \newcommand{\Dhat}{{\,\widehat{\!D}}} \newcommand{\dhat}{{\,\widehat{\!d}}} \newcommand{\Ehat}{{\,\widehat{\!E}}} \newcommand{\ehat}{{\,\widehat{\!e}}} \newcommand{\Fhat}{{\,\widehat{\!F}}} \newcommand{\fhat}{{\,\widehat{\!f}}} \newcommand{\Ghat}{{\,\widehat{\!G}}} \newcommand{\ghat}{{\,\widehat{\!g}}} \newcommand{\Hhat}{{\,\widehat{\!H}}} \newcommand{\hhat}{{\,\widehat{\!h}}} \newcommand{\Ihat}{{\,\widehat{\!I}}} \newcommand{\ihat}{{\,\widehat{\!i}}} \newcommand{\Jhat}{{\,\widehat{\!J}}} \newcommand{\jhat}{{\,\widehat{\!j}}} \newcommand{\Khat}{{\,\widehat{\!K}}} \newcommand{\khat}{{\,\widehat{\!k}}} \newcommand{\Lhat}{{\,\widehat{\!L}}} \newcommand{\lhat}{{\,\widehat{\!l}}} \newcommand{\Mhat}{{\,\widehat{\!M}}} \newcommand{\mhat}{{\,\widehat{\!m}}} \newcommand{\Nhat}{{\,\widehat{\!N}}} \newcommand{\nhat}{{\,\widehat{\!n}}} \newcommand{\Ohat}{{\,\widehat{\!O}}} \newcommand{\ohat}{{\,\widehat{\!o}}} \newcommand{\Phat}{{\,\widehat{\!P}}} \newcommand{\phat}{{\,\widehat{\!p}}} \newcommand{\Qhat}{{\,\widehat{\!Q}}} \newcommand{\qhat}{{\,\widehat{\!q}}} \newcommand{\Rhat}{{\,\widehat{\!R}}} \newcommand{\rhat}{{\,\widehat{\!r}}} \newcommand{\Shat}{{\,\widehat{\!S}}} \newcommand{\shat}{{\,\widehat{\!s}}} \newcommand{\That}{{\,\widehat{\!T}}} \newcommand{\that}{{\,\widehat{\!t}}} \newcommand{\Uhat}{{\,\widehat{\!U}}} \newcommand{\uhat}{{\,\widehat{\!u}}} \newcommand{\Vhat}{{\,\widehat{\!V}}} \newcommand{\vhat}{{\,\widehat{\!v}}} \newcommand{\What}{{\,\widehat{\!W}}} \newcommand{\what}{{\,\widehat{\!w}}} \newcommand{\Xhat}{{\,\widehat{\!X}}} \newcommand{\xhat}{{\,\widehat{\!x}}} \newcommand{\Yhat}{{\,\widehat{Y}}} \newcommand{\yhat}{{\,\widehat{\!y}}} \newcommand{\Zhat}{{\,\widehat{\!Z}}} \newcommand{\zhat}{{\,\widehat{\!z}}} \newcommand{\alphahat}{\operatorname{\;\widehat{\!\alpha}}} \newcommand{\betahat}{\operatorname{\;\widehat{\!\beta}}} \newcommand{\gammahat}{\operatorname{\;\widehat{\!\gamma}}} \newcommand{\Gammahat}{\operatorname{\;\widehat{\!\Gamma}}} \newcommand{\deltahat}{\operatorname{\;\widehat{\!\delta}}} \newcommand{\Deltahat}{\operatorname{\;\widehat{\!\Delta}}} \newcommand{\epsilonhat}{\operatorname{\;\widehat{\!\epsilon}}} \newcommand{\zetahat}{\operatorname{\;\widehat{\!\zeta}}} \newcommand{\etahat}{\operatorname{\;\widehat{\!\eta}}} \newcommand{\thetahat}{\operatorname{\;\widehat{\!\theta}}} \newcommand{\Thetahat}{\operatorname{\;\widehat{\!\Theta}}} \newcommand{\iotahat}{\operatorname{\;\widehat{\!\iota}}} \newcommand{\kappahat}{\operatorname{\;\widehat{\!\kappa}}} \newcommand{\lambdahat}{\operatorname{\;\widehat{\!\lambda}}} \newcommand{\Lambdahat}{\operatorname{\;\widehat{\!\Lambda}}} \newcommand{\muhat}{\operatorname{\;\widehat{\!