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diff --git a/Master/texmf-dist/doc/latex/tableaux/exemples.tex b/Master/texmf-dist/doc/latex/tableaux/exemples.tex new file mode 100644 index 00000000000..6a590897af2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tableaux/exemples.tex @@ -0,0 +1,227 @@ +\documentclass[a4paper]{article} +\usepackage{minimum,ifthen,tableau} +\usepackage{fancyvrb} +\usepackage{fvrb-ex} + +\fvset{xrightmargin=0cm,frame=none} + +\newcommand{\coordp}[2] +{\begin{pmatrix} +#1 \\ #2 +\end{pmatrix}} + +\newpsstyle{hachured}{fillstyle=hlines,hatchwidth=0.2pt,hatchsep=2pt} + +\usepackage{bbm} +\newcommand{\GR}{\mathbbm{R}} +\newcommand{\txR}[1][x]{\forall #1 \in \GR \quad} + +\newcommand{\ssi}[1][,]{si, et seulement si#1 } + + +\begin{document} + +\begin{verbatim} + {\setlength{\TabTitreL}{1cm} + \begin{MonTableau}{3}{6}{.75} + + \small + + \TabNewCol{0} + \rTabPut{Br}{-.15}{.25}{$x$} + \rTabPut{Br}{-.15}{.40}{$x$} + \rTabPut{Br}{-.15}{.40}{$x^2-12$} + \rTabPut{Br}{-.15}{.40}{$f(x)$} + + \TabNewCol{0} + \rTabPut{Bl}{.15}{.25}{$-\infty$} + + \TabNewCol{.25} + \rTabPut{B}{0}{.25}{$-2\sqrt{3}$} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{.5} + \rTabPut{B}{0}{.25}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{.75} + \rTabPut{B}{0}{.25}{$2\sqrt{3}$} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{1} + \rTabPut{Br}{-.1}{.25}{$+\infty$} + + \rput(.125,.5){$-$}\rput(.375,.5){$-$}\rput(.625,.5){$+$}\rput(.875,.5){$+$} + \rput(.125,1.5){$+$}\rput(.375,1.5){$-$}\rput(.625,1.5){$-$}\rput(.875,1.5){$+$} + \rput(.125,2.5){$-$}\rput(.375,2.5){$+$}\rput(.625,2.5){$-$}\rput(.875,2.5){$+$} + + \end{MonTableau}} +\end{verbatim} + +Ce qui donne: + +\begin{enumerate} + +\begin{minipage}{8.2cm} + +\item $\txR f(x)=x(x-2\sqrt{3})(x+2\sqrt{3})$. +\item Un produit de facteur est nul \ssi au moins est de ses facteurs + est nul: $$f(x)=0\Leftrightarrow x\in\{-2\sqrt{3};0;2\sqrt{3}\}$$ +\item Tableau de signes ci-contre: + $$f(x)<0\Leftrightarrow x\in]-\infty;-2\sqrt{3}[\cup]0;2\sqrt{3}[$$ + +\end{minipage}\hfill +\begin{minipage}{7cm} + {\setlength{\TabTitreL}{1cm} + \begin{MonTableau}{3}{6}{.75} + + \small + + \TabNewCol{0} + \rTabPut{Br}{-.15}{.25}{$x$} + \rTabPut{Br}{-.15}{.40}{$x$} + \rTabPut{Br}{-.15}{.40}{$x^2-12$} + \rTabPut{Br}{-.15}{.40}{$f(x)$} + + \TabNewCol{0} + \rTabPut{Bl}{.15}{.25}{$-\infty$} + + \TabNewCol{.25} + \rTabPut{B}{0}{.25}{$-2\sqrt{3}$} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{.5} + \rTabPut{B}{0}{.25}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{.75} + \rTabPut{B}{0}{.25}{$2\sqrt{3}$} + \rTabPut[1]{B}{0}{.40}{} + \rTabPut[2]{B}{0}{.40}{\TabZ} + \rTabPut[2]{B}{0}{.40}{\TabZ} + + \TabNewCol{1} + \rTabPut{Br}{-.1}{.25}{$+\infty$} + + \rput(.125,.5){$-$}\rput(.375,.5){$-$}\rput(.625,.5){$+$}\rput(.875,.5){$+$} + \rput(.125,1.5){$+$}\rput(.375,1.5){$-$}\rput(.625,1.5){$-$}\rput(.875,1.5){$+$} + \rput(.125,2.5){$-$}\rput(.375,2.5){$+$}\rput(.625,2.5){$-$}\rput(.875,2.5){$+$} + + \end{MonTableau}}\vfill +\end{minipage} +\end{enumerate} + +\newpage + +\begin{Example} + {\setlength{\TabTitreL}{1cm} + \begin{MonTableau}{1}{9}{1.5} + + \psframe[style=hachured,linestyle=none](.3,1)(.45,0) + + \TabNewCol{0} + \rTabPut{Br}{-.15}{.25}{$x$} + \rTabPut{Br}{-.15}{.40}{$f(x)$} + + \TabNewCol{0} + \rTabPut{Bl}{.15}{.25}{$0$} + \rTabPut{Bl}{.15}{.60}{$\frac{3}{2}$} + + \TabNewCol{.30} + \rTabPut{B}{0}{.25}{$1$} + \rTabPut{Br}{-.15}{.80}{$+\infty$} + \psline[style=TabDblBarre](.3,0)(.3,1) + + \TabNewCol{.45} + \rTabPut{B}{0}{.25}{$\frac{3}{2}$} + \rTabPut[2]{B}{0}{.10}{\TabZ} + + \TabNewCol{1} + \rTabPut{Br}{-.15}{.25}{$+\infty$} + \rTabPut{Br}{-.15}{.40}{$1$} + + \TabFleche{B1}{C1} + \TabFleche{D1}{E1} + + \end{MonTableau}} +\end{Example} + +\newpage + +\begin{center} +\begin{Example} + \begin{MonTableau}{6}{12}{1.2} + + \TabNewCol{0} + \rTabPut{B}{-.75}{.25}{$t$} + \rTabPut{B}{-.75}{.20}{\TabTitre{Sgn.}{x'(t)}} + \rTabPut{B}{-.75}{.20}{\TabTitre{Var.}{x}} + \rTabPut{B}{-.75}{.20}{\TabTitre{Var.}{y}} + \rTabPut{B}{-.75}{.20}{\TabTitre{Sgn.}{y'(t)}} + \rTabPut{B}{-.75}{.40}{$\vec{T}$} + \rTabPut{B}{-.75}{.40}{$m_T$} + + \TabNewCol{0} + \rTabPut{B}{.5}{.25}{$0$} + \rTabPut{B}{.5}{.40}{$1,5$} + \rTabPut{B}{.5}{.40}{$2$} + \rTabPut{B}{.5}{.15}{$0$} + \rTabPut{B}{.5}{.40}{$1,5$} + \rTabPut{B}{.5}{.40}{$\coordp{1,5}{1,5}$} + \rTabPut{B}{.5}{.40}{$1$} + + % On recopie 4 fois cette dernière colonne et on ajuste + \TabNewCol{.25} + \rTabPut{B}{0}{.25}{$1$} + \rTabPut{B}{0}{.40}{$0$} + \rTabPut{B}{0}{.75}{$4$} + \rTabPut{B}{0}{.60}{$4$} + \rTabPut{B}{0}{.40}{$3$} + \rTabPut{B}{0}{.40}{$\coordp{0}{3}$} + \rTabPut{B}{0}{.40}{$\infty$} + + \TabNewCol{.5} + \rTabPut{B}{0}{.25}{$2$}\rTabPut{B}{0}{.40}{$-1.5$} + \rTabPut{B}{0}{.40}{$2$}\rTabPut{B}{0}{.75}{$6$} + \rTabPut{B}{0}{.40}{$0$}\rTabPut{B}{0}{.40}{$\coordp{-1.5}{0}$} + \rTabPut{B}{0}{.40}{$0$} + + \TabNewCol{.75} + \rTabPut{B}{0}{.25}{$3$}\rTabPut{B}{0}{.40}{$0$} + \rTabPut{B}{0}{.15}{$0$}\rTabPut{B}{0}{.60}{$4$} + \rTabPut{B}{0}{.40}{$-2$}\rTabPut{B}{0}{.40}{$\coordp{0}{-2}$} + \rTabPut{B}{0}{.40}{$\infty$} + + \TabNewCol{1} + \rTabPut{B}{-.5}{.25}{$4$}\rTabPut{B}{-.5}{.40}{$1$} + \rTabPut{B}{-.5}{.40}{$2$}\rTabPut{B}{-.5}{.15}{$0$} + \rTabPut{B}{-.5}{.40}{$1,5$}\rTabPut{B}{-.5}{.40}{$\coordp{1}{-1}$} + \rTabPut{B}{-.5}{.40}{$-1$} + + % les signes + et - on fait tout simplement + \rput(.145,0.5){$+$}\rput(.145,3.5){$+$} + \rput(.375,0.5){$-$}\rput(.375,3.5){$+$} + \rput(.625,0.5){$-$}\rput(.625,3.5){$-$} + \rput(.850,0.5){$+$}\rput(.850,3.5){$-$} + + % les flèches + \TabFleche{B2}{C2}\TabFleche{C2}{D2}\TabFleche{D2}{E2}\TabFleche{E2}{F2} + \TabFleche{B3}{C3}\TabFleche{C3}{D3}\TabFleche{D3}{E3}\TabFleche{E3}{F3} + + \TabTitreFerme\TabFerme + \end{MonTableau} +\end{Example} +\end{center} + + +\end{document} |