The pbsheet class^{∗}

Djalil Chafaï

                     http://www.lsp.ups-tlse.fr/Chafai/
                    djalil DOT chafai AT laposte DOT net

February 14, 2004

1 Introduction

The pbsheet L^{A}TEX 2ε class is designed to simplify the typesetting of problems sheets with Mathematics and Computer Science content. It is intended to simplify teachers work. The author uses it for his French Agrégation teaching activities, cf.

http://www.lsp.ups-tlse.fr/Chafai/agregteam.html. Also, only the French

language is handled in the current version of pbsheet. An example is provided, in French too. Please be patient.

2 Usage

In the future versions of pbsheet, I will put here the description of all the macros and environments provided by pbsheet.cls. However, the example provided is very explicit and will help you a lot.

3 Remark on EPS and PDF graphics

To add a Bounding Box to an EPS file, one can use the epsffit program:

         epsffit -c llx lly urx ury oldfile.eps newfile.eps

The epsffit binary is provided by the Debian package psutils. To convert an EPS file to a PDF file, one can use the epstopdf program:

                         epstopdf file.eps

which produces file.pdf. The epstopdf binary is provided by the Debian pack-

age tetex-bin.

4 To do for next version

• Translate everything in English, including the Matlab files;

• Add Scilab examples; • Check for packages versions (recent listings for Scilab for example);

∗This document corresponds to pbsheet v0.1, dated 2004/02/14, .dtx pbsheet file.

• Add automatic inclusion of macros via a suitable class option;

• Add multilingual support via Babel;

• Provide more examples;

• Enhence the help file generated via pbsheet.dtx. Add documentation for macros and environments;

• Provide scripts for EPS to PDF conversion;

• Modify the \bibliography macro to automatically extract the BibTeX .bib filename by using the .tex filename of the TEX file. This will ensure interoperability with AUCTeX/RefTeX/BibCite.

5 Implementation

 1 %%
 2 \LoadClassWithOptions{article} \ProcessOptions\relax
 3 %%
 4 \ifx\pdfoutput\undefined
 5 \usepackage[latin1]{inputenc}
 6 \usepackage[T1]{fontenc}
 7 \usepackage{url}
 8 \usepackage[dvips]{graphicx}
 9 \newcommand{\phantomsection}{\null} %% provided by hyperref.
10 \else
11 \pdfoutput=1\pdfcompresslevel=9\pdfadjustspacing=1
12 \usepackage[pdftex,bookmarks,a4paper,colorlinks]{hyperref}
13 \usepackage{aeguill}
14 \usepackage[pdftex]{graphicx}
15 \hypersetup{bookmarksnumbered,plainpages=false,hypertexnames=false}
16 \hypersetup{pagecolor=blue,linkcolor=blue,citecolor=blue,urlcolor=blue}
17 \hypersetup{pdfcreator=PDFLaTeX with pbsheet class}
18 \fi
19 \RequirePackage{amsmath,amsfonts,amssymb,amsthm,latexsym}
20 \RequirePackage[a4paper,portrait]{geometry}
21 \RequirePackage{rotating}
22 \RequirePackage{moreverb}
23 \RequirePackage[latin1]{inputenc}
24 \RequirePackage{xspace}
25 \RequirePackage[francais]{babel}
26 \RequirePackage{color}
27 \RequirePackage{listings}
28 \ifx\pdfoutput\undefined
29 \else %% listings/hyperref compatibility.
30 \makeatletter
31 \providecommand*{\toclevel@lstlisting}{0}
32 \makeatother
33 \fi
34 %%%%
35 %%%% Macros et Environments

36 %%%%
37 %%
38 \newcommand{\MFILE}[1]{
39 \begin{lstinputlisting}[language=Matlab]{#1.m}%
40 \label{code:#1}%
41 \end{lstinputlisting}

42 }

43 %%
44 \newcommand{\SCEFILE}[1]{
45 \begin{lstinputlisting}[language=Scilab]{#1.sce}%
46 \label{code:#1}%
47 \end{lstinputlisting}

48 }

49 %%
50 \newcommand{\SCIFILE}[1]{
51 \begin{lstinputlisting}[language=Scilab]{#1.sci}%
52 \label{code:#1}%
53 \end{lstinputlisting}

