\RequirePackage{rawfonts}
\ifx\@bases@loaded\undefined \input bases.sty \else\fi
\ifx\@boxes@loaded\undefined \input boxes.sty \else\fi
% ======================================================================
% ======================== SMASHES =====================================
% ======================================================================
\newif\iftop@
\newif\ifbot@
\def\topsmash{\top@true\bot@false\smash@}
\def\botsmash{\top@false\bot@true\smash@}
\def\smash{\top@true\bot@true\smash@}
\def\smash@{\relax\ifmmode\def\next{\mathpalette\mathsm@sh}\else
\let\next\makesm@sh\fi\next}
\def\finsm@sh{\iftop@\ht\z@\z@\fi\ifbot@\dp\z@\z@\fi\box\z@}
\newdimen\buffer@
\buffer@\fontdimen13 \tenex
\newdimen\buffer
\buffer\buffer@
\def\ChangeBuffer#1{\fontdimen13 \tenex#1\relax
\global\buffer\fontdimen13 \tenex}
\def\ResetBuffer{\fontdimen13 \tenex\buffer@\global\buffer\buffer@}
\def\shave#1{\mathop{\hbox{$\fontdimen13 \tenex\z@
\displaystyle{#1}$}}\fontdimen13 \tenex\buffer}
\def\topshave#1{\topsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}
\def\botshave#1{\botsmash{\displaystyle{#1}}\vphantom{\shave{#1}}}
% ======================================================================
% ======================== ALIGNEMENTS =================================
% ======================================================================
\def\topaligned{{}\,\vtop\aligned@}
\def\botaligned{{}\,\vbox\aligned@}
\def\aligned{{}\,\vcenter\aligned@}
\def\aligned@{\bgroup\vspace@\Let@
\ifinany@\else\openup\jot\fi\m@th\ialign
\bgroup\hfil\strut@$\displaystyle{##}$&$\displaystyle{{}##}$\hfil\crcr}
\def\endaligned{\crcr\egroup\egroup}
\let\endtopaligned\endaligned
\let\endbotaligned\endaligned
\newcount\atcount@
\newtoks\hashtoks@
\hashtoks@{#}
\def\alignedat#1{{}\,\vcenter\bgroup\doat@{#1}\vspace@\Let@
\ifinany@\else\openup\jot\fi\m@th\ialign\bgroup\span\preamble@@\crcr}
\def\doat@#1{\toks@{\hfil\strut@$\displaystyle{\the\hashtoks@}$&$\displaystyle
{{}\the\hashtoks@}$\hfil}\atcount@#1\relax\advance\atcount@\m@ne
\loop\ifnum\atcount@>\z@\toks@=\expandafter{\the\toks@&\hfil$\displaystyle
{\the\hashtoks@}$&$\displaystyle{{}\the\hashtoks@}$\hfil}\advance
\atcount@\m@ne\repeat\xdef\preamble@{\the\toks@}\xdef\preamble@@{\preamble@}}
\let\endalignedat\endaligned
\def\gathered{{}\,\vcenter\bgroup\vspace@\Let@
\ifinany@\else\openup\jot\fi\m@th\ialign
\bgroup\hfil\strut@$\displaystyle{##}$\hfil\crcr}
\def\endgathered{\crcr\egroup\egroup}
\newif\iftopfolded@
\newif\ifbotfolded@
\def\topfoldedtext{\topfolded@true\botfolded@false\foldedtext@}
\def\botfoldedtext{\botfolded@true\topfolded@false\foldedtext@}
\def\foldedtext{\topfolded@false\botfolded@false\foldedtext@}
\Invalid@\foldedwidth
\def\foldedtext@{\relaxnext@
\def\next@{\ifx\next\foldedwidth\let\next\nextii@\else
\def\next{\nextii@\foldedwidth{.3\hsize}}\fi\next}%
\def\nextii@\foldedwidth##1##2{\setbox\z@\vbox
{\normalbaselines\hsize##1\relax
\tolerance1600 \noindent\ignorespaces##2}\ifbotfolded@\box\z@\else
\iftopfolded@\vtop{\unvbox\z@}\else\vcenter{\box\z@}\fi\fi}%
\futurelet\next\next@}
\newif\iftagsleft@
\def\TagsOnLeft{\global\tagsleft@true}
\def\TagsOnRight{\global\tagsleft@false}
\TagsOnLeft
\newif\ifmathtags@
\def\TagsAsMath{\global\mathtags@true}
\def\TagsAsText{\global\mathtags@false}
\TagsAsText
\def\tagform@#1{\hbox{\rm(\ignorespaces#1\unskip)}}
\def\thetag{\leavevmode\tagform@}
\def\tag#1$${\iftagsleft@\leqno\else\eqno\fi\maketag@#1\maketag@$$}
\def\maketag@{\relaxnext@
\def\next@{\ifx\next"\let\next@\nextii@\else\let\next@\nextiii@\fi\next@}%
\def\nextii@"##1"##2\maketag@{\hbox{\rm##1}}%
\def\nextiii@##1\maketag@{\ifmathtags@\tagform@{$##1$}\else
\tagform@{##1}\fi}%
\futurelet\next\next@}
\def\intertext@{\def\intertext##1{\noalign{\vskip\abovedisplayskip
\vbox{\normalbaselines\noindent##1}\vskip\belowdisplayskip}}}
\def\align{\relaxnext@\ifingather@\let\next\galign@\else
\ifmmode\ifinner\def\next{\onlydmatherr@\align}\else
\let\next\align@\fi\else
\def\next{\onlydmatherr@\align}\fi\fi\next}
\newcount\and@
\def\align@{\inalign@true\inany@true
\def\tag{\ifnum\and@=\z@\def\next{&&}\else\def\next{&}\fi\next}
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\iftagsleft@\let\next\lalign@\else\let\next\ralign@\fi\next}
\newdimen\lwidth@
\newdimen\rwidth@
\newdimen\maxlwidth@
\newdimen\maxrwidth@
\newdimen\totwidth@
