\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{francois_meria}
\RequirePackage{latexsym}
\RequirePackage{amsfonts}
\RequirePackage{amsmath}
\RequirePackage{amssymb}
\RequirePackage{amsthm}
\RequirePackage[cyr]{aeguill}
\RequirePackage{fancybox}
\RequirePackage{lastpage}
\RequirePackage{geometry}
\geometry{ hmargin=1.5cm, vmargin=1.5cm }
\RequirePackage{fancyhdr}
\RequirePackage{multicol,multirow}
\RequirePackage{enumerate}
\RequirePackage{array}
\RequirePackage{eurosym}
\RequirePackage{tabularx}
\RequirePackage{color}
\usepackage{pst-all,pst-eucl}
\usepackage{calc}
\usepackage{xlop}
\RequirePackage[french]{babel}
\RequirePackage[latin1]{inputenc}
\RequirePackage[T1]{fontenc}
\newcommand{\V}{\overrightarrow}
\def\euro{\mbox{\raisebox{.25ex}{{\it =}}\hspace{-.5em}{\sf C}}~}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\D}{\mathbb{D}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\diff}{\textrm{d}}
\newcommand{\e}{\textrm{e}}
\newcommand{\RE}{(O~;~\V{i},~\V{j})}
\newcommand{\RC}{(O~;~\V{u},~\V{v})}
\newcommand{\REP}{\mbox{$\left(O,\vec{\imath},\vec{\jmath}\right)$}}
\newcommand{\REPB}{\mbox{$\left(O,\vec{u},\vec{v}\right)$}}
\newcommand{\cad}{c.-à-d.}
\newcommand{\ie}{\textit{i.e.}}
\theoremstyle{definition}
\newtheorem{definition}{Définition}\newtheorem{activite}{Activité}
\newtheorem{theoreme}{Théorème}\newtheorem{remarque}{Remarque}\newtheorem{consequence}{Conséquence}[section]
\newtheorem{corollaire}[theoreme]{Corollaire}
\newtheorem{lemme}[theoreme]{Lemme}
\newtheorem{proposition}[theoreme]{Proposition}
\newtheorem{exemple}{Exemple}\newtheorem{propdefi}[definition]{Proposition-définition}
\newtheorem*{notation}{Notation}
\newtheorem{propriete}[theoreme]{Propriété}
\newtheorem{exercice}{Exercice}\newtheorem{methode}{Méthode}
\newtheorem{q}{Question}
\renewcommand{\floatpagefraction}{.9}
\renewcommand{\textfraction}{.1}
\newcommand{\QCM}[4]{
\begin{tabular}[t]{p{13cm}c}
#1 & \psset{xunit=1 cm}
\begin{pspicture}(-0.3,0)(1.5,0.5)
\pspolygon(0,0)(1.5,0)(1.5,-.5)(0,-.5)
\psline(.5,0)(.5,-.5) \psline(1,0)(1,-.5)
\uput[90](0.25,0){A} \uput[90](0.75,0){B} \uput[90](1.25,0){C}
\end{pspicture} \\
A : #2 \qquad B : #3 \qquad C : #4 & \\
\end{tabular}}
\newcounter{nexo}
\setcounter{nexo}{0}
\newcommand{\exo}{
\stepcounter{nexo}
{\textbf{$\triangleright$ Exercice \arabic{nexo} :}}
}
\newenvironment{questions}{\begin{enumerate}[1 $\, \diamond$]}{\end{enumerate}}
\def\m@th{\mathsurround=0pt}
\def\trou#1{
\setbox0=\hbox{\textbf{#1}} \dp0=0pt \m@th
\underline{\hbox{\hskip\wd0}}
}
\newcolumntype{I}{!{\vrule width 1.5pt}} \newlength\savedwidth
\newcommand\whline{\noalign{\global\savedwidth\arrayrulewidth\global\arrayrulewidth
1.5pt} \hline \noalign{\global\arrayrulewidth\savedwidth}}
\newcommand{\figurec}[2]{\begin{figure}[h]\begin{center}#1\end{center}\caption{#2}\end{figure}}
\def\d{$\diamond \,$}
\def\*{\times}
\def\Euro{\textgreek{\euro}\ }
\def\m@th{\mathsurround=0pt}
\def\trou#1{
\setbox0=\hbox{\textbf{#1}} \dp0=0pt \m@th
