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diff --git a/Master/texmf-dist/doc/latex/resolsysteme/ResolSysteme-exemples.tex b/Master/texmf-dist/doc/latex/resolsysteme/ResolSysteme-exemples.tex new file mode 100644 index 00000000000..f9daeb9826c --- /dev/null +++ b/Master/texmf-dist/doc/latex/resolsysteme/ResolSysteme-exemples.tex @@ -0,0 +1,103 @@ +% !TeX document-id = {f9c98d52-d889-44e1-8a1d-1b1aa5b344f6} +% !TeX TXS-program:compile = txs:///pdflatex + +\documentclass[french,a4paper,10pt]{article} +\usepackage[margin=1.5cm]{geometry} +\usepackage{ResolSysteme} +\usepackage{systeme} +\usepackage{babel} +\usepackage[most]{tcolorbox} +\sisetup{locale=FR,output-decimal-marker={,}} +\newtcblisting{ShowCodeTeX}[1][]{colback=white,colframe=red!75!black,listing options={style=tcblatex},#1} + +\begin{document} + +\part*{Version \og classique \fg{} avec xint} + +\section{Préambule sans utiliser python} + +\begin{ShowCodeTeX}[listing only] +\documentclass[french,a4paper,10pt]{article} +\usepackage[margin=1.5cm]{geometry} +\usepackage{ResolSysteme} %version classique +\usepackage{systeme} +\sisetup{locale=FR,output-decimal-marker={,}} +\end{ShowCodeTeX} + +\section{Déterminant d'une matrice, 2x2 ou 3x3} + +\begin{ShowCodeTeX} +Le déterminant de $A=\begin{pNiceMatrix} 1&2 \\ 3&4 \end{pNiceMatrix}$ est +$\det(A)=\DetMatrice(1,2 § 3,4)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +Le déterminant de $A=\begin{pNiceMatrix} -1&{0,5} \\ \frac12&4 \end{pNiceMatrix}$ est +$\det(A)=\DetMatrice[dec](-1,0.5 § 1/2,4)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +Le dét. de $A=\begin{pNiceMatrix} -1&\frac13&4 \\ \frac13&4&-1 \\ -1&0&0 \end{pNiceMatrix}$ est +$\det(A) \approx \DetMatrice[dec=3](-1,1/3,4 § 1/3,4,-1 § -1,0,0)$. +\end{ShowCodeTeX} + +\section{Inverse d'une matrice, 2x2 ou 3x3} + +\begin{ShowCodeTeX} +L'inverse de $A=\begin{pNiceMatrix} 1&2 \\ 3&4 \end{pNiceMatrix}$ est +$A^{-1}=\MatriceInverse<cell-space-limits=2pt>(1,2 § 3,4)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +L'inverse de $A=\begin{pNiceMatrix} 1&2 \\ 3&4 \end{pNiceMatrix}$ est +$A^{-1}=\MatriceInverse*<cell-space-limits=2pt>(1,2 § 3,4)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +L'inverse de $A=\begin{pNiceMatrix} 1&2 \\ 3&4 \end{pNiceMatrix}$ est +$A^{-1}=\MatriceInverse[d]<cell-space-limits=2pt>(1,2 § 3,4)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +L'inverse de $A=\begin{pNiceMatrix} 1&2&3\\4&5&6\\7&8&8 \end{pNiceMatrix}$ est +$A^{-1}=\MatriceInverse<cell-space-limits=2pt>(1,2,3 § 4,5,6 § 7,8,8)$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +L'inverse de $A=\begin{pNiceMatrix} 1&2&3\\4&5&6\\7&8&8 \end{pNiceMatrix}$ est +$A^{-1}=\MatriceInverse[n]<cell-space-limits=2pt>(1,2,3 § 4,5,6 § 7,8,8)$. +\end{ShowCodeTeX} + +\section*{Résolution d'un système, 2x2 ou 3x3} + +\begin{ShowCodeTeX} +La solution de $\systeme{-9x-8y=-8,3x-6y=-7}$ est $\mathcal{S}=% +\left\lbrace \SolutionSysteme(-9,-8 § 3,-6)(-8,-7) \right\rbrace$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +La solution de $\systeme{-9x-8y=-8,3x-6y=-7}$ est $\mathcal{S}=% +\left\lbrace \SolutionSysteme*[d](-9,-8 § 3,-6)(-8,-7) \right\rbrace$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +La solution de $\systeme{x+y+z=-1,3x+2y-z=6,-x-y+2z=-5}$ est $\mathcal{S}=% +\left\lbrace \SolutionSysteme(1,1,1 § 3,2,-1 § -1,-1,2)(-1,6,-5) \right\rbrace$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +La solution de $\systeme{x+y+z=-1,3x+2y-z=6,-x-y+2z=-5}$ est donnée par $X=% +\SolutionSysteme(1,1,1 § 3,2,-1 § -1,-1,2)(-1,6,-5)[Matrice]$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +La solution de $\systeme{3x+y-2z=-1,2x-y+z=4,x-y-2z=5}$ est $\mathcal{S}=% +\left\lbrace \SolutionSysteme(3,1,-2 § 2,-1,1 § 1,-1,-2)(-1,4,5) \right\rbrace$. +\end{ShowCodeTeX} + +\begin{ShowCodeTeX} +La solution de $\systeme{3x+y-2z=-1,2x-y+z=4,x-y-2z=5}$ est $\mathcal{S}=% +\left\lbrace \SolutionSysteme*[d](3,1,-2 § 2,-1,1 § 1,-1,-2)(-1,4,5) \right\rbrace$. +\end{ShowCodeTeX} + +\end{document}
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