54 }

55 %%
56 \newcommand{\FFIG}[5]{%%  fname cm scale floatparams caption
57 %% here, floatparams is in the set {vflt,rflt,lflt}, cf. floatflt doc.
58 \begin{floatingfigure}[#4]{#2}%
59  \begin{center}%
60  \includegraphics[scale=#3]{#1}%
61  \caption{#5}%
62  \label{fi:#1}%
63  \end{center}%
64 \end{floatingfigure}%

65 }

66 %%
67 \newcommand{\FIG}[4]{%% fname scale floatparams caption
68 \begin{figure}[#3]%
69 \begin{center}%
70 \includegraphics[scale=#2]{#1}%
71 \caption{{#4}}%
72 \label{fi:#1}%
73 \end{center}%
74 \end{figure}

75 }

76 %%
77 \makeatletter%
78 \newcommand{\@TITRE}{Feuille de Travaux Pratiques}
79 \newcommand{\@AUTEUR}{Anonyme}
80 \newcommand{\@DATE}{\today}
81 \newcommand{\@FORMATION}{Agr\'egation de math\'ematiques%
82 -- Oral de mod\'elisation stochastique}
83 \newcommand{\@ANNEE}{Ann\'ee}
84 \newcommand{\@ETABLISSEMENT}{\'Etablissement}
85 \newcommand{\@WEB}{http://www.lsp.ups-tlse.fr/Chafai/agregteam.html}
86 \newcommand{\@MEL}{anonyme@pas.net}
87 \newcommand{\TITRE}[1]{%
88 \renewcommand{\@TITRE}{#1}}
89 \newcommand{\AUTEUR}[1]{%

 90 \renewcommand{\@AUTEUR}{#1}}
 91 \newcommand{\DATE}[1]{%
 92 \renewcommand{\@DATE}{#1}}
 93 \newcommand{\FORMATION}[1]{%
 94 \renewcommand{\@FORMATION}{#1}}
 95 \newcommand{\ANNEE}[1]{%
 96 \renewcommand{\@ANNEE}{#1}}
 97 \newcommand{\ETABLISSEMENT}[1]{%
 98 \renewcommand{\@ETABLISSEMENT}{#1}}
 99 \newcommand{\WEB}[1]{%
100 \renewcommand{\@WEB}{#1}}
101 \newcommand{\MEL}[1]{%
102 \renewcommand{\@MEL}{#1}}
103 \makeatother

104 %%

105 \makeatletter
106 \newcommand{\PREMIEREPAGE}{%
107 \newpage\null%
108 \begin{center}%
109  \hrule height .2pt%
110  \medskip{\Large\bfseries\@TITRE\par}\medskip%
111  \hrule height .2pt%
112 \end{center}%
113 \bigskip%\vfil%

114 }

115 \makeatother

116 %%

117 \theoremstyle{plain}%
118 \newtheorem{thm}{Theor\`eme}[section]%
119 \newtheorem{cor}[thm]{Corollaire}%
120 \newtheorem{prop}[thm]{Proposition}%
121 \newtheorem{lem}[thm]{Lemme}%
122 \theoremstyle{definition}%
123 \newtheorem{defi}[thm]{D\'efinition}%
124 \newtheorem{xpl}[thm]{Exemple}%
125 \newtheorem{exo}[thm]{Exercice}%
126 \newtheorem{hyp}[thm]{Hypoth\`ese}%
127 \newtheorem{eur}[thm]{Heuristique}%
128 \newtheorem{pro}[thm]{Probl\`eme}%
129 \theoremstyle{remark}%
130 \newtheorem{rem}[thm]{Remarque}%
131 %%%%
132 %%%% Commands to be executed before \begin{document}
133 %%%%

134 %%

135 \geometry{left=2.5cm,right=2.5cm}

136 %%

137 \lstset{extendedchars=true,%
138  basicstyle=\small,%
139  commentstyle=\ttfamily\color[rgb]{0,0,0.5},%
140  stringstyle=\color[rgb]{0,0.5,0},%
141  frame=tblr,frameround=tttt,%
142  %%labelstyle=\tiny,labelstep=1,labelsep=10pt