\def\measure@#1\endalign{\lwidth@\z@\rwidth@\z@
\maxlwidth@\z@\maxrwidth@\z@\and@\z@
\setbox\@ne\vbox{\everycr{\noalign{\global\and@\z@}}\Let@
\halign{\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
\global\lwidth@\wd\z@
\ifdim\lwidth@>\maxlwidth@\global\maxlwidth@\lwidth@\fi
\global\advance\and@\@ne
&\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}\global\rwidth@\wd\z@
\ifdim\rwidth@>\maxrwidth@\global\maxrwidth@\rwidth@\fi
\global\advance\and@\@ne
&\eat@{\everycr{}##}\crcr#1\crcr}}\totwidth@\maxlwidth@
\advance\totwidth@\maxrwidth@}
\def\displ@y@{\global\dt@ptrue\openup\jot\m@th
\everycr{\noalign{\global\and@\z@\ifdt@p\global\dt@pfalse
\vskip-\lineskiplimit\vskip\normallineskiplimit\else
\penalty\interdisplaylinepenalty\fi}}}
\def\black@#1{\noalign{\ifdim#1>\displaywidth
\dimen@\prevdepth\nointerlineskip
\vskip-\ht\strutbox@\vskip-\dp\strutbox@
\vbox{\noindent\hbox to#1{\strut@\hfill\strut@}}%
\prevdepth\dimen@\fi}}
\def\ralign@#1\endalign{\measure@#1\endalign\and@\z@
\ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi\Let@
\tabskip\centering@\halign to\displaywidth
{\hfil\strut@\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
\global\lwidth@\wd\z@\box\z@\global\advance\and@\@ne
\tabskip\z@skip&\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}%
\global\rwidth@\wd\z@\box\z@\hfill\global\advance\and@\@ne
\tabskip\centering@&\setbox\z@\hbox{\everycr{}\strut@\maketag@##\maketag@}%
\dimen@\displaywidth\advance\dimen@-\totwidth@
\divide\dimen@\tw@\advance\dimen@\maxrwidth@\advance\dimen@-\rwidth@
\ifdim\dimen@>\tw@\wd\z@\llap{\box\z@}\else
\llap{\vtop{\normalbaselines\null\box\z@}}\fi
\tabskip\z@skip\crcr#1\crcr\black@\totwidth@}}
\newdimen\lineht@
\def\lalign@#1\endalign{\measure@#1\endalign\and@\z@
\ifdim\totwidth@>\displaywidth\let\displaywidth@\totwidth@\else
\let\displaywidth@\displaywidth\fi
\ifingather@\everycr{\noalign{\global\and@\z@}}\else\displ@y@\fi\Let@
\tabskip\centering@\halign to\displaywidth
{\hfil\strut@\setbox\z@\hbox{$\displaystyle{\everycr{}##}$}%
\global\lwidth@\wd\z@\global\lineht@\ht\z@\box\z@\global\advance\and@\@ne
\tabskip\z@skip&\setbox\z@\hbox{$\displaystyle{{}\everycr{}##}$}%
\global\rwidth@\wd\z@\ifdim\ht\z@>\lineht@\global\lineht@\ht\z@\fi
\box\z@\hfil\global\advance\and@\@ne
\tabskip\centering@&\kern-\displaywidth@
\setbox\z@\hbox{\everycr{}\strut@\maketag@##\maketag@}%
\dimen@\displaywidth\advance\dimen@-\totwidth@
\divide\dimen@\tw@\advance\dimen@\maxlwidth@\advance\dimen@-\lwidth@
\ifdim\dimen@>\tw@\wd\z@\rlap{\box\z@}\else
\rlap{\vbox{\normalbaselines\box\z@\vbox to\lineht@{}}}\fi
\tabskip\displaywidth@\crcr#1\crcr\black@\totwidth@}}
\def\galign@#1\endalign{\vcenter{\m@th\align@#1\endalign}}
\newbox\savealignat@
\newif\ifxat@
\newif\ifmeasuring@
\def\alignat{\relaxnext@\ifmmode\ifinner\def\next{\onlydmatherr@\alignat}\else
\let\next\alignat@\fi\else\def\next{\onlydmatherr@\alignat}\fi\next}
\def\alignat@#1#2\endalignat{\inany@true\xat@false
\def\tag{\xdef\tag@{}\count@#1\relax\multiply\count@\tw@
\loop\ifnum\count@>\and@\xdef\tag@{&\tag@}\advance\count@\m@ne\repeat\tag@}%
\vspace@\allowdisplaybreak@\displaybreak@\intertext@
\displ@y@\measuring@true\setbox\savealignat@\hbox{$\displaystyle\Let@
\attag@{#1}\vbox{\halign{\span\preamble@@\crcr#2\crcr}}$}
\measuring@false\Let@
\attag@{#1}\tabskip\centering@\halign to\displaywidth
{\span\preamble@@\crcr#2\crcr\black@{\wd\savealignat@}}}
% \xalignat not implemented...
% ======================================================================
% ======================== DIVERS ======================================
% ======================================================================
% la plupart de ces macros se suffisent a elles-memes. Si vous n'en utilisez
% qu'une ou deux, essayez d'abord de ne prendre que celles-la.
%
\def\careof{\leavevmode\hbox{\raise.75ex\hbox{c}\kern-.15em
/\kern-.125em\smash{\lower.3ex\hbox{o}}}}
%
% \Comment does nothing except ignore its parameter
%
\def\Comment#1{}
% \annexes est analogue a \appendix
\def\annexes#1{\par
\setcounter{chapter}{\z@}
\setcounter{section}{\z@}
\def\@chapapp{#1}
\def\thechapter{\Alph{chapter}}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \Uppercase is a macro that will convert its argument to
% uppercase. The TeX primitive by itself doesn't work
% in such a functional manner since it works "in the mouth."
