%%%Quelques environnements personnels %%Une ou plusieurs remarques \newcounter{remarque} \newcommand{\remarque}{\addtocounter{remarque}{1} \par \quad {\bf \arabic{remarque}}.\, } \newenvironment{rqs}{\begin{quote} \normalfont\footnotesize \pagebreak[2] {\bf Remarques} \nopagebreak[4] \setcounter{remarque}{0} \setlength{\parskip}{0.25\parskip} \renewcommand{\item}{\remarque} } {\end{quote}} %%Pour les remarques constituees d'une unique remarque !!! \newenvironment{rem}{\begin{quote} %% \setlength{\theorempreskipamount}{1em} \normalfont\footnotesize {{\bf Remarque} --} }{\end{quote}} %%Pour les preuves \newenvironment{preuve}{\pagebreak[2] \vspace{0.5em} \par \noindent {\bf Preuve~:} \nopagebreak[4] %\vspace{0.25em} \nopagebreak %\samepage \begin{list}{}{\setlength{\leftmargin}{0.5\leftmargin} \setlength{\topsep}{0pt} \setlength{\itemindent}{\parindent} \setlength{\listparindent}{\parindent} } \item } {\hfill $\square$ \vspace{1em} \end{list}} %%Preuves avec un titre au choix \newenvironment{demo}[1]{\pagebreak[2] \vspace{0.5em} \par \noindent {\bf #1} \nopagebreak[4] %\vspace{0.25em} \nopagebreak %\samepage \begin{list}{}{\setlength{\leftmargin}{0.5\leftmargin} \setlength{\topsep}{0pt} \setlength{\itemindent}{\parindent} \setlength{\listparindent}{\parindent} } \item } {\hfill $\square$ \vspace{1em} \end{list}} %%%Quelques commandes personnelles %%\newcommand{\pbullet}{\par{$\bullet \;$}} \newcommand{\pbullet}{$\bullet \;$} \newcommand{\paragraphe}[1]{\vspace{1em} \pagebreak[2] {\sl \bfseries \noindent \boldmath #1} \vspace{0.5em} \nopagebreak[4] } \newcommand{\nom}{\begin{center} {\large Emmanuel }{\large \sc Hallouin}\\ {\large Universit\'e de Poitiers\\ Laboratoire de Math\'ematiques\\ URA D 1322\\ 40, avenue du Recteur Pineau\\ 86022 POITIERS Cedex}\\ \end{center}} %%Des operateur qui n'existent pas en TeX \newcommand{\ann}{\operatorname{ann}} \newcommand{\Aut}{\operatorname{Aut}} \newcommand{\carac}{\operatorname{carac}} \newcommand{\ch}{\operatorname{ch}} \newcommand{\coeff}{\operatorname{coeff}} \newcommand{\ct}{\operatorname{ct}} \newcommand{\diag}{\operatorname{diag}} \newcommand{\Dif}[2]{#1 \negthinspace #2} \newcommand{\dis}{\operatorname{dis}} \newcommand{\Frac}{\operatorname{Frac}} \newcommand{\Gal}{\operatorname{Gal}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\haut}{\operatorname{ht}} \newcommand{\Id}{\operatorname{Id}} \newcommand{\Ima}{\operatorname{Im}} \newcommand{\Ker}{\operatorname{Ker}} \newcommand{\lc}{\operatorname{lc}} \newcommand{\Mat}{\operatorname{Mat}} \newcommand{\Norme}{\operatorname{N}} \newcommand{\ordre}{\operatorname{ordre}} \newcommand{\Perm}{\operatorname{Perm}} \newcommand{\pgcd}{\operatorname{pgcd}} \newcommand{\ppcm}{\operatorname{ppcm}} \newcommand{\rad}{\operatorname{rad}} \newcommand{\Rad}{\operatorname{Rad}} \newcommand{\res}{\operatorname{res}} \newcommand{\rg}{\operatorname{rg}} \newcommand{\sh}{\operatorname{sh}} \newcommand{\Spec}{\operatorname{Spec}} \newcommand{\stab}{\operatorname{stab}} \newcommand{\Stab}{\operatorname{Stab}} \newcommand{\Tr}{\operatorname{Tr}} \newcommand{\Vect}{\operatorname{Vect}} %%Raccourcis