143 } 144 %%

145 \makeatletter
146 \renewcommand{\@evenfoot}
147 {\tiny\normalfont
148 \@DATE. Copyright  \@AUTEUR\ \@MEL. GNU FDL Copyleft.
149 %%  \url{http://www.gnu.org/copyleft/fdl.html}.
150 \hfil \upshape Page n{\thepage}.}
151 \renewcommand{\@evenhead}
152 {\tiny\scshape \@ETABLISSEMENT\ -- \@FORMATION\ --
153 \normalfont\bfseries\@ANNEE.
154 \normalfont\hfil \upshape Page n{\thepage}.}
155 \renewcommand{\@oddfoot}{\@evenfoot}
156 \renewcommand{\@oddhead}{\@evenhead}
157 \makeatother
158 %% smaller sections titles
159 \makeatletter
160 \renewcommand{\section}{\@startsection%
161 {section}%                           % name
162 {1}%                                 % level
163 {0em}%                               % indent
164 {\baselineskip}%                     % beforeskip
165 {0.5\baselineskip}%                  % afterskip
166 {\normalfont\large\bfseries}}%       % style
167 \renewcommand{\subsection}{\@startsection%
168 {subsection}%                        % name
169 {2}%                                 % level
170 {0em}%                               % indent
171 {\baselineskip}%                     % beforeskip
172 {0.25\baselineskip}%                 % afterskip
173 {\normalfont\bfseries}%              % style

174 }

175 \makeatother

176 %%

177 %% Macros

178 %%

179 \newcommand{\DOIFPDF}[2]{\ifx\pdfoutput\undefined #2\else#1\fi}
180 %% For nice typesetting of the actual engine name.
181 \newcommand{\EngineName}{\DOIFPDF{\texttt{pdf}\LaTeX}{\LaTeXe}}
182 %% For short rough notes and warnings.
183 \newcommand{\NB}[1]{{\large\textbf{*** #1 ***}}}
184 %% To force maths mode.
185 \newcommand{\EM}{\ensuremath}
186 %%% Limits
187 \newcommand{\limLeb}[2]
188 {\underset{#1\to+\infty}{\overset{\bL^{#2}}{\longrightarrow}}}
189 \newcommand{\limE}[1]
190 {\underset{#1\to+\infty}{\overset{\text{tr.}}{\longrightarrow}}}
191 \newcommand{\limW}[1]
192 {\underset{#1\to+\infty}{\overset{\text{weak}}{\longrightarrow}}}
193 \newcommand{\limP}[1]
194 {\underset{#1\to+\infty}{\overset{\dP}{\longrightarrow}}}
195 \newcommand{\limL}[1]
196 {\underset{#1\to+\infty}{\overset{\cL}{\longrightarrow}}}
197 \newcommand{\limn}[1]

