%                                                          >> macutil.tex
%
% Macros utilitaires pour L'Enseignement Math‚matique
%
% **************************************************************************
% *  Version du 10 janvier 2002     Copyright L'Enseignement Math‚matique  *
% **************************************************************************
%
%
\ifx\MACUTIL\undefined\let\MACUTIL=Y\else\endinput \fi
%
% D‚finitions utiles:
%
\def\Emaj{\smash{\'E}}
\let\nm=\nomathbreak
\def\tvi{\vrule height 12pt depth 5pt width 0pt}
\def\hfq{\hfill\quad}
\def\cc#1{\hfq#1\hfq}
\def\mM#1{\unskip~m\EMraise{\sevenpol #1}}       %% mŠtres carr‚s, etc.
%
% CaractŠres Blackboard (openface):
%
\let\Ang=\AA                                     %% Angstr”m
\def\AA{{\Bbb A}}
\def\BB{{\Bbb B}}
\def\CC{{\Bbb C}}
\def\DD{{\Bbb D}}
\def\EE{{\Bbb E}}
\def\FF{{\Bbb F}}
\def\GG{{\Bbb G}}
\def\HH{{\Bbb H}}
\def\II{{\Bbb I}}
\def\JJ{{\Bbb J}}
\def\KK{{\Bbb K}}
\def\LL{{\Bbb L}}
\def\MM{{\Bbb M}}
\def\NN{{\Bbb N}}
\def\OO{{\Bbb O}}
\def\PP{{\Bbb P}}
\def\QQ{{\Bbb Q}}
\def\RR{{\Bbb R}}
\def\SS{{\Bbb S}}
\def\TT{{\Bbb T}}
\def\UU{{\Bbb U}}
\def\VV{{\Bbb V}}
\def\WW{{\Bbb W}}
\def\XX{{\Bbb X}}
\def\YY{{\Bbb Y}}
\def\ZZ{{\Bbb Z}}
%
% Majuscules scriptes:
%
\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\Jj{{\Cal J}}
\def\Kk{{\Cal K}}
\def\Ll{{\Cal L}}
\def\Mm{{\Cal M}}
\def\Nn{{\Cal N}}
\def\Oo{{\Cal O}}
\def\Pp{{\Cal P}}
\def\Qq{{\Cal Q}}
\def\Rr{{\Cal R}}
\def\Ss{{\Cal S}}
\def\Tt{{\Cal T}}
\def\Uu{{\Cal U}}
\def\Vv{{\Cal V}}
\def\Ww{{\Cal W}}
\def\Xx{{\Cal X}}
\def\Yy{{\Cal Y}}
\def\Zz{{\Cal Z}}
%
% Lettres gothiques:
%
\def\AAA{{\goth A}}
\def\aaa{{\goth a}}
\def\BBB{{\goth B}}
\def\bbb{{\goth b}}
\def\CCC{{\goth C}}
\def\ccc{{\goth c}}
\def\DDD{{\goth D}}
\def\ddd{{\goth d}}
\def\EEE{{\goth E}}
\def\eee{{\goth e}}
\def\FFF{{\goth F}}
\def\fff{{\goth f}}
\def\GGG{{\goth G}}
\def\ggg{{\goth g}}
\def\HHH{{\goth H}}
\def\hhh{{\goth h}}
\def\III{{\goth I}}
\def\iii{{\goth i}}
\def\JJJ{{\goth J}}
\def\jjj{{\goth j}}
\def\KKK{{\goth K}}
\def\kkk{{\goth k}}
\def\LLL{{\goth L}}
\def\lll{{\goth l}}
\def\MMM{{\goth M}}
\def\mmm{{\goth m}}
\def\NNN{{\goth N}}
\def\nnn{{\goth n}}
\def\OOO{{\goth O}}
\def\ooo{{\goth o}}
\def\PPP{{\goth P}}
\def\ppp{{\goth p}}
\def\QQQ{{\goth Q}}
\def\qqq{{\goth q}}
\def\RRR{{\goth R}}
\def\rrr{{\goth r}}
\def\SSS{{\goth S}}
\def\sss{{\goth s}}
\def\TTT{{\goth T}}
\def\ttt{{\goth t}}
\def\UUU{{\goth U}}
\def\uuu{{\goth u}}
\def\VVV{{\goth V}}
\def\vvv{{\goth v}}
\def\WWW{{\goth W}}
\def\www{{\goth w}}
\def\XXX{{\goth X}}
\def\xxx{{\goth x}}
\def\YYY{{\goth Y}}
\def\yyy{{\goth y}}
\def\ZZZ{{\goth Z}}
\def\zzz{{\goth z}}
%
% Lettres surmont‚es d'une barre:
%
\def\Abar{{\,\overline{\!A}}}
\def\Bbar{{\,\overline{\!B}}}
\def\Cbar{{\,\overline{\!C}}}
\def\dbar{{\,\overline{\!d}}}
\def\Dbar{{\,\overline{\!D}}}
\def\Ebar{{\,\overline{\!E}}}
\def\Fbar{{\,\overline{\!F}}}
\def\Gbar{{\,\overline{\!G}}}
