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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /macros/latex/contrib/tableaux/exemples.tex
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+\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}