198 {\underset{#1\to+\infty}{\longrightarrow}}
199 \newcommand{\mylim}[2]
200 {\underset{#1\to#2}{\longrightarrow}}
201 \newcommand{\limPS}[1]
202 {\underset{#1\to+\infty}{\overset{\text{p.s.}}{\longrightarrow}}}
203 \newcommand{\limAS}[1]
204 {\underset{#1\to+\infty}{\overset{\text{a.s.}}{\longrightarrow}}}
205 %% Time
206 \makeatletter
207 \providecommand{\timenow}{\@tempcnta\time%
208 \@tempcntb\@tempcnta%
209 \divide\@tempcntb60%
210 \ifnum10>\@tempcntb0\fi\number\@tempcntb%
211 \multiply\@tempcntb60%
212 \advance\@tempcnta-\@tempcntb%
213 :\ifnum10>\@tempcnta0\fi\number\@tempcnta}
214 \makeatother
215 %% Mathmode double capital letters.
216 \newcommand{\dA}{\EM{\mathbb{A}}}
217 \newcommand{\dB}{\EM{\mathbb{B}}}
218 \newcommand{\dC}{\EM{\mathbb{C}}}
219 \newcommand{\dD}{\EM{\mathbb{D}}}
220 \newcommand{\dE}{\EM{\mathbb{E}}}
221 \newcommand{\dF}{\EM{\mathbb{F}}}
222 \newcommand{\dG}{\EM{\mathbb{G}}}
223 \newcommand{\dH}{\EM{\mathbb{H}}}
224 \newcommand{\dI}{\EM{\mathbb{I}}}
225 \newcommand{\dJ}{\EM{\mathbb{J}}}
226 \newcommand{\dK}{\EM{\mathbb{K}}}
227 \newcommand{\dL}{\EM{\mathbb{L}}}
228 \newcommand{\dM}{\EM{\mathbb{M}}}
229 \newcommand{\dN}{\EM{\mathbb{N}}}
230 \newcommand{\dO}{\EM{\mathbb{O}}}
231 \newcommand{\dP}{\EM{\mathbb{P}}}
232 \newcommand{\dQ}{\EM{\mathbb{Q}}}
233 \newcommand{\dR}{\EM{\mathbb{R}}}
234 \newcommand{\dS}{\EM{\mathbb{S}}}
235 \newcommand{\dT}{\EM{\mathbb{T}}}
236 \newcommand{\dU}{\EM{\mathbb{U}}}
237 \newcommand{\dV}{\EM{\mathbb{V}}}
238 \newcommand{\dW}{\EM{\mathbb{W}}}
239 \newcommand{\dX}{\EM{\mathbb{X}}}
240 \newcommand{\dY}{\EM{\mathbb{Y}}}
241 \newcommand{\dZ}{\EM{\mathbb{Z}}}
242 %% Mathmode Roman capital letters.
243 \newcommand{\rA}{\EM{\mathrm{A}}}
244 \newcommand{\rB}{\EM{\mathrm{B}}}
245 \newcommand{\rC}{\EM{\mathrm{C}}}
246 \newcommand{\rD}{\EM{\mathrm{D}}}
247 \newcommand{\rE}{\EM{\mathrm{E}}}
248 \newcommand{\rF}{\EM{\mathrm{F}}}
249 \newcommand{\rG}{\EM{\mathrm{G}}}
250 \newcommand{\rH}{\EM{\mathrm{H}}}
251 \newcommand{\rI}{\EM{\mathrm{I}}}

252 \newcommand{\rJ}{\EM{\mathrm{J}}}
253 \newcommand{\rK}{\EM{\mathrm{K}}}
254 \newcommand{\rL}{\EM{\mathrm{L}}}
255 \newcommand{\rM}{\EM{\mathrm{M}}}
256 \newcommand{\rN}{\EM{\mathrm{N}}}
257 \newcommand{\rO}{\EM{\mathrm{O}}}
258 \newcommand{\rP}{\EM{\mathrm{P}}}
259 \newcommand{\rQ}{\EM{\mathrm{Q}}}
260 \newcommand{\rR}{\EM{\mathrm{R}}}
261 \newcommand{\rS}{\EM{\mathrm{S}}}
262 \newcommand{\rT}{\EM{\mathrm{T}}}
263 \newcommand{\rU}{\EM{\mathrm{U}}}
264 \newcommand{\rV}{\EM{\mathrm{V}}}
265 \newcommand{\rW}{\EM{\mathrm{W}}}
266 \newcommand{\rX}{\EM{\mathrm{X}}}
267 \newcommand{\rY}{\EM{\mathrm{Y}}}
268 \newcommand{\rZ}{\EM{\mathrm{Z}}}
269 %% Mathmode calligraphic capital letters.
270 \newcommand{\cA}{\EM{\mathcal{A}}}
271 \newcommand{\cB}{\EM{\mathcal{B}}}
272 \newcommand{\cC}{\EM{\mathcal{C}}}
273 \newcommand{\cD}{\EM{\mathcal{D}}}
274 \newcommand{\cE}{\EM{\mathcal{E}}}
275 \newcommand{\cF}{\EM{\mathcal{F}}}
276 \newcommand{\cG}{\EM{\mathcal{G}}}
277 \newcommand{\cH}{\EM{\mathcal{H}}}
278 \newcommand{\cI}{\EM{\mathcal{I}}}
279 \newcommand{\cJ}{\EM{\mathcal{J}}}
280 \newcommand{\cK}{\EM{\mathcal{K}}}
281 \newcommand{\cL}{\EM{\mathcal{L}}}
282 \newcommand{\cM}{\EM{\mathcal{M}}}
283 \newcommand{\cN}{\EM{\mathcal{N}}}
284 \newcommand{\cO}{\EM{\mathcal{O}}}
285 \newcommand{\cP}{\EM{\mathcal{P}}}
286 \newcommand{\cQ}{\EM{\mathcal{Q}}}
287 \newcommand{\cR}{\EM{\mathcal{R}}}
288 \newcommand{\cS}{\EM{\mathcal{S}}}
289 \newcommand{\cT}{\EM{\mathcal{T}}}
290 \newcommand{\cU}{\EM{\mathcal{U}}}
291 \newcommand{\cV}{\EM{\mathcal{V}}}
292 \newcommand{\cW}{\EM{\mathcal{W}}}
293 \newcommand{\cX}{\EM{\mathcal{X}}}
294 \newcommand{\cY}{\EM{\mathcal{Y}}}
295 \newcommand{\cZ}{\EM{\mathcal{Z}}}
296 %% Mathmode bold capital letters.
297 \newcommand{\bA}{\EM{\mathbf{A}}}
298 \newcommand{\bB}{\EM{\mathbf{B}}}
299 \newcommand{\bC}{\EM{\mathbf{C}}}
300 \newcommand{\bD}{\EM{\mathbf{D}}}
301 \newcommand{\bE}{\EM{\mathbf{E}}}
302 \newcommand{\bF}{\EM{\mathbf{F}}}
303 \newcommand{\bG}{\EM{\mathbf{G}}}
304 \newcommand{\bH}{\EM{\mathbf{H}}}
305 \newcommand{\bI}{\EM{\mathbf{I}}}