\mu}}} \newcommand{\nuhat}{\operatorname{\;\widehat{\!\nu}}} \newcommand{\xihat}{\operatorname{\;\widehat{\!\xi}}} \newcommand{\Xihat}{\operatorname{\;\widehat{\!\Xi}}} \newcommand{\pihat}{\operatorname{\;\widehat{\!\pi}}} \newcommand{\rhohat}{\operatorname{\;\widehat{\!\rho}}} \newcommand{\sigmahat}{\operatorname{\;\widehat{\!\sigma}}} \newcommand{\Sigmahat}{\operatorname{\;\widehat{\!\Sigma}}} \newcommand{\tauhat}{\operatorname{\;\widehat{\!\tau}}} \newcommand{\phihat}{\operatorname{\;\widehat{\!\phi}}} \newcommand{\Phihat}{\operatorname{\;\widehat{\!\Phi}}} \newcommand{\chihat}{\operatorname{\;\widehat{\!\chi}}} \newcommand{\psihat}{\operatorname{\;\widehat{\!\psi}}} \newcommand{\Psihat}{\operatorname{\;\widehat{\!\Psi}}} \newcommand{\omegahat}{\operatorname{\;\widehat{\!\omega}}} \newcommand{\Omegahat}{\operatorname{\;\widehat{\!\Omega}}} % Mixed symbols \newcommand{\Kkbar}{{\hspace{1pt}\overline{\hspace{-1pt}\Kk}}} \newcommand{\Kkbf}{{\boldsymbol{\Kk}}} \newcommand{\Kkbfbar}{{\hspace{1pt}\overline{\hspace{-1pt}\Kkbf}}} %%% Lettres grasses en formules: \newcommand{\aalpha}{{\boldsymbol{\alpha}}} \newcommand{\bbeta}{{\boldsymbol{\beta}}} \newcommand{\ggamma}{{\boldsymbol{\gamma}}} \newcommand{\gGamma}{{\boldsymbol{\Gamma}}} \newcommand{\ddelta}{{\boldsymbol{\delta}}} \newcommand{\dDelta}{{\boldsymbol{\Delta}}} \newcommand{\zzeta}{{\boldsymbol{\zeta}}} \newcommand{\eeta}{{\boldsymbol{\eta}}} \newcommand{\eepsilon}{{\boldsymbol{\epsilon}}} \newcommand{\ttheta}{{\boldsymbol{\theta}}} \newcommand{\tTheta}{{\boldsymbol{\Theta}}} \newcommand{\kkappa}{{\boldsymbol{\kappa}}} \newcommand{\llambda}{{\boldsymbol{\lambda}}} \newcommand{\lLambda}{{\boldsymbol{\Lambda}}} \newcommand{\mmu}{{\boldsymbol{\mu}}} \newcommand{\nnu}{{\boldsymbol{\nu}}} \newcommand{\xxi}{{\boldsymbol{\xi}}} \newcommand{\xXi}{{\boldsymbol{\Xi}}} \newcommand{\ppi}{{\boldsymbol{\pi}}} \newcommand{\pPi}{{\boldsymbol{\Pi}}} \newcommand{\rrho}{{\boldsymbol{\rho}}} \newcommand{\ssigma}{{\boldsymbol{\sigma}}} \newcommand{\sSigma}{{\boldsymbol{\Sigma}}} \newcommand{\ttau}{{\boldsymbol{\tau}}} \newcommand{\pphi}{{\boldsymbol{\phi}}} \newcommand{\ppsi}{{\boldsymbol{\psi}}} \newcommand{\pPsi}{{\boldsymbol{\Psi}}} \newcommand{\cchi}{{\boldsymbol{\chi}}} \newcommand{\oomega}{{\boldsymbol{\omega}}} \newcommand{\oOmega}{{\boldsymbol{\Omega}}} \newcommand{\iiota}{{\boldsymbol{\iota}}} \renewcommand{\aa}{{\boldsymbol{a}}} \newcommand{\aA}{{\boldsymbol{A}}} \newcommand{\bb}{{\boldsymbol{b}}} \newcommand{\bB}{{\boldsymbol{B}}} \newcommand{\cc}{{\boldsymbol{c}}} \newcommand{\cC}{{\boldsymbol{C}}} \newcommand{\dd}{{\boldsymbol{d}}} \newcommand{\dD}{{\boldsymbol{D}}} \newcommand{\ee}{{\boldsymbol{e}}} \newcommand{\eE}{{\boldsymbol{E}}} \newcommand{\ff}{{\boldsymbol{f}}} \newcommand{\fF}{{\boldsymbol{F}}} \newcommand{\gvg}{>\!