\def\Hbar{{\,\overline{\!H}}}
\def\Ibar{{\,\overline{\!I}}}
\def\Jbar{{\,\overline{\!J}}}
\def\kbar{{\bar k}}
\def\Kbar{{\,\overline{\!K}}}
\def\Lbar{{\,\overline{\!L}}}
\def\Mbar{{\,\overline{\!M}}}
\def\Nbar{{\,\overline{\!N}}}
\def\Obar{{\,\overline{\!O}}}
\def\Pbar{{\,\overline{\!P}}}
\def\Qbar{{\,\overline{\!Q}}}
\def\Rbar{{\,\overline{\!R}}}
\def\Sbar{{\,\overline{\!S}}}
\def\Tbar{{\,\overline{\!T}}}
\def\Ubar{{\,\overline{\!U}}}
\def\Vbar{{\,\overline{\!V}}}
\def\Wbar{{\,\overline{\!W}}}
\def\Xbar{{\,\overline{\!X}}}
\def\Ybar{{\,\overline{\!Y}}}
\def\Zbar{{\,\overline{\!Z}}}
%
% Lettres surmont‚es d'un tilde:
%
\def\Atilde{{\,\widetilde{\!A}}}
\def\Btilde{{\,\widetilde{\!B}}}
\def\Ctilde{{\,\widetilde{\!C}}}
\def\Dtilde{{\,\widetilde{\!D}}}
\def\Etilde{{\,\widetilde{\!E}}}
\def\Ftilde{{\,\widetilde{\!F}}}
\def\ftilde{\,\widetilde{\!f}}
\def\Gtilde{{\,\widetilde{\!G}}}
\def\Htilde{{\,\widetilde{\!H}}}
\def\Itilde{{\,\widetilde{\!I}}}
\def\Jtilde{{\,\widetilde{\!J}}}
\def\Ktilde{{\,\widetilde{\!K}}}
\def\Ltilde{{\,\widetilde{\!L}}}
\def\Mtilde{{\,\widetilde{\!M}}}
\def\Ntilde{{\,\widetilde{\!N}}}
\def\Otilde{{\,\widetilde{\!O}}}
\def\Ptilde{{\,\widetilde{\!P}}}
\def\Qtilde{{\,\widetilde{\!Q}}}
\def\Rtilde{{\,\widetilde{\!R}}}
\def\Stilde{{\,\widetilde{\!S}}}
\def\Ttilde{{\,\widetilde{\!T}}}
\def\Utilde{{\,\widetilde{\!U}}}
\def\Vtilde{{\,\widetilde{\!V}}}
\def\Wtilde{{\,\widetilde{\!W}}}
\def\Xtilde{{\,\widetilde{\!X}}}
\def\Ytilde{{\,\widetilde{\!Y}}}
\def\Ztilde{{\,\widetilde{\!Z}}}
%
% Lettres surmont‚es d'un chapeau:
%
\def\Ahat{{\,\widehat{\!A}}}
\def\Bhat{{\,\widehat{\!B}}}
\def\Chat{{\,\widehat{\!C}}}
\def\Dhat{{\,\widehat{\!D}}}
\def\Ehat{{\,\widehat{\!E}}}
\def\Fhat{{\,\widehat{\!F}}}
\def\fhat{\,\widehat{\!f}}
\def\Ghat{{\,\widehat{\!G}}}
\def\Hhat{{\,\widehat{\!H}}}
\def\Ihat{{\,\widehat{\!I}}}
\def\Jhat{{\,\widehat{\!J}}}
\def\Khat{{\,\widehat{\!K}}}
\def\Lhat{{\,\widehat{\!L}}}
\def\Mhat{{\,\widehat{\!M}}}
\def\Nhat{{\,\widehat{\!N}}}
\def\Ohat{{\,\widehat{\!O}}}
\def\Phat{{\,\widehat{\!P}}}
\def\Qhat{{\,\widehat{\!Q}}}
\def\Rhat{{\,\widehat{\!R}}}
\def\Shat{{\,\widehat{\!S}}}
\def\That{{\,\widehat{\!T}}}
\def\Uhat{{\,\widehat{\!U}}}
\def\Vhat{{\,\widehat{\!V}}}
\def\What{{\,\widehat{\!W}}}
\def\Xhat{{\,\widehat{\!X}}}
\def\Yhat{{\,\widehat{\!Y}}}
\def\Zhat{{\,\widehat{\!Z}}}
%
% Lettres grecques:
%
%\let\epsilon=\varepsilon
%\let\kappa=\varkappa
%\let\phi=\varphi
%
% Symboles sp‚ciaux:
%
\font\zsymb=psyr at 9pt
\def\bullet{\leavevmode\unkern{\zsymb\char"B7}\kern.32em\ignorespaces}
\def\regis{\leavevmode\raise.5ex\hbox{\zsymb\char"D2}}
\def\Bullet{\text{\zsymb\char"B7}}
\def\Regis{\text{\raise.5ex\hbox{\zsymb\char"D2}}}
%
% Arrangements sp‚ciaux:
%
\def\set#1{\left\{{@,@, #1 @,@,}\right\}}               % {...}
\def\nb#1{{\left\vert{@,@, #1 @,@,}\right\vert}}        % |...|
\def\norm#1{{\left\Vert{@,@, #1 @,@,}\right\Vert}}      % ||...||
\def\equ#1{\left[{@,@, #1 @,@,}\right]}                 % [...]