306 \newcommand{\bJ}{\EM{\mathbf{J}}}
307 \newcommand{\bK}{\EM{\mathbf{K}}}
308 \newcommand{\bL}{\EM{\mathbf{L}}}
309 \newcommand{\bM}{\EM{\mathbf{M}}}
310 \newcommand{\bN}{\EM{\mathbf{N}}}
311 \newcommand{\bO}{\EM{\mathbf{O}}}
312 \newcommand{\bP}{\EM{\mathbf{P}}}
313 \newcommand{\bQ}{\EM{\mathbf{Q}}}
314 \newcommand{\bR}{\EM{\mathbf{R}}}
315 \newcommand{\bS}{\EM{\mathbf{S}}}
316 \newcommand{\bT}{\EM{\mathbf{T}}}
317 \newcommand{\bU}{\EM{\mathbf{U}}}
318 \newcommand{\bV}{\EM{\mathbf{V}}}
319 \newcommand{\bW}{\EM{\mathbf{W}}}
320 \newcommand{\bX}{\EM{\mathbf{X}}}
321 \newcommand{\bY}{\EM{\mathbf{Y}}}
322 \newcommand{\bZ}{\EM{\mathbf{Z}}}
323 %% Useful shortcuts to some Greek letters and symbols.
324 \newcommand{\al}{\alpha}
325 \newcommand{\be}{\beta}
326 \newcommand{\De}{\Delta}
327 \newcommand{\de}{\delta}
328 \newcommand{\ga}{\gamma}
329 \newcommand{\Ga}{\Gamma}
330 \newcommand{\g}{\gamma}
331 \newcommand{\gn}{\g_n}
332 \newcommand{\gt}[1]{\g^{\otimes #1}}
333 \newcommand{\la}{\lambda}
334 \newcommand{\La}{\Lambda}
335 \newcommand{\lan}{\la_n}
336 \newcommand{\na}{\nabla}
337 \newcommand{\Om}{\Omega}
338 \newcommand{\om}{\omega}
339 \newcommand{\ph}{\Phi}
340 \newcommand{\Si}{\Sigma}
341 \newcommand{\si}{\sigma}
342 \newcommand{\Te}{\Theta}
343 \newcommand{\te}{\theta}
344 \newcommand{\ta}{\tau}
345 \newcommand{\Ups}{\Upsilon}
346 \newcommand{\veps}{\varepsilon}
347 \newcommand{\vphi}{\varphi}
348 \newcommand{\bul}{\EM{\bullet}}
349 %% Functional prototype with dimensioning.
350 \newcommand{\p}[4]{{#3}\!\left#1{#4}\right#2}
351 %% Norms and related.
352 \newcommand{\ABS}[1]{\EM{{\left| #1 \right|}}} % |1|
353 \newcommand{\BRA}[1]{\EM{{\left\{#1\right\}}}} % {1}
354 \newcommand{\DP}[1]{\EM{{\left<#1\right>}}} % <1>
355 \newcommand{\NRM}[1]{\EM{{\left\| #1\right\|}}} % ||1||
356 \newcommand{\NI}[1]{\EM{{\left\| #1\right\|}_\infty}} % infinite norm.
357 \newcommand{\OSC}[1]{\EM{{\p(){\mathrm{osc}}{#1}}}} % oscillation.
358 \newcommand{\PAR}[1]{\EM{{\left(#1\right)}}} % (1)
359 \newcommand{\BPAR}[1]{\EM{{\biggl(#1\biggr)}}} % (1)