\!>} \renewcommand{\gg}{{\boldsymbol{g}}} \newcommand{\gG}{{\boldsymbol{G}}} \newcommand{\hh}{{\boldsymbol{h}}} \newcommand{\hH}{{\boldsymbol{H}}} \newcommand{\ii}{{\boldsymbol{i}}} \newcommand{\iI}{{\boldsymbol{I}}} \newcommand{\jj}{{\boldsymbol{j}}} \newcommand{\jJ}{{\boldsymbol{J}}} \newcommand{\kk}{{\boldsymbol{k}}} \newcommand{\kK}{{\boldsymbol{K}}} \newcommand{\lbf}{{\boldsymbol{l}}} \newcommand{\lL}{{\boldsymbol{L}}} \newcommand{\mm}{{\boldsymbol{m}}} \newcommand{\mM}{{\boldsymbol{M}}} \newcommand{\nn}{{\boldsymbol{n}}} \newcommand{\nN}{{\boldsymbol{N}}} \newcommand{\oo}{{\boldsymbol{o}}} \newcommand{\oO}{{\boldsymbol{O}}} \newcommand{\pp}{{\boldsymbol{p}}} \newcommand{\pP}{{\boldsymbol{P}}} \newcommand{\qq}{{\boldsymbol{q}}} \newcommand{\qQ}{{\boldsymbol{Q}}} \newcommand{\rr}{{\boldsymbol{r}}} \newcommand{\rR}{{\boldsymbol{R}}} \renewcommand{\ss}{{\boldsymbol{s}}} \newcommand{\sS}{{\boldsymbol{S}}} \newcommand{\tbf}{{\boldsymbol{t}}} \newcommand{\tT}{{\boldsymbol{T}}} \newcommand{\uu}{{\boldsymbol{u}}} \newcommand{\uU}{{\boldsymbol{U}}} \newcommand{\vv}{{\boldsymbol{v}}} \newcommand{\vV}{{\boldsymbol{V}}} \newcommand{\ww}{{\boldsymbol{w}}} \newcommand{\wW}{{\boldsymbol{W}}} \newcommand{\xx}{{\boldsymbol{x}}} \newcommand{\xX}{{\boldsymbol{X}}} \newcommand{\yy}{{\boldsymbol{y}}} \newcommand{\yY}{{\boldsymbol{Y}}} \newcommand{\zz}{{\boldsymbol{z}}} \newcommand{\zZ}{{\boldsymbol{Z}}} \newcommand{\one}{\boldsymbol{1}} \newcommand{\zero}{\boldsymbol{0}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% for pleasant looking := or =: \newcommand*{\defeq}{\mathrel{\vcenter{\baselineskip0.5ex\lineskiplimit0pt \hbox{\scriptsize.}\hbox{\scriptsize.}}}=} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Operators and not only \newcommand{\Ad}{\operatorname{Ad}} \newcommand{\aff}{\operatorname{\mathbf{aff}}} \newcommand{\Alb}{\operatorname{Alb}} \newcommand{\Aff}{\operatorname{Aff}} \newcommand{\Alt}{\operatorname{Alt}} \newcommand{\Arg}{\operatorname{Arg}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\Bl}{\operatorname{Bl}} \newcommand{\card}{\operatorname{card}} \newcommand{\ch}{\operatorname{char}} \newcommand{\codim}{\operatorname{codim}} \newcommand{\coker}{\operatorname{coker}} \newcommand{\conv}{\operatorname{\mathbf{conv}}} \newcommand{\cone}{\operatorname{\mathbf{cone}}} \newcommand{\cosec}{\operatorname{cosec}} \newcommand{\cotan}{\operatorname{cotan}} \newcommand{\Der}{\operatorname{Der}} \newcommand{\Diff}{\operatorname{Diff}} \newcommand{\Div}{\operatorname{Div}} % \newcommand{\div}{\operatorname{div}} \newcommand{\Eend}{\Ee