\def\vect#1#2{\bmatrix#1\\#2\endbmatrix}                % [vecteur colonne]
\def\gen#1{{\left\langle{@,@, #1 @,@,}\right\rangle}}   % <...>
\def\fibprod#1{\times_{#1}}                             % produit fibr‚
\def\id{\text{\it id}}                            % identit‚
\def\idd{\text{\sevenpolit id}}                   % identit‚ (petite taille)
\def\cross{^{\times}}                             % ^x
\def\inv{^{-1}}                                   % inverse
\def\red{_{\text{red}}}                           % sch‚ma r‚duit
\def\rest#1{\vert_{#1}}                           % restriction
%
\def\sumprime{\sideset \and' \to\sum}             % somme prime
%
\def\Ssum{\Sigma\,}                               % sommation (petit symbole)
\let\til=\widetilde
%
% Op‚rateurs:
%
\def\Aut{\operatorname{Aut}}
\def\Br{\operatorname{Br}}
\def\CHAR{\operatorname{char}}       % \char d‚signe les caractŠres en TeX!
\def\codim{\operatorname{codim}}
\def\coker{\operatorname{coker}}
\def\Div{\operatorname{Div}}
\def\Gal{\operatorname{Gal}}
\def\Galk{\Gal(\kbar/k)}
\def\GalK{\Gal(\Kbar/K)}
\def\GL{\operatorname{GL}}
\def\Hom{\operatorname{Hom}}
\def\im{\operatorname{Im}}
\def\mult{\operatorname{mult}}
\def\ord{\operatorname{ord}}
\def\Pic{\operatorname{Pic}}
\def\Proj{\operatorname{Proj}}
\def\rank{\operatorname{rank}}
\def\re{\operatorname{Re}}
\def\Res{\operatorname{Res}}
\def\SEC{\operatorname{sec}}             % \sec r‚serv‚ pour les sections
\def\SL{\operatorname{SL}}
\def\SO{\operatorname{SO}}
\def\Spec{\operatorname{Spec}}
\def\SU{\operatorname{SU}}
\def\supp{\operatorname{supp}}
\def\Sym{\operatorname{Sym}}
%
% FlŠches:
%
\def\ttvvii{\vrule height 1.3ex depth 0pt width 0pt}
\def\VEC#1{\overrightarrow{\ttvvii{#1}}}         % flŠche au-dessus  
\let\embeds=\hookrightarrow
\let\epi=\twoheadrightarrow
\def\notimplies{\nRightarrow}
\def\getsfrom{\leftarrow\joinrel\mapstochar}
\def\up#1{\leavevmode\raise.18ex\hbox{#1}}
\def\rat{\up{${\ssize \relbar\relbar\to}\,$}}    % flŠche pointill‚e
\def\srat{\up{${\sssize -\!-\!-\!\to}$}}         % idem (petite taille)
\def\simm{\overset\sim\to\rightarrow}            % -~->
\def\simml{\overset\sim\to\leftarrow}            % <-~-
\def\simmx{\overset\approx\to\longrightarrow}
\def\df{\overset\text{def}\to=}                  % =^def
\def\longrarr{\hbox to 15mm{\enspace\rightarrowfill}}
\def\longdarr{\hbox to 15mm{\hfill$\relbar\relbar\to$\hfill}}
\def\darr{\mathrel{\downarrow}}
\setbox111=\hbox{\raise.65ex\hbox to 5mm{\hfill$\shortmid$\hfill}}
\setbox112=\hbox{\raise1.2ex\hbox to 5mm{\hfill$\shortmid$\hfill}}
\setbox113=\hbox to 5mm{\hfill$\darr$\hfill}
\def\dar{\left\downarrow\vbox to 5.6mm{}\right.}
\def\ddar{\vcenter{\offinterlineskip{\copy111\copy112\copy113}}}
%
% Quelques c‚sures difficiles:
%
\hyphenation{Sprin-ger
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
bio-logie bio-lo-gique bio-lo-gi-ques
civi-li-sa-tion civi-li-sa-tions civi-li-ser
com-mer-cial com-mer-ciale com-mer-ciaux com-mer-ciales
con-ve-nu con-ve-nue con-ve-nus con-ve-nues
cor-res-pon-dance
di-mi-nuer en-cou-rait en-cou-raient
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-dien in-diens in-dien-ne in-dien-nes
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-pu-la-tion mani-pu-la-tions 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
pater-na-lisme 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
recher-che recher-ches recon-nais-sable recon-nais-sa-bles
re-de-va-ble re-de-va-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
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
}
%
% Mots fr‚quents:
%
\def\car.{carac\-t\'e\-ris\-tique}
\def\dev.{d\'e\-ve\-lop\-p}
\def\extr.{ex\-t\'e\-rieur}
\def\intr.{in\-t\'e\-rieur}
%