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\Uppercase#1{\uppercase\expandafter{#1}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \Lowercase is a macro that will convert its argument to
% lowercase. The TeX primitive by itself doesn't work
% in such a functional manner since it works "in the mouth."
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\Lowercase#1{\lowercase\expandafter{#1}}
% Symboles divers
\def\pyth+{\mathbin{++}}
\def\Pyth-{\mathbin{--}}
\def\sqbull{\vrule height .9ex width .8ex depth -.1ex } % square bullet
\def\pave{\hbox{\hskip.5pt\vrule height.4em width.4em depth \z@}}
\def\vl{\leavevmode\hbox{\tt\char`\|}} % vertical line
\def\dn{\leavevmode\hbox{\tt\char'14}} % downward arrow
\def\up{\leavevmode\hbox{\tt\char'13}} % upward arrow
\def\vs{\leavevmode\hbox{\tt\char`\ }} % visible space
\def\degre{\ifmmode{^\circ}\else{$^\circ$}\fi}
\let\degres=\degre
\def\relstack#1#2{\mathrel{\mathop{#2}\limits_{#1}}}
\def\hlstack#1#2#3{\mathrel{\mathop{#2}\limits_{#1}^{#3}}}
\def\build#1_#2^#3{\mathrel{\mathop{\kern \z@#1}\limits_{#2}^{#3}}}
% petite boite
\def\pbt#1{\leavevmode\thinspace\hbox{\vrule\vtop{\vbox{\hrule\kern\p@
\hbox{\vphantom{\tt/}\thinspace{\tt#1}\thinspace}}
\kern\p@\hrule}\vrule}\thinspace} % petite boite
% \arrows makes things like <--- text --->
\def\arrows#1#2{% #1=width, #2=text
{\setbox0=\hbox{$\mkern-2mu\mathord-\mkern-2mu$}
\hbox to #1{\kern-.055556em$\leftarrow\mkern-6mu$%
\cleaders\copy0\hfil
\kern.4em #2\kern.4em
\cleaders\copy0\hfil
$\mkern-6mu\rightarrow$\kern-.055556em}}}
% \Arrows makes things like <=== text ===>
\def\Arrows#1#2{% #1=width, #2=text
{\setbox0=\hbox{$\mkern-2mu\mathord=\mkern-2mu$}
\hbox to #1{\kern-.055556em$\Leftarrow\mkern-6mu$%
\cleaders\copy0\hfil
\kern.4em #2\kern.4em
\cleaders\copy0\hfil
$\mkern-6mu\Rightarrow$\kern-.055556em}}}
\def\boxed#1{\setbox\z@\hbox{$\displaystyle{#1}$}\hbox{\lower.4\ex@
\hbox{\lower3\ex@\hbox{\lower\dp\z@\hbox{\vbox{\hrule height.4\ex@
\hbox{\vrule width.4\ex@\hskip3\ex@\vbox{\vskip3\ex@\box\z@\vskip3\ex@}%
\hskip3\ex@\vrule width.4\ex@}\hrule height.4\ex@}}}}}}
% signature
\def\signed#1#2{{\unskip\nobreak\hfil\penalty50
\hskip2em\hbox{}\nobreak\hfil\sl#1\/ \rm(#2)
\parfillskip=\z@ \finalhyphendemerits=\z@ \endgraf}}
\def\wdesclabel#1{\hspace\labelsep \bf #1}
\def\wdesc#1{\list{}{\settowidth\labelwidth{#1}\leftmargin\labelwidth
\advance\leftmargin\labelsep
\let\makelabel\wdesclabel}}
\let\endwdesc\endlist
\def\qed{\ifhmode\unskip\nobreak\fi\ifmmode\ifinner\else\hskip5\p@\fi\fi
\hbox{\hskip5\p@\vrule width4\p@ height6\p@ depth1.5\p@\hskip\p@}}
\def\cqfd{\unskip\kern 6pt\penalty 500 \raise -2pt\hbox{\vrule\vbox
to10pt{\hrule width 4pt \vfill\hrule}\vrule}}
% Vertical `laps'; cf. \llap and \rlap
\def\ulap#1{\vbox to \z@{\vss#1}}
\def\dlap#1{\vbox to \z@{#1\vss}}
% And a horizontal `lap' that takes up no space on either side.
\def\zlap#1{\hbox to \z@{\hss#1\hss}}
% And a vertical `lap' that takes up no space on either side.
\def\vlap#1{\vbox to \z@{\vss#1\vss}}
% Avoid unwanted vertical glue when making up pages.
\def \basezero{\baselineskip\z@ \lineskip\z@}
% Struts give ascenders and descenders to assist in baseline alignment
% (e.g. of adjoining vertical boxes); useful only with text fonts.