nd\/} \newcommand{\End}{\operatorname{End}} \newcommand{\ev}{\operatorname{ev}} \newcommand{\except}{\operatorname{except}} \newcommand{\Ext}{\operatorname{Ext}} \newcommand{\Extcal}{\Ee xt} \newcommand{\ext}{\operatorname{ext}} \newcommand{\Gal}{\operatorname{Gal}} \newcommand{\gl}{\ggg\hspace{.02ex}\lll\hspace{.1ex}} % \newcommand{\Gr}{G} % \newcommand{\Gr}{\operatorname{Gr}} \newcommand{\gradient}{\raisebox{.2ex}{$\bigtriangledown$}} \newcommand{\hcf}{\operatorname{hcf}\,} \newcommand{\Hilb}{\operatorname{Hilb}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\Homcal}{\Hh om} \newcommand{\id}{\textsl{id}} \newcommand{\im}{\operatorname{im}} \newcommand{\Iso}{\operatorname{Iso}} \newcommand{\Jac}{\operatorname{Jac}} \newcommand{\lct}{\operatorname{lct}} % log canonical threshold \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\Lie}{\operatorname{Lie}} \newcommand{\Log}{\operatorname{Log}} \newcommand{\mult}{\operatorname{mult}} \newcommand{\ord}{\operatorname{ord}} \newcommand{\NE}{\operatorname{NE}} \newcommand{\NEbar}{\overline{\operatorname{NE}}} \newcommand{\NS}{\operatorname{NS}} \newcommand{\Num}{\operatorname{Num}} \newcommand{\Newt}{\operatorname{Newt}} \newcommand{\Pic}{\operatorname{Pic}} \newcommand{\Projbf}{\mathbf{Proj\,}} \newcommand{\Proj}{\operatorname{Proj}} \newcommand{\rank}{\operatorname{rank}} \newcommand{\re}{\operatorname{Re}} \newcommand{\Res}{\operatorname{Res}} \newcommand{\rg}{\operatorname{rg}} \newcommand{\Sec}{\operatorname{Sec}} \newcommand{\setwith}{\hspace{.6ex}\middle|\hspace{.6ex}} \newcommand{\set}[2]{\left\{ {#1} \setwith {#2} \right\}} \newcommand{\Sim}{\operatorname{S}} \newcommand{\sla}{\sss\hspace{.02ex}\lll\hspace{.1ex}} \newcommand{\Span}{\operatorname{Span}} \newcommand{\Spec}{\operatorname{Spec}} \newcommand{\Specbf}{\mathbf{Spec\,}} \newcommand{\Spm}{\operatorname{Spm}} \newcommand{\Sing}{\operatorname{Sing}} \newcommand{\supp}{\operatorname{supp}} \newcommand{\Sym}{\operatorname{Sym}} \newcommand{\td}{\operatorname{td}} \newcommand{\tr}{\operatorname{tr}} \newcommand{\trace}{\operatorname{trace}} \newcommand{\Tr}{\operatorname{Tr}} \newcommand{\Trace}{\operatorname{Tr}} \newcommand{\Vect}{\operatorname{Vect}} \newcommand{\vol}{\operatorname{Vol}} %%%%%%%%%%%%%%%%% %%% classical groups % \newcommand{\lineargroup}[1]{\textsl{#1}} \newcommand{\lineargroup}[1]{\operatorname{#1}} \newcommand{\GA}{\lineargroup{GA}} \newcommand{\GL}{\lineargroup{GL}} \newcommand{\SL}{\lineargroup{SL}} \newcommand{\SO}{\lineargroup{SO}} \newcommand{\SU}{\lineargroup{SU}} \newcommand{\PGL}{\lineargroup{PGL}} \renewcommand{\O}{\lineargroup{O}} \newcommand{\U}{\lineargroup{U}} \newcommand{\Bigwedge}{% \mathchoice{% \tikz[baseline=.3ex]{% \path[use