pour certaines instructions \newcommand{\id}{\mathfrak} \newcommand{\ideng}[1]{\left\langle #1 \right\rangle} \newcommand{\num}[1]{$\text{n}^\circ \text{#1}$} \newcommand{\mapsgets}{\leftarrow\joinrel\mapstochar} \newcommand{\longmapsgets}{\longleftarrow\joinrel\mapstochar} \newcommand{\HH}{\mathbb H} \newcommand{\NN}{\mathbb N} \newcommand{\ZZ}{\mathbb Z} \newcommand{\QQ}{\mathbb Q} \newcommand{\RR}{\mathbb R} \newcommand{\CC}{\mathbb C} \newcommand{\FF}{\mathbb F} \newcommand{\UU}{\mathbb U} \newcommand{\PP}{\mathbb P} \newcommand{\OO}{\mathcal O} %%Préférence pour le franÁais \renewcommand{\geq}{\geqslant} \renewcommand{\leq}{\leqslant} %%L'outil reserve \catcode`\@=11 % registres de brouillon \def \reserve#1/#2{\begingroup \dimen@\prevdepth \setbox0\vbox{#2}% \dimen@i=\dp0 \advance\dimen@i by\ht0 \ht0=0pt \dp0=\dimen@i \skip@\baselineskip \multiply\skip@ by#1 \advance\skip@ by\baselineskip \global\dimen@i\wd0 \global\advance\dimen@i+5mm \nointerlineskip \nobreak \rightline{\vbox to0pt{\vskip\skip@\box0\vss}}% \nobreak \prevdepth\dimen@ \tolerance2000 \hfuzz2pt \hbadness2000 \interlinepenalty\@M \def\par{\endgraf\nobreak}% \@M = 10000 \everypar{\hangindent-\dimen@i \hangafter#1 \everypar{\hangindent-\dimen@i \hangafter0 }}} \def \endreserve#1/{\ifnum#1=\z@ \endgroup \else \everypar{\hangindent-\dimen@i \hangafter-#1 \def\par{\endgraf \endgroup}} \fi} %%Les extensions \catcode `\@ = 11 \newdimen \@fieldextensionwidth \def \fieldextensionwidth {\@fieldextensionwidth } \def \fieldextension #1#2% {\begingroup \countdef \@@counter@@ 0 \countdef \@@fieldcount@@ 1 \@@counter@@ 0 \@@fieldcount@@ #1% \chardef \@@fields@@ 0 \chardef \@@extensions@@ 1 \ifinner \let \@@style@@ \textstyle \else \let \@@style@@ \displaystyle \fi \ifdim \@fieldextensionwidth = 0pt \@fieldextensionwidth 1.5cm \fi \setbox \@@fields@@ \hbox {$\@@style@@ {#2}$}% \setbox \@@extensions@@ \hbox {\kern \wd \@@fields@@ }% \@processfieldextension } \def \@processfieldextension #1#2% {\advance \@@counter@@ by 1 \ifnum \@@counter@@ = \@@fieldcount@@ \def \@@next@@ {\global \@fieldextensionwidth 0pt \vbox {\box \@@extensions@@ \box \@@fields@@ }\endgroup }% \else \let \@@next@@ \@processfieldextension \fi \setbox 2 \hbox {\vrule height 0pt depth 2mm \vbox {\hbox to \@fieldextensionwidth {\strut \hfil $\@@style@@ {#1}$\hfil }\hrule }% \vrule height 0pt depth 2mm }% \setbox 3 \hbox {$\@@style@@ {#2}$}% \setbox \@@fields@@ \hbox {\unhbox 0 \kern -0.4em \kern \wd2 \copy3 }% \setbox \@@extensions@@ \hbox {\unhbox 1 \kern -0.2em \box2 \kern -0.2em \kern \wd3 }% \@@next@@ } \catcode `\@ = 12 %%$$ %%\fieldextension 2 {K} {n} {E} {k} {F} %%$$ %%\fieldextensionwidth = 3cm %%$$ %%\fieldextension 2 {K} {n} {E} {k} {F} %%$$ %% %%$$ %%\fieldextension 2 {K} {n\over k} {K(x^p)} k {K(x)} %%$$ %% %%$ %%\fieldextension 2 {K} {n\over k} {K(x^p)} k {K(x)} %%$ %%