%
\def \d@sh#1{\nobreak\thinspace#1\penalty\z@\thinspace}
\def \dash{\d@sh{--}}
\def \Dash{\d@sh{---}}
\def\pdmil{\leavevmode\kern.1em
\raise.5ex\hbox{\the\scriptscriptfont0 0}\kern-.1em
/\kern-.15em\lower.25ex\hbox{\the\scriptscriptfont0 000}}
\def\pmil{\leavevmode\kern.1em
\raise.5ex\hbox{\the\scriptscriptfont0 0}\kern-.1em
/\kern-.15em\lower.25ex\hbox{\the\scriptscriptfont0 00}}
\def\pct{\leavevmode\kern.1em
\raise.5ex\hbox{\the\scriptscriptfont0 0}\kern-.1em
/\kern-.15em\lower.25ex\hbox{\the\scriptscriptfont0 0}}
\def\circledx{\protect\pcircled}
\def\pcircled#1{{\rm\ooalign{\hfil
\raise.07ex\hbox{#1}\hfil\crcr\mathhexbox20D}}}
\newbox\cr@
\sbox\cr@{\rule[-2.5pt]{\z@}{8pt}\begin{picture}(10,6)
\put(2,-1){\vector(-1,0){2}}
\put(2,3){\oval(12,8)[r]}
\end{picture}}
\newcommand\Carrtn{\usebox\cr@}
\def\flushpar{\par\noindent}
\def\emptypage{\eject\@@line{}\vfil\eject} % faire une page vide (TeXbook 114)
\def\emptyline{\break\hbox{}\hfil\break}
\def\cbox#1{\hbox{$\vcenter{#1}$}}
\def\cc#1{\hfill\quad#1\quad\hfill}
\long\def\ctitre#1{\vbox{\leftskip=\z@ plus 1fil
\rightskip=\z@ plus 1fil \parfillskip=\z@#1}}
\def\ycopyright{\copyright~\uppercase\expandafter{\romannumeral\year}\relax}
\def\sur{\above .2pt}
%\def\oldstyle{\fam\@ne\tenmi}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% OLDSTYLE
\ifx\@ptsize\undefined
\let\@ptsize=100
\fi
\ifcase\@ptsize
\def\oldstyle{\fam\@ne\tenmi}
\or
\def\oldstyle{\fam\@ne\elvmi}
\or
\def\oldstyle{\fam\@ne\twlmi}
\else
\def\oldstyle{\fam\@ne\twtymi}
\fi
\def\biffe#1{\setbox0=\hbox{#1}%
%\ifvmode\indent\fi\raise0.4ex\hbox to\wd0{\vbox{\box0\vskip-0.48ex\hrule height.08ex}}}
\ifvmode\indent\fi\raise0.5ex\hbox to\wd0{\vbox{\box0\vskip-0.58ex\hrule height.08ex}}}
\newcount\@spr
\def\spread#1{\relax\bgroup\@spr=#1\dimen@\@spr\jot\advance\dimen@\dimen@\vskip-\dimen@\bgroup\@spr=#1\openup#1\jot}
\def\endspread{\removelastskip\vskip\belowdisplayskip\egroup\egroup}
% ======================================================================
% ======================== DIVERS MATH =================================
% ======================================================================
\let\dsize\displaystyle
\let\tsize\textstyle
\let\ssize\scriptstyle
\let\sssize\scriptscriptstyle
\def\dfrac#1#2{{\displaystyle{#1\over#2}}}
\def\tfrac#1#2{{\textstyle{#1\over#2}}}
\def\fracwithdelims#1#2#3#4{{#3\overwithdelims#1#2#4}}
\def\binom#1#2{{#1\choose#2}}
\def\dbinom#1#2{{\displaystyle{#1\choose#2}}}
\def\tbinom#1#2{{\textstyle{#1\choose#2}}}
\def\snug{\unskip\kern-\mathsurround}
\def\overset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
\mathbin{\mathop{\kern\z@#2}\limits^{#1}}\else\ifdim\wd\tw@>\z@
\mathrel{\mathop{\kern\z@#2}\limits^{#1}}\else
{\mathop{\kern\z@#2}\limits^{#1}}{}\fi\fi}
\def\underset#1\to#2{\binrel@{#2}\ifdim\wd\tw@<\z@
\mathbin{\mathop{\kern\z@#2}\limits_{#1}}\else\ifdim\wd\tw@>\z@
\mathrel{\mathop{\kern\z@#2}\limits_{#1}}\else
{\mathop{\kern\z@#2}\limits_{#1}}{}\fi\fi}
\def\oversetbrace#1\to#2{\overbrace{#2}^{#1}}
\def\undersetbrace#1\to#2{\underbrace{#2}_{#1}}
\def\sideset#1\and#2\to#3{%
\setbox\@ne\hbox{$\dsize{\vphantom{#3}}#1{#3}\m@th$}%
\setbox\tw@\hbox{$\dsize{#3}#2\m@th$}%
\kern\wd\@ne\kern-\wd\tw@\mathop{\hskip\wd\tw@\hskip-\wd\@ne
{\vphantom{#3}}#1{#3}#2}}
\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalsize\rmfamily\normalfont...}\vss}}}}
\def\ddddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
\hbox{\normalsize\rmfamily\normalfont....}\vss}}}}
\def\spdot{^{\hbox{\raise\ex@\hbox{\normalsize\rmfamily\normalfont.}}}}
\def\spddot{^{\hbox{\raise\ex@\hbox{\normalsize\rmfamily\normalfont..}}}}
\def\spdddot{^{\hbox{\raise\ex@\hbox{\normalsize\rmfamily\normalfont...}}}}
\def\spddddot{^{\hbox{\raise\ex@\hbox{\normalsize\rmfamily\normalfont....}}}}
\def\spbar{^-}
\def\spvec{^\rightarrow}
\def\sptilde{^\sim}
\def\spcheck{^\vee}