\underline{\hbox{\hskip\wd0}}
}
\newcommand{\ecriture}[1]{
\pspicture(.5,1)
\rput(0,-.55) {
\psline[linewidth=.5pt, linecolor=blue](0,.5)(18,.5)
\psline[linewidth=.2pt, linecolor=blue](0,.95)(18,.95)
\psline[linewidth=.5pt, linecolor=blue](0,1.5)(18,1.5)}
\endpspicture
{\Huge \cursive #1}
}
\newcommand{\machine}[4]{
\begin{pspicture}
\rput(0,0){\rnode{A}{#1}}
\rput(3,0.11){\rnode{B}{#2}}
\psset{nodesep=5pt}
\ncarc[arcangleA=25,arcangleB=25]{->}{A}{B}\mput*{\ovalnode{m}{#3}}
\ncarc[arcangleA=25,arcangleB=25]{->}{B}{A}\mput*{\ovalnode{d}{#4}}
\end{pspicture}
\hskip 3.1cm}
\newcommand{\cylindre}[5]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](#4,#3){HG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,#3){HD}
\pstGeonode[PointSymbol=none,PointName=none](#4,0){BG}
\pstGeonode[PointSymbol=none,PointName=none](-#4,0){BD}
\pstLineAB{HG}{BG}
\pstLineAB{HD}{BD}
\psplot[linestyle=dashed]{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp #5 mul #3 add}
\psplot{-#4}{#4}{#4 2 exp x 2 exp sub .5 exp -#5 mul #3 add}
}
\newcommand{\cone}[7]{
\pstGeonode[PointSymbol=*,PointName=#2](0,0){#1}
\pstGeonode[PointSymbol=none,PointName=none](10,0){Aamoi}
\pstGeonode[PointSymbol=none,PointName=none](0,#3){Hsommet}
\pstMiddleAB[PointSymbol=none,PointName=none]{#1}{Hsommet}{Milieuu}
\pstInterCC[PointSymbol=none,PointName=none,RadiusA=\pstDistVal{#6}]{#1}{}{Milieuu}{Hsommet}{Ibidon}{Jbidon}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Jbidon}{Jbidon'}
\pstProjection[PointSymbol=none,PointName=none]{#1}{Aamoi}{Ibidon}{Ibidon'}
\psplot[linestyle=dashed]{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp #7 mul}
\psplot{-#6}{#6}{#6 2 exp x 2 exp sub .5 exp -#7 mul}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=#5]{#1}{Hsommet}{#4}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Jbidon'}{Jbidon}{T1}
\pstHomO[HomCoef=#7,PointSymbol=none,PointName=none]{Ibidon'}{Ibidon}{T2}
\pstLineAB{#4}{T1}
\pstLineAB{#4}{T2}
}
\newcommand{\rapporteur}{
\SpecialCoor
\pscircle{5}
\multido{\i=0+1}{181}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4.5}
\multido{\i=0+10}{19}{\psline(5;\i)}
\pscircle[fillcolor=white,fillstyle=solid,linestyle=none]{4}
\pscircle[fillcolor=white,fillstyle=solid]{3}
\psframe[fillcolor=white,fillstyle=solid,linestyle=none](5,-5.1)(-5,-1.75)
\pscircle[fillcolor=white,fillstyle=solid]{.5}
\psframe[fillcolor=white,fillstyle=solid](-5,-1.75)(5,0)
\psline[linecolor=white](-.5,0)(.5,0)
\psline[linecolor=white](-3,0)(-4,0)
\psline[linecolor=white](3,0)(4,0)
\pscircle[fillcolor=white,fillstyle=solid]{.05}
\NormalCoor
}
\newcommand{\smallbox}{
\begin{pspicture}(.5,.5)
\pspolygon(0,0)(.25,0)(.25,.25)(0,.25)
\end{pspicture}}
\renewcommand{\vec}[1]
{\mathord{\setbox0\hbox{$#1$} \mathop{\smash{#1}\setbox1\copy0\ht1 0.8\ht0
\vphantom{\copy1}\mskip0.8\thinmuskip}
\limits^{\hbox to\wd0{$\mskip0.8\thinmuskip$\rightarrowfill}}\mskip-0.8\thinmuskip}}
\newcommand{\system}[2]{
\left\{
\begin{array}{l}
#1\\
#2
\end{array}
\right.