as bounding box] (0, 0) rectangle (1.55ex, 2.2ex); \draw[-] (0, 0) -- (.8ex, 2.15ex) -- (1.6ex, 0); } }{\tikz[baseline=.0ex]{% (0, 0) rectangle (1.3ex, 1.7ex); \draw[-] (0, 0) -- (.6ex, 1.6ex) -- (1.2ex, 0); } }{\wedge}{\wedge} } % \newcommand{\dual}{^\ast} \newcommand{\dual}{^\vee} \newlength{\tmpH} % lengths for the next command \newlength{\tmpW} \newcommand{\overarc}[1]{% \settoheight{\tmpH}{#1} \settowidth{\tmpW}{#1} \begin{tikzpicture} \useasboundingbox (0,0) rectangle ++(1\tmpW+.5ex,1\tmpH); \path (0,0) node[anchor=south west, inner sep=0pt] {$#1$}; \draw[very thin] (.2ex,1\tmpH+.4ex) to[out=17, in=163] ++(1\tmpW,0); \end{tikzpicture} } \newenvironment{psmallmatrix}% {\left(\begin{smallmatrix}}{\end{smallmatrix}\right)} \newenvironment{vsmallmatrix}% {\left|\begin{smallmatrix}}{\end{smallmatrix}\right|} \newcommand{\lcmatrix}[2][]{% \ifthenelse{\equal{#1}{}}{% \mathchoice{% \begin{pmatrix}#2\end{pmatrix}}{% \begin{psmallmatrix}#2\end{psmallmatrix}}{% \begin{psmallmatrix}#2\end{psmallmatrix}}{% \begin{psmallmatrix}#2\end{psmallmatrix}} }{ \mathchoice{% \begin{vmatrix}#2\end{vmatrix}}{% \begin{vsmallmatrix}#2\end{vsmallmatrix}}{% \begin{vsmallmatrix}#2\end{vsmallmatrix}}{% \begin{vsmallmatrix}#2\end{vsmallmatrix}} } } \newcommand{\amatrix}[1]{% augmanted matrix \vcenter{% \hbox{% \begin{tikzpicture}[% every node/.style={outer sep=0pt, inner xsep=-.4ex, inner ysep=0ex}, pivot/.style={% circle, fill=R!70!O, fill opacity=.2, inner sep=.5ex, text opacity=1 }] \matrix[matrix of math nodes, nodes={outer sep=0pt, inner xsep=.8ex, inner ysep=.65ex}, %align=right, left delimiter=(, right delimiter=), ampersand replacement=\&] { #1 \\}; \end{tikzpicture} } } } \newcommand{\inv}{^{-1}} \newcommand{\gge}{{>\!\!>}} \newcommand{\lle}{{\ll}} %%% Arrows % \let\embeds=\hookrightarrow \let\lra=\longrightarrow \newcommand{\lrarrow}[1]{\stackrel{#1}{\longrightarrow}} \newcommand{\dashto}{% \mathrel{\tikz{\draw[->, dashed, dash pattern=on 2.5pt off 2pt] (0,0) -- ++(.97em, 0);}\hspace{.2ex}} } \newcommand{\longdashto}{% \mathrel{\tikz{\draw[->, dashed, dash pattern=on 2.5pt off 2pt] (0,0) -- ++(1.5em, 0);}\hspace{.2ex}} } \newcommand{\tendsto}[1][]{% \hspace{1ex}% \ifthenelse{\equal{#1}{}}{% \underset{n\to+\infty}{% \tikz{\draw[->] (0,0) -- ++(4em, 0); } } }{% \underset{#1}{% \tikz{\draw[->] (0,0) -- ++(4em, 0); } } }% \hspace{1ex} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \renewcommand{\vector}[1]{\overarrow{#1}} \renewcommand{\vector}[1]{{\overrightarrow{#1}}} \let\vecteur=\vector %%% Vectors \newcommand{\Avec}{{\overrightarrow{A}}} \newcommand{\avec}{{\overrightarrow{a}}} \newcommand{\Bvec}{{\overrightarrow{B}}} \newcommand{\bvec}{{\overrightarrow{b}}} \newcommand{\Cvec}{{\overrightarrow{C}}} \newcommand{\cvec}{{\overrightarrow{c}}} \newcommand{\Dvec}{{\overrightarrow{D}}} \newcommand{\dvec}{{\overrightarrow{d}}} \newcommand{\Evec}{{\overrightarrow{E}}} \newcommand{\evec}{{\overrightarrow{e}}} \newcommand{\Fvec}{{\overrightarrow{F}}} \newcommand{\fvec}{{\overrightarrow{f}}} \newcommand{\Gvec}{{\overrightarrow{G}}} \newcommand{\gvec}{{\overrightarrow{g}}} \newcommand{\Hvec}{{\overrightarrow{H}}} \newcommand{\hvec}{{\overrightarrow{h}}} \newcommand{\Ivec}{{\overrightarrow{I}}} \newcommand{\ivec}{{\overrightarrow{i}}} \newcommand{\Jvec}{{\overrightarrow{J}}} \newcommand{\jvec}{{\overrightarrow{j}}} \newcommand{\Kvec}{{\overrightarrow{K}}} \newcommand{\kvec}{{\overrightarrow{k}}} \newcommand{\Lvec}{{\overrightarrow{L}}} \newcommand{\lvec}{{\overrightarrow{l}}} \newcommand{\Mvec}{{\overrightarrow{M}}} \newcommand{\mvec}{{\overrightarrow{m}}} \newcommand{\Nvec}{{\overrightarrow{N}}} \newcommand{\nvec}{{\overrightarrow{n}}} \newcommand{\Ovec}{{\overrightarrow{O}}} \newcommand{\ovec}{{\overrightarrow{o}}} \newcommand{\Pvec}{{\overrightarrow{P}}} \newcommand{\pvec}{{\overrightarrow{p}}} \newcommand{\Qvec}{{\overrightarrow{Q}}} \newcommand{\qvec}{{\overrightarrow{q}}} \newcommand{\Rvec}{{\overrightarrow{R}}} \newcommand{\rvec}{{\overrightarrow{r}}} \newcommand{\Svec}{{\overrightarrow{S}}} \newcommand{\svec}{{\overrightarrow{s}}} \newcommand{\Tvec}{{\overrightarrow{T}}} \newcommand{\tvec}{{\overrightarrow{t}}} \newcommand{\Uvec}{{\overrightarrow{U}}} \newcommand{\uvec}{{\overrightarrow{u}}} \newcommand{\Vvec}{{\overrightarrow{V}}} \newcommand{\vvec}{{\overrightarrow{v}}} \newcommand{\Wvec}{{\overrightarrow{W}}} \newcommand{\wvec}{{\overrightarrow{w}}} \newcommand{\Xvec}{{\overrightarrow{X}}} \newcommand{\xvec}{{\overrightarrow{x}}} \newcommand{\Yvec}{{\overrightarrow{Y}}} \newcommand{\yvec}{{\overrightarrow{y}}} \newcommand{\Zvec}{{\overrightarrow{Z}}} \newcommand{\zvec}{{\overrightarrow{z}}} %%% Varia % \newcommand{\opluslim}{\operatornamewithlimits{\oplus}} \newcommand{\ie}{\idestdefinition} \newcommand{\eg}{{\itshape e.g.}~} \newcommand{\cf}{{\itshape cf.}~} \newcommand{\Cf}{{\itshape Cf.