\def\sphat{^{\mathchoice{}{}{\,\,\botsmash{\hbox{\lower 4\ex@\hbox
{$\widehat{\null}$}}}}{\,\botsmash{\hbox{\lower3\ex@\hbox
{$\hat{\null}$}}}}}}
\def\spacute{^{\!\botsmash{\hbox{\lower\@ne ex\hbox{\'{}}}}}}
\def\spgrave{^{\mathchoice{}{}{}{\!}%
\botsmash{\hbox{\lower\@ne ex\hbox{\`{}}}}}}
\def\spbreve{^{\!\botsmash{\hbox{\lower4\ex@\hbox{\u{}}}}}}
\def\operatorname#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nolimits@}
\def\operatornamewithlimits#1{\mathop{\newmcodes@\kern\z@\fam\z@#1}\nlimits@}
\def\qopname@#1{\mathop{\fam\z@#1}\nolimits@}
\def\qopnamewl@#1{\mathop{\fam\z@#1}\nlimits@}
\def\arccos{\qopname@{arccos}}
\def\arcsin{\qopname@{arcsin}}
\def\arctan{\qopname@{arctan}}
\def\arg{\qopname@{arg}}
\def\cos{\qopname@{cos}}
\def\cosh{\qopname@{cosh}}
\def\cot{\qopname@{cot}}
\def\coth{\qopname@{coth}}
\def\csc{\qopname@{csc}}
\def\deg{\qopname@{deg}}
\def\det{\qopnamewl@{det}}
\def\dim{\qopname@{dim}}
\def\exp{\qopname@{exp}}
\def\gcd{\qopnamewl@{gcd}}
\def\hom{\qopname@{hom}}
\def\inf{\qopnamewl@{inf}}
\def\injlim{\qopnamewl@{inj\,lim}}
\def\ker{\qopname@{ker}}
\def\lg{\qopname@{lg}}
\def\lim{\qopnamewl@{lim}}
\def\liminf{\qopnamewl@{lim\,inf}}
\def\limsup{\qopnamewl@{lim\,sup}}
\def\ln{\qopname@{ln}}
\def\log{\qopname@{log}}
\def\max{\qopnamewl@{max}}
\def\min{\qopnamewl@{min}}
\def\Pr{\qopnamewl@{Pr}}
\def\projlim{\qopnamewl@{proj\,lim}}
\def\sec{\qopname@{sec}}
\def\sin{\qopname@{sin}}
\def\sinh{\qopname@{sinh}}
\def\sup{\qopnamewl@{sup}}
\def\tan{\qopname@{tan}}
\def\tanh{\qopname@{tanh}}
\def\varinjlim{\mathop{\vtop{\ialign{$##$\cr
\hfil{\fam\z@ lim}\hfil\cr\noalign{\nointerlineskip}%
{-}\mkern-6mu\cleaders\hbox{$\mkern-2mu{-}\mkern-2mu$}\hfill
\mkern-6mu{\to}\cr\noalign{\nointerlineskip\kern-\ex@}\cr}}}}
\def\varprojlim{\mathop{\vtop{\ialign{$##$\cr
\hfil{\fam\z@ lim}\hfil\cr\noalign{\nointerlineskip}%
{\leftarrow}\mkern-6mu\cleaders\hbox{$\mkern-2mu{-}\mkern-2mu$}\hfill
\mkern-6mu{-}\cr\noalign{\nointerlineskip\kern-\ex@}\cr}}}}
\def\varliminf{\mathop{\underline{\vrule height\z@ depth.2exwidth\z@
\hbox{\rm lim}}}}
\def\varlimsup{\mathop{\overline{\hbox{\rm lim}}}}
\def\multilimits@{\bgroup\vspace@\Let@
\baselineskip\fontdimen10 \scriptfont\tw@
\advance\baselineskip\fontdimen12 \scriptfont\tw@
\lineskip\thr@@\fontdimen8 \scriptfont\thr@@
\lineskiplimit\thr@@\fontdimen8 \scriptfont\thr@@
\vbox\bgroup\ialign\bgroup\hfil$\scriptstyle{##}$\hfil\cr}
\def\Sb{_\multilimits@}
\def\endSb{\cr\egroup\egroup\egroup}
\def\Sp{^\multilimits@}
\let\endSp\endSb
\newcount\skewcharcount@
\newcount\familycount@
\def\theskewchar@{\global\familycount@\@ne
\global\skewcharcount@\the\skewchar\textfont\@ne
\ifnum\fam>\m@ne\ifnum\fam<17
\global\familycount@\the\fam\relax
\global\skewcharcount@\the\skewchar\textfont\the\fam\relax\fi\fi
\ifnum\skewcharcount@>\m@ne
\ifnum\skewcharcount@<128
\global\multiply\familycount@256
\global\advance\skewcharcount@\familycount@
\global\advance\skewcharcount@28672
\mathchar\skewcharcount@\else
\global\skewcharcount@\m@ne\fi\else
\global\skewcharcount@\m@ne\fi}
\newcount\pointcount@
\def\getpoints@#1.#2\getpoints@{\pointcount@#1 }
\def\accentfam@{7}
\def\noaccents@{\def\accentfam@{0}}
\def\makeacc@#1#2{\def#1{\mathaccent"\accentfam@#2 }}
\def\Makeacc@#1#2{\relaxnext@\def#1{\relax\ifmmode\def\next{\mathaccent@
{"\accentfam@#2 }}\else\def\next{\Err@{Use
\string#1\space only in math mode}}\fi\next}}
\makeacc@\hat{05E} \Makeacc@\Hat{05E}
\makeacc@\check{014} \Makeacc@\Check{014}
\makeacc@\tilde{07E} \Makeacc@\Tilde{07E}
\makeacc@\acute{013} \Makeacc@\Acute{013}
\makeacc@\grave{012} \Makeacc@\Grave{012}
\makeacc@\dot{05F} \Makeacc@\Dot{05F}
\makeacc@\ddot{07F} \Makeacc@\Ddot{07F}
\makeacc@\breve{015} \Makeacc@\Breve{015}
\makeacc@\bar{016} \Makeacc@\Bar{016}
\def\vec{\mathaccent"017E }
\def\Vec{\relaxnext@\ifmmode\def\next{\mathaccent@{"017E }}\else