360 \newcommand{\BABS}[1]{\EM{{\biggl|#1\biggr|}}} % (1)
361 \newcommand{\pd}{\EM{\partial}} % derivee partielle
362 \newcommand{\PD}[2]{\EM{{\frac{\partial #1}{\partial #2}}}}%part. deriv.
363 \newcommand{\SBRA}[1]{\EM{{\left[#1\right]}}} % [1]
364 \newcommand{\VT}[1]{\EM{{\|#1\|}_{\text{\scriptsize VT}}}} % tot. var.
365 \newcommand{\LIP}[1]{\EM{\|#1\|_{\mathrm{Lip}}}} % Lipschitz norm.
366 \newcommand{\WH}[1]{\widehat{#1}}
367 %% Fonctionals and functions.
368 \newcommand{\sentf}{\bH}
369 \newcommand{\sent}[1]{\p(){\sentf}{#1}}
370 \newcommand{\bentf}[1]{\bH_{#1}}
371 \newcommand{\bent}[2]{\p(){\bentf{#1}}{#2}}
372 \newcommand{\eentf}{\bN}
373 \newcommand{\eent}[1]{\p(){\eentf}{#1}}
374 \newcommand{\entf}[1]{\mathbf{Ent}_{#1}}
375 \newcommand{\ent}[2]{\p(){\entf{#1}}{#2}}
376 \newcommand{\ientf}[1]{\bH^{#1}}
377 \newcommand{\ient}[2]{\p(){\ientf{#1}}{#2}}
378 \newcommand{\rentf}{\mathbf{Ent}}
379 \newcommand{\rent}[2]{\p(){\rentf}{#1\,\vert\,#2}}
380 \newcommand{\entr}{\mathbf{Ent}_r}
381 \newcommand{\enef}[1]{\boldsymbol{\mathcal{E}}_{#1}}
382 \newcommand{\ene}[2]{\p(){\enef{#1}}{#2}}
383 \newcommand{\imutf}{\bI}
384 \newcommand{\imut}[1]{\p(){\imutf}{#1}}
385 \newcommand{\fcrf}{\dI}
386 \newcommand{\fcr}[1]{\p(){\fcrf}{#1}}
387 \newcommand{\fishf}{\bJ}
388 \newcommand{\fish}[1]{\p(){\fishf}{#1}}
389 \newcommand{\fishmf}{\dJ}
390 \newcommand{\fishm}[1]{\p(){\fishmf}{#1}}
391 \newcommand{\moyf}[1]{\bE_{#1}}
392 \newcommand{\moy}[2]{\p(){\moyf{#1}}{#2}}
393 \newcommand{\econd}[2]{\p(){\moyf{}}{#1\,\vert\,#2}}
394 \newcommand{\bmoy}[2]{\moyf{#1}\!\biggl(#2\biggr)}
395 \newcommand{\corrf}[1]{\mathbf{Cor}_{#1}}
396 \newcommand{\corr}[3]{\p(){\corrf{#1}}{#2,#3}}
397 \newcommand{\covf}[1]{\mathbf{Cov}_{#1}}
398 \newcommand{\cov}[3]{\p(){\covf{#1}}{#2,#3}}
399 \newcommand{\bcov}[3]{\covf{#1}\!\biggl(#2,#3\biggr)}
400 \newcommand{\suppf}{\mathrm{supp}}
401 \newcommand{\supp}[1]{\suppf\PAR{#1}}
402 \newcommand{\DIMF}{\mathrm{dim}}
403 \newcommand{\DIM}[1]{\DIMF\PAR{#1}}
404 \newcommand{\RANGEF}{\mathrm{range}}
405 \newcommand{\RANGE}[1]{\RANGEF\PAR{#1}}
406 \newcommand{\varf}[1]{\mathbf{Var}_{#1}}
407 \newcommand{\var}[2]{\p(){\varf{#1}}{#2}}
408 \newcommand{\bvar}[2]{\varf{#1}\!\biggl(#2\biggr)}
409 \newcommand{\Kf}{\bK}
410 \newcommand{\K}[1]{\p(){\Kf}{#1}}
411 \newcommand{\vrs}[1]{\mathbf{L}_{#1}}
412 \newcommand{\lik}[1]{\vrs{#1}}
413 %% Sets, spaces, and functional spaces.