}~} %%% software \newcommand{\scilab}{{\color{B!40!black}\texttt{scilab}}} \newcommand{\python}{{\color{B!40!black}\texttt{python}}} \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} \newcommand{\ceil}[1]{\left\lceil#1\right\rceil} \newcommand{\fpart}[1]{\left\langle#1\right\rangle} \newcommand{\norm}[1]{\|#1\|} % \newcommand{\n}{\Vert} \newcommand{\textq}[1]{\quad\text{#1}\quad} \newcommand{\textql}[1]{\quad\text{#1}} \newcommand{\textqr}[1]{\text{#1}\quad} \newcommand{\textqq}[1]{\qquad\text{#1}\qquad} % \newcommand{\attention}[2][]{% % {\ifthenelse{\equal{#1}{}}{\color{R}}{\color{#1}}\hfill#2} % } %%% emphasized, margin par % \renewcommand{\emph}[1]{\textit{#1}} \newcommand{\sidenote}[2][]{% \marginpar{% \ifthenelse{\equal{#1}{}}{\color{DarkB}}{\color{#1}}% \textsf{\scriptsize #2}} } % Quelques casures difficiles: % \usepackage{hyphenat} \hyphenation{Sprin-ger inter-sec-tion ab-solu ab-so-lue ab-so-lus ab-so-lues ab-so-lu-ment as-so-cia-tion as-so-cia-tions aupa-ra-vant auto-bio-gra-phi-que auto-bio-gra-phi-ques cha-rac-te-ristic cor-res-pon-dance dimen-sion-nel di-mi-nuer en-cou-rait en-cou-raient equi-va-lent exa-mi-nera exem-ple exem-ples exis-te exis-ter ima-gi-ne ima-gi-na-tion ima-gi-naire im-por-tance in-tui-tif in-tui-tifs in-tui-tive in-tui-tives in-tui-ti-ve-ment jeune- jeu-nes la-quel-le li-ber-taire li-ber-tai-res long-temps mani-fold mani-folds mani-pu-la-tion mani-pu-la-tions mathe-ma-ti-que mathe-ma-ti-quement mo-derne mo-der-nes mo-der-ni-sa-tion mo-di-fier mo-di-fie mo-di-fient mon-ta-gne mon-ta-gnes mon-ta-gneux mon-ta-gneu-se mon-ta-gneu-ses mytho-lo-gique mytho-lo-giques orien-ta-lisme orien-ta-lismes per-met-tre per-met-tent per-met-tant po-pu-laire po-pu-lai-res po-pu-la-tion po-pu-la-tions pri-son-nier pri-son-niers puis-que quel-que quel-ques rami-fi-cation recher-che recher-ches recon-nais-sable recon-nais-sa-bles re-la-tif re-la-tifs re-la-tive re-la-tives re-la-ti-ve-ment res-pon-sable res-pon-sa-bles sa-tis-fait sa-tis-faite sa-tis-faits sa-tis-fai-tes sa-tis-fai-re se-con-daire se-con-dai-res si-tua-tion si-tua-tions suf-fi-sam-ment sui-vant sui-vent sui-vre sym-metric tota-li-taire tota-li-taires ty-pi-que ty-pi-ques ty-pi-que-ment vien-nent vio-len-ce voca-bu-laire voca-bu-lai-res ap-pli-cation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% subscripts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % It defines the length mylength only to make possible the use of % \fontdimen below in the command \equalheight. \makeatletter \AtBeginDocument{ \sbox{\@tempboxa}{% \ensuremath{\xdef\mylength{\the\fontdimen17\textfont2}}% }% } \makeatother \newcommand{\equalheight}{% \fontdimen16\textfont2=3pt \fontdimen17\textfont2=3pt } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% simple colored text %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % A boxed colored text is available with boxedEnvironments.sty % through the command \noticeB. \newcommand{\textc}[2][]{% {\ifthenelse{\equal{#1}{}}{\color{DarkB}}{\color{#1}}#2}}