\def\next{\Err@{Use \string\vec\space only in math mode}}\fi\next}
\newdimen\accentdimen@
\newcount\accentmu@
\def\unbracefonts@{\let\Cal@\Cal@@\let\rom@\rom@@\let\bold@\bold@@
\let\slanted@\slanted@@}
\def\mathaccent@#1#2{\relaxnext@\ifnum\fam=\m@ne\xdef\thefam@{1}\else
\xdef\thefam@{\the\fam}\fi
\accentdimen@\z@
\setbox\z@\hbox{\unbracefonts@$\fam\thefam@#2$}%
\ifdim\accentdimen@=\z@\def\next{\mathaccent#1{#2}}%
\setbox\@ne\hbox{\unbracefonts@$\fam\thefam@#2\theskewchar@$}%
\setbox\tw@\hbox{$\ifnum\skewcharcount@=\m@ne\else
\mathchar\skewcharcount@\fi$}%
\global\accentdimen@\wd\@ne\global\advance\accentdimen@-\wd\z@
\global\advance\accentdimen@-\wd\tw@
\global\multiply\accentdimen@\tw@
\dimentomu@\accentdimen@\accentmu@\global\advance\accentmu@\@ne\else
\def\next{{\mathaccent#1{#2\mkern\accentmu@ mu}\mkern-\accentmu@ mu}{}}\fi
\next}
\def\dimentomu@#1#2{\multiply#1 100
\expandafter\getpoints@\the#1\getpoints@
\multiply\pointcount@18
\divide\pointcount@\@m
\global#2\pointcount@}
\def\newbox@{\alloc@4\box\chardef\insc@unt}
\def\accentedsymbol#1#2{\expandafter\newbox@\csname\expandafter
\eat@\string#1@box\endcsname
\expandafter\setbox\csname\expandafter\eat@
\string#1@box\endcsname\hbox{$#2$}\def
#1{\expandafter\copy\csname\expandafter\eat@\string#1@box\endcsname{}}}
\def\dmatherr@#1{\Err@{\string#1\space not allowed in display math mode}}
\def\nonmatherr@#1{\Err@{\string#1\space allowed only in math mode}}
\def\mathbreak{\relax\ifmmode\ifinner\break\else
\dmatherr@\mathbreak\fi\else\nonmatherr@\mathbreak\fi}
\def\nomathbreak{\relax\ifmmode\ifinner\nobreak\else
\dmatherr@\nomathbreak\fi\else\nonmatherr@\nomathbreak\fi}
\def\allowmathbreak{\relax\ifmmode\ifinner\allowbreak\else
\dmatherr@\allowmathbreak\fi\else\nonmatherr@\allowmathbreak\fi}
\newcount\thickness
%\Invalid@\thickness
\def\thickfrac{\relaxnext@
\def\next@{\ifx\next\thickness\let\next@\nextii@\else
\def\next@{\nextii@\thickness1}\fi\next@}%
\def\nextii@\thickness##1##2##3{{##2\above##1\ex@##3}}%
\futurelet\next\next@}
\def\fracwithdelims#1#2#3#4{{#3\overwithdelims#1#2#4}}
\def\thickfracwithdelims#1#2{\relaxnext@\def\ldelim@{#1}\def\rdelim@{#2}%
\def\next@{\ifx\next\thickness\let\next@\nextii@\else
\def\next@{\nextii@\thickness1}\fi\next@}%
\def\nextii@\thickness##1##2##3{{##2\abovewithdelims
\ldelim@\rdelim@##1\ex@##3}}%
\futurelet\next\next@}
\def\pod#1{\allowbreak\ifinner\mkern8mu\else\mkern18mu\fi(#1)}
\newcount\cfraccount@
\def\gloop@#1\repeat{\gdef\body{#1}\iterate}
\def\cfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
\iffalse{\fi\def\\{\over\displaystyle}\iffalse}\fi}
\def\lcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut
\iffalse{\fi\def\\{\hfill\over\displaystyle}\iffalse}\fi}
\def\rcfrac{\bgroup\bgroup\advance\cfraccount@\@ne\strut\hfill
\iffalse{\fi\def\\{\over\displaystyle\hfill}\iffalse}\fi}
\def\endcfrac{\gloop@\ifnum\cfraccount@>\z@\global\advance\cfraccount@\m@ne
\egroup\hskip-\nulldelimiterspace\egroup\repeat}
%\def\adots{\mathinner{\mkern1mu\raise\p@\vbox{\kern7\p@\hbox{.}}\mkern2mu
% \raise4\p@\hbox{.}\mkern2mu\raise7\p@\hbox{.}\mkern1mu}}
%\def\adots{\mathinner{\mkern2mu\raise\p@\hbox{.}
%\mkern3mu\raise4pt\hbox{.}\mkern1mu\raise7pt\hbox{.}}}
%%
%\def\adots{\mathinner{\mkern1mu\raise\p@\hbox{.}\mkern2mu
% \raise4\p@\hbox{.}\mkern2mu\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}}
% from yhmath
\def\adots{\mathinner{\mkern2mu\raise\p@\hbox{.}
\mkern2mu\raise4\p@\hbox{.}\mkern1mu
\raise7\p@\vbox{\kern7\p@\hbox{.}}\mkern1mu}}
% -----------------------------------------------------------------------------
% variantes grecques & \Per, \Ser
% -----------------------------------------------------------------------------
%\mathchardef\itGamma="0100
%\mathchardef\itDelta="0101
%\mathchardef\itTheta="0102
%\mathchardef\itLambda="0103
%\mathchardef\itXi="0104
%\mathchardef\itPi="0105