414 \newcommand{\C}[1]{\p(){\cC}{#1}}
415 \newcommand{\Cb}[1]{\p(){\cC_b}{#1}}
416 \newcommand{\Cc}[1]{\p(){\cC_c}{#1}}
417 \newcommand{\Cn}[2]{\p(){\cC^{#1}}{#2}}
418 \newcommand{\Ci}[1]{\Cn{\infty}{#1}}
419 \newcommand{\Cic}[1]{\p(){\cC_c^\infty}{#1}}
420 \newcommand{\Cnc}[2]{\p(){\cC_c^{#1}}{#2}}
421 \newcommand{\Cnb}[2]{\p(){\cC_b^{#1}}{#2}}
422 \newcommand{\Cib}[1]{\p(){\cC_b^\infty}{#1}}
423 \newcommand{\leb}[2]{\p(){\bL^{#1}}{#2}}
424 \newcommand{\lebb}[1]{\bL^{#1}}
425 %% Determinant, trace, ...
426 \newcommand{\Tr}{\mathrm{Tr\,}}
427 \newcommand{\Det}[1]{\mathrm{Det}\,}
428 \newcommand{\TR}[1]{\p(){\mathrm{Tr}}{#1}}
429 \newcommand{\DIAG}[1]{\p(){\mathrm{Diag}}{#1}}
430 \newcommand{\DET}[1]{\p(){\mathrm{Det}}{#1}}
431 \newcommand{\SIG}[1]{\p(){\mathrm{Sign}}{#1}}
432 \newcommand{\KER}[1]{\p(){\mathrm{Ker}}{#1}}
433 \newcommand{\RG}[1]{\p(){\mathrm{Range}}{#1}}
434 \newcommand{\DIAM}[1]{\p(){\mathrm{Diam}}{#1}}
435 \newcommand{\ID}{\mathbf{Id}}
436 \newcommand{\Id}{\mathrm{Id}}
437 \newcommand{\Mo}{\mathbf{1}}
438 \newcommand{\Vo}{\mathrm{1}}
439 %%% Semi-groups, generators, carre-du-champ, ...
440 \newcommand{\CD}{CD(\rho ,\infty)}
441 \newcommand{\GA}{\boldsymbol{\Gamma}}
442 \newcommand{\GD}{\GA_{\!\!{\mathbf 2}}}
443 \newcommand{\GI}{\bL}
444 \newcommand{\GR}{\nabla}
445 \newcommand{\GIV}{\EM{\overrightarrow{\GI}}}
446 \newcommand{\GIB}{\EM{\overline{\GI}}}
447 \newcommand{\LA}{\boldsymbol{\Delta}}
448 \newcommand{\ROT}{\mathbf{rot}\,}
449 \newcommand{\DIV}{\mathbf{div}\,}
450 \newcommand{\PT}[1][t]{\mathbf{P}_{\!#1}}
451 \newcommand{\SGf}[1]{{\mathbf P}_{#1}}
452 \newcommand{\SG}[2]{\p(){\SGf{\!#1}}{#2}}
453 \newcommand{\SGQf}[1]{{\mathbf Q}_{#1}}
454 \newcommand{\SGQ}[2]{\p(){\SGQf{#1}}{#2}}
455 \newcommand{\isopf}{\mathbf{I}}
456 \newcommand{\isop}[1]{\p(){\isopf}{#1}}
457 \newcommand{\disop}[1]{\p(){\isopf'}{#1}}
458 \newcommand{\ddisop}[1]{\p(){\isopf''}{#1}}
459 \newcommand{\HESS}[1]{\GR^2\!{#1}}
460 \newcommand{\Hess}[1]{{\p(){\mathrm{Hess}}{#1}}}
461 \newcommand{\HAM}{\bH}
462 \newcommand{\POT}{\bV}
463 \newcommand{\PF}{\bZ}
464 \newcommand{\DOM}{\EM{\cD_2(\GI)}}
465 \newcommand{\laV}{\EM{\overrightarrow{\la}}}
466 \newcommand{\DOML}{\EM{\cD_2\PAR{\GI}}}
467 \newcommand{\DOMB}{\EM{\cD_2(\GIB)}}