}
\newcommand{\interv}[2]{$\left[#1~;~#2\right]$}
\newcommand{\point}[3]{$#1\left(#2~;~#3\right)$}
\newcommand{\pcaxplusblitteral}[3]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} + #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(5,-0.2){$#2x$}
\put(9.5,-0.2){$#2x+#3$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxplusbcalcul}[4]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{b}
\opcopy{#4}{x}
\opmul*{a}{x}{c}
\opadd*{c}{b}{d}
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} + #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$#4$}
\put(5,-0.2){$\opprint{c}$}
\put(10,-0.2){$\opprint{d}$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxmoinsblitteral}[3]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} - #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(5,-0.2){$#2x$}
\put(9.5,-0.2){$#2x-#3$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxmoinsbcalcul}[4]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{b}
\opcopy{#4}{x}
\opmul*{a}{x}{c}
\opsub*{c}{b}{d}
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} - #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$#4$}
\put(5,-0.2){$\opprint{c}$}
\put(10,-0.2){$\opprint{d}$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxplusbresolution}[4]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} + #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(5,-0.2){$#2x$}
\put(9.5,-0.2){$#2x+#3$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
\vskip 0.3cm
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-2.7)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{b}
\opcopy{#4}{c}
\opsub*{c}{b}{k}
\opdiv*[period,decimalsepsymbol={,}]{k}{a}{q}{r}
\psline{<-}(1.2,0)(4.2,0) \psline{<-}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \div #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} - #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(-0.2,-0.2){$\boxed{\dfrac{\opprint{k}}{\opprint{a}}}$}
\put(5,-0.2){$\opprint{k}$}
\put(10,-0.2){$\opprint{c}$}
\put(-1.6,-0.2){$#1~:$}
\put(0.2,-1.8){La valeur de la solution}
\put(0.2,-2.5){(peut-être approchée) est $\opprint{q}$.}
\endpspicture
\end{center}
\end{minipage}
\end{minipage}
}}
\newcommand{\pcaxmoinsbresolution}[4]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(4.2,0) \psline{->}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \times #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} - #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(5,-0.2){$#2x$}
\put(9.5,-0.2){$#2x-#3$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
\vskip 0.3cm
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-2.7)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{b}
\opcopy{#4}{c}
\opadd*{c}{b}{k}
\opdiv*[period,decimalsepsymbol={,}]{k}{a}{q}{r}
\psline{<-}(1.2,0)(4.2,0) \psline{<-}(6.4,0)(9.4,0)
\put(2,0.5){$\begin{array}{c} \div #2 \\ \end{array}$}
\put(7.2,0.5){$\begin{array}{c} + #3 \\ \end{array}$}
\psline[linestyle=dotted](4.4,-0.4)(6.2,-0.4)
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(-0.2,-0.2){$\boxed{\dfrac{\opprint{k}}{\opprint{a}}}$}
\put(5,-0.2){$\opprint{k}$}
\put(10,-0.2){$\opprint{c}$}
\put(-1.6,-0.2){$#1~:$}
\put(0.2,-1.8){La valeur de la solution}
\put(0.2,-2.5){(peut-être approchée) est $\opprint{q}$.}
\endpspicture
\end{center}
\end{minipage}
\end{minipage}
}}
\newcommand{\pcaxlitteral}[2]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} \times #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(10,-0.2){$#2x$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxcalcul}[3]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{x}
\opmul*{a}{x}{c}
\psline{->}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} \times #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$\opprint{x}$}
\put(10,-0.2){$\opprint{c}$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
}}
\newcommand{\pcaxresolution}[3]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} \times #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(10,-0.2){$#2x$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
\vskip 0.3cm
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-2.7)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{c}
\opdiv*{c}{a}{q}{r}
\psline{<-}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} \div #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(-0.3,-0.2){$\boxed{\dfrac{\opprint{c}}{\opprint{a}}}$}
\put(10,-0.2){$\opprint{c}$}
\put(-1.6,-0.2){$#1~:$}
\put(0.2,-1.8){La valeur de la solution}
\put(0.2,-2.5){(peut-être approchée) est $\opprint{q}$.}
\endpspicture
\end{center}
\end{minipage}
\end{minipage}
}}
\newcommand{\pcxplusaresolution}[3]{\shadowbox{
\begin{minipage}[c]{0.4\textwidth}
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-0.8)(11,1.3)
\psline{->}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} + #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(0.2,-0.2){$x$}
\put(10,-0.2){$x+#2$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
\vskip 0.3cm
\begin{minipage}[c]{0.4\textwidth}
\begin{center}\psset{unit=0.5cm}
\pspicture(-1.5,-2.7)(11,1.3)
\opcopy{#2}{a}
\opcopy{#3}{c}
\opsub*{c}{a}{d}
\psline{<-}(1.2,0)(9.4,0)
\put(4.5,0.2){$\begin{array}{c} - #2 \\ \end{array}$}
\psline[linestyle=dotted](9.6,-0.4)(11.4,-0.4)
\put(-0.3,-0.2){$\boxed{\opprint{d}}$}
\put(10,-0.2){$\opprint{c}$}
\put(-1.6,-0.2){$#1~:$}
\endpspicture
\end{center}
\end{minipage}
\end{minipage}
}}
\endinput