%\mathchardef\itSigma="0106
%\mathchardef\itUpsilon="0107
%\mathchardef\itPhi="0108
%\mathchardef\itPsi="0109
%\mathchardef\itOmega="010A
\def\hexnumber@#1{\ifnum#1<10 \number#1\else
\ifnum#1=10 A\else\ifnum#1=11 B\else\ifnum#1=12 C\else
\ifnum#1=13 D\else\ifnum#1=14 E\else\ifnum#1=15 F\fi\fi\fi\fi\fi\fi\fi}
%\def\bffam@{\hexnumber@\bffam}
%\mathchardef\boldGamma="0\bffam@00
%\mathchardef\boldDelta="0\bffam@01
%\mathchardef\boldTheta="0\bffam@02
%\mathchardef\boldLambda="0\bffam@03
%\mathchardef\boldXi="0\bffam@04
%\mathchardef\boldPi="0\bffam@05
%\mathchardef\boldSigma="0\bffam@06
%\mathchardef\boldUpsilon="0\bffam@07
%\mathchardef\boldPhi="0\bffam@08
%\mathchardef\boldPsi="0\bffam@09
\mathchardef\Ser"2278
\mathchardef\Per"227B
% -----------------------------------------------------------------------------
% radicaux, \uproot et \leftroot
\def\@sqrt@#1{\radical"270370 {#1}}
\Invalid@\leftroot
\Invalid@\uproot
\newcount\uproot@
\newcount\leftroot@
\def\root{\relaxnext@
\def\next@{\ifx\next\uproot\let\next\nextii@\else
\ifx\next\leftroot\let\next\nextiii@\else
\let\next\plainroot@\fi\fi\next}%
\def\nextii@\uproot##1{\uproot@##1\relax\futurelet\next\nextiv@}%
\def\nextiv@{\ifx\next\space@\def\next. {\futurelet\next\nextv@}\else
\def\next.{\futurelet\next\nextv@}\fi\next.}%
\def\nextv@{\ifx\next\leftroot\let\next\nextvi@\else
\let\next\plainroot@\fi\next}%
\def\nextvi@\leftroot##1{\leftroot@##1\relax\plainroot@}%
\def\nextiii@\leftroot##1{\leftroot@##1\relax\futurelet\next\nextvii@}%
\def\nextvii@{\ifx\next\space@
\def\next. {\futurelet\next\nextviii@}\else
\def\next.{\futurelet\next\nextviii@}\fi\next.}%
\def\nextviii@{\ifx\next\uproot\let\next\nextix@\else
\let\next\plainroot@\fi\next}%
\def\nextix@\uproot##1{\uproot@##1\relax\plainroot@}%
\bgroup\uproot@\z@\leftroot@\z@\futurelet\next\next@}
\def\plainroot@#1\of#2{\setbox\rootbox\hbox{$\m@th\scriptscriptstyle{#1}$}%
\mathchoice{\r@@t\displaystyle{#2}}{\r@@t\textstyle{#2}}
{\r@@t\scriptstyle{#2}}{\r@@t\scriptscriptstyle{#2}}\egroup}
\def\r@@t#1#2{\setbox\z@\hbox{$\m@th#1\@sqrt@{#2}$}%
\dimen@\ht\z@\advance\dimen@-\dp\z@
\setbox1\hbox{$\m@th#1\mskip\uproot@ mu$}\advance\dimen@ by1.667\wd\@ne
\mkern-\leftroot@ mu\mkern5mu\raise.6\dimen@\copy\rootbox
\mkern-10mu\mkern\leftroot@ mu\box\z@}
\def\tcheche#1{#1\mkern2.5mu\check{}}
\def\sh{\mathop{\rm sh}\nolimits}
\def\ch{\mathop{\rm ch}\nolimits}
\def\Arctg{\mathop{\rm Arctg}\nolimits}
\def\arctg{\mathop{\rm arctg}\nolimits}
\def\Arcsin{\mathop{\rm Arcsin}\nolimits}
\def\arcsin{\mathop{\rm arcsin}\nolimits}
\def\Arccos{\mathop{\rm Arccos}\nolimits}
\def\arccos{\mathop{\rm arccos}\nolimits}
\def\minmax{\mathop{\rm min\,max}}
\def\pgcd{\mathop{\rm pgcd}\nolimits}
\def\tg{\mathop{\rm tg}\nolimits}
\def\th{\mathop{\rm th}\nolimits}
\def\Arcth{\mathop{\rm Arcth}\nolimits}
\def\arcth{\mathop{\rm arcth}\nolimits}
\def\intvp{\ifinner\rlap{\raise-.05ex\hbox{\kern.30em\large\rm\char"20}}\else{\scriptstyle\rlap{\raise-0.3ex\hbox{\kern.45em\LARGE\rm\char"20}}}\fi\int}
\def\cintvp{\ifinner\rlap{\raise.1ex\hbox{\kern.2em\tiny\rm C}}\else{\rlap{\raise-0.3ex\hbox{\kern.2em\large\rm C}}}\fi\int}
\def\system#1{\let\next=\\\let\\=\cr\left\{\null\,\vcenter{\openup1\jot\m@th
\ialign{\strut\hfil$##$&$##$\hfil&&\enspace$##$\enspace&
\hfil$##$&$##$\hfil\crcr#1\crcr}}\right.\let\\=\next}
%
% variantes de \shortstack
%
\newif\if@shs\@shsfalse
\let\bshortstack\shortstack
\def\tshortstack{\@ifnextchar[{\@tshortstack}{\@tshortstack[c]}}
\def\@tshortstack[#1]{\leavevmode
\vtop\bgroup\baselineskip-1pt\lineskip 3pt\let\mb@l\hss
\let\mb@r\hss \expandafter\let\csname mb@#1\endcsname\relax
\let\\\@stackcr\@itshortstack}
\def\@itshortstack#1{\halign{\mb@l ##\unskip\mb@r\cr #1\crcr}\egroup}
\def\cshortstack{\@ifnextchar[{\@cshortstack}{\@cshortstack[c]}}
\def\@cshortstack[#1]{\leavevmode \@shsfalse