468 \newcommand{\DOMV}{\EM{\cD_2(\GIV)}}
469 \newcommand{\GAV}{\EM{\overrightarrow{\GA}}}
470 \newcommand{\D}{\mathbf{D}}
471 %% Topology.
472 \newcommand{\inter}[1]{{\overset{\circ}{#1}}} % interior
473 \newcommand{\adher}[1]{{\overline{#1}}} % adherence
474 \newcommand{\ADH}[1]{\mathbf{adh}(#1)}
475 \newcommand{\INT}[1]{\mathbf{int}(#1)}
476 %% Miscellany.
477 \newcommand{\DOTIMES}{\otimes\cdots\otimes}
478 \newcommand{\DOPLUS}{\oplus\cdots\oplus}
479 \newcommand{\CARD}{\mathrm{card}}
480 \newcommand{\SSK}[1]{\substack{#1}}
481 \renewcommand{\leq}{\leqslant}
482 \renewcommand{\geq}{\geqslant}
483 \newcommand{\bs}{\EM{\backslash}}
484 \newcommand{\Inf}{\boldsymbol{\inf}}
485 \newcommand{\Sup}{\boldsymbol{\sup}}
486 \newcommand{\ds}[1]{\EM{\displaystyle{#1}}}
487 \newcommand{\eg}{\overset{\Delta}{=}}
488 \newcommand{\fdefeq}{\overset{\text{df.}}{=}}
489 \newcommand{\edefeq}{\overset{\text{def.}}{=}}
490 \newcommand{\defeq}{:=}
491 \newcommand{\equ}{\; \Leftrightarrow \;}
492 \newcommand{\ex}{\exists \,}
493 \newcommand{\imp}{\Rightarrow  \;}
494 \newcommand{\ssi}{{\it ssi}}
495 \newcommand{\tout}{\forall \,}
496 \newcommand{\tq}{\,|\,}
497 \newcommand{\st}{\,|\,}
498 %\newcommand{\1}{\hbox{1}\!\!\hbox{I}} %Bugs with xy package...
499 \newcommand{\DSFRAC}[2]{\EM{\frac{\ds{#1}}{\ds{#2}}}}
500 \newcommand{\SR}[2]{\EM{\strackrel{#1}{#2}}}
501 %Some Babel extension.
502 \def\Ieme{\up{\lowercase{ime}}\xspace}
503 %% Vectors and matrices.
504 \newcommand{\VECTOR}[1]{\PAR{\begin{array}{c} #1 \end{array}}}
505 \newcommand{\BIMATRIX}[1]{\PAR{\begin{array}{cc} #1 \end{array}}}
506 \newcommand{\Vector}[2]{\PAR{\begin{array}{#1} #2 \end{array}}}
507 \newcommand{\Bimatrix}[2]{\PAR{\begin{array}{#1} #2 \end{array}}}
508 %%%%
509 %%%% Commands to be executed just after \begin{document}
510 %%%%
511 \AtBeginDocument{%
512 \selectlanguage{francais}%
513 \graphicspath{{images/}{img/}{Images}{Img}{ps}{eps}{PS}{EPS}%
514 {postscript}{postscripts}{pdf}{PDF}}%
515 \PREMIEREPAGE%

516 }

517 %%%%
518 %%%% Commands to be executed just before \end{document}
519 %%%%
520 \AtEndDocument{\vfill}

521 %