\ifmmode \vcenter \else \@shstrue $\vcenter\fi\bgroup\baselineskip-1pt\lineskip 3pt\let\mb@l\hss
\let\mb@r\hss \expandafter\let\csname mb@#1\endcsname\relax
\let\\\@stackcr\@icshortstack}
\def\@icshortstack#1{\halign{\mb@l ##\unskip\mb@r\cr #1\crcr}\egroup\if@shs $\fi}
%%% \stackword
\def\stackword#1{\leavevmode\lower3pt\hbox{\shortstack{\@stackrest#1\endolist}}}
\let\bstackword\stackword
\def\tstackword#1{\tshortstack{\@stackrest#1\endolist}}
\def\cstackword#1{\leavevmode\lower3pt\hbox{\cshortstack{\@stackrest#1\endolist}}}
\def\endolist{\endolist}
\def\@stackrest{\afterassignment\@stacksymbol
\let\next= }
\def\@stacksymbol{\ifx\next\endolist
\let\next\relax
%\kern-0.25em
\else
\next\hfill\\%
\let\next\@stackrest
\fi
\next}
%%% end of \stackword
%%% \uppercasefirst
{\obeyspaces%
\gdef\uppercasefirst#{\begingroup\obeyspaces\let =\@capaftersp%
\@UppercaseSec}}
\def\@UppercaseSec#1{\futurelet\next\@CapAFTERsp#1{}\endgroup}
\def\@capaftersp{\space\futurelet\next\@CapAFTERsp}
\def\@CapAFTERsp{\ifx\next\egroup\let\next\relax\else
\ifx\next\@capaftersp \unskip \let\next\relax \else
\def\next##1{\uppercase{##1}}\fi\fi \next}
%% Exemple : \uppercasefirst{space: from {nasa} {}to the final frontier.}
%%% end of \uppercasefirst
%%=======================================
%% changemargin
%%=======================================
%\newenvironment{changemargin}[2]{\begin{list}{}{
% \setlength{\topsep}{0pt}\setlength{\leftmargin}{0pt}
% \setlength{\rightmargin}{0pt}
% \setlength{\listparindent}{\parindent}
% \setlength{\itemindent}{\parindent}
% \setlength{\parsep}{0pt plus 1pt}
% \addtolength{\leftmargin}{#1}\addtolength{\rightmargin}{#2}
% }\item[] }{\end{list}}
\def\checkbox{\hbox{$\Box$ \hspace{-1.35em} \raisebox{0.4em}{$\surd$}}}
\newcommand{\braopket}[3]{%
\left\langle\vphantom{#2#3}#1\,\vrule\,\relax#2\,\vrule\,\relax\vphantom{#1#2}#3\right\rangle}
\newcommand{\fancyfrac}[2]{\raisebox{0.3ex}{#1}
\hspace*{-0.1em}/\hspace*{-0.1em}\raisebox{-0.3ex}{#2}}
\def\degr{\hbox{$^\circ$}}
\def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\arcmin{\hbox{$^\prime$}}
\def\arcsec{\hbox{$^{\prime\prime}$}}
\def\fd{\hbox{$.\!\!^{\rm d}$}}
\def\fh{\hbox{$.\!\!^{\rm h}$}}
\def\fm{\hbox{$.\!\!^{\rm m}$}}
\def\fs{\hbox{$.\!\!^{\rm s}$}}
\def\fdg{\hbox{$.\!\!^\circ$}}
\def\farcm{\hbox{$.\mkern-4mu^\prime$}}
\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}
\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}
\def\micron{\hbox{$\mu$m}}
\let\la=\lesssim
\let\ga=\gtrsim
\def\case#1#2{\hbox{$\frac{#1}{#2}$}}
\def\slantfrac#1#2{\hbox{$\,^#1\!/_#2$}}
\def\onehalf{\slantfrac{1}{2}}
\def\onethird{\slantfrac{1}{3}}
\def\twothirds{\slantfrac{2}{3}}
\def\onequarter{\slantfrac{1}{4}}
\def\threequarters{\slantfrac{3}{4}}
\def\ubvr{\hbox{$U\!BV\!R$}}
\def\ub{\hbox{$U\!-\!B$}}
\def\bv{\hbox{$B\!-\!V$}}
\def\vr{\hbox{$V\!-\!R$}}
\def\ur{\hbox{$U\!-\!R$}}
\def\ion#1#2{#1$\;${\small\rm\@Roman{#2}}\relax}
\def\nodata{\multicolumn{1}{c}{$\cdots$}}
\newcount\lecurrentfam
%\def\LaTeX{\lecurrentfam=\the\fam \leavevmode L\raise.42ex
%\hbox{$\fam\lecurrentfam\scriptscriptstyle\kern-.3em A$}\kern-.15em\TeX}
\def\sizrpt{
(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
\typeout{
(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
}}
\newcommand{\bfmdot}[1]{\mbox{\boldmath\bf
\rlap{$#1$}\setbox0=\hbox{$\dot{\phantom{#1}}$}% create fat & bold \dot
\kern-0.025em\copy0\kern-\wd0
\kern0.05em\copy0\kern-\wd0
\kern-0.025em\raise.0433em\box0}}
%
\def\underdotline#1{{\leavevmode\setbox0=\hbox{#1}\rlap{\raise-0.28em\hbox to\wd0{%
\rm\tiny\cleaders\hbox{.\kern-0.1ex}\hfill}}\box0}}
%
% ^---- dots here -- could be anything
%
%Morten Welinder
%
[email protected]
%
\def\underanyline#1#2{{\leavevmode\setbox0=\hbox{#2}\rlap{\raise-0.28em\hbox to\wd0{%
\rm\tiny\cleaders\hbox{#1\kern-0.1ex}\hfill}}\box0}}
%
%
% Mc
\def\Mc{M\kern-.05em\raise.5ex\hbox{\b c}\kern-.05em}
