

\documentclass[12pt]{article}
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\usepackage[dvips,colorlinks=true,linkcolor=0.2white]{hyperref}
\usepackage[xcas]{pro-mat}
\usepackage{graphicx}
\usepackage{listings,luximono}

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\title{Opérations sur les matrices avec \texttt{pro-mat.sty} de la famille \texttt{professor}}


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keywordstyle =\color{0.2white}\usefont{OT1}{cmtt}{b}{n},basicstyle=\ttfamily,commentstyle=\normalfont\scriptsize\slshape,
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\begin{document}

\lat

\maketitle

La page dédiée à \texttt{pro-graphes.sty} se trouve à cette adresse~:

\begin{center}
  \href{http://mathsp.tuxfamily.org/spip.php?article213}{http://mathsp.tuxfamily.org/spip.php?article213}
\end{center}



\section{Écrire une matrice}

\begin{matmat}
 matmat([[112,2,cos(alpha)],[sqrt(2),0,1],[1/2,2,3]])
 \end{matmat}


\begin{lstlisting}
\begin{matmat}
 matmat([[112,2,cos(alpha)],[sqrt(2),0,1],[1/2,2,3]])
 \end{matmat}
\end{lstlisting}

\section{Produit de matrices}
Un produit de matrices de tailles différentes :

 \begin{promat}
 promat([[112,2,0],[0,0,1],[1,2,3]],[[1],[5],[0]],[["R","Z"]])
 \end{promat}

\begin{lstlisting}
\begin{promat}
 promat([[112,2,0],[0,0,1],[1,2,3]],[[1],[5],[0]],[["R","Z"]])
 \end{promat}
\end{lstlisting}

Un carré de matrice carré avec l'option trigo...
\begin{promat}
promat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[["R","R","R^2"],trigo])
\end{promat}

\begin{lstlisting}
\begin{promat}
promat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[["R","R","R^2"],trigo])
\end{promat}
\end{lstlisting}

Un produit de matrices de même taille sans option :
\begin{promat}
 promat([[1,2,0],[0,0,1],[1,2,3]],[[1,4,0],[5,6,0],[0,0,1]],[[]])
\end{promat}

\begin{lstlisting}
\begin{promat}
 promat([[1,2,0],[0,0,1],[1,2,3]],[[1,4,0],[5,6,0],[0,0,1]],[[]])
\end{promat}
\end{lstlisting}



\begin{promat}
promat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[[x],[y],[z]],[["R","U","R\\times U"]])
\end{promat}



\begin{lstlisting}
\begin{promat}
promat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[[x],[y],[z]],[["R","U","R\\times U"]])
\end{promat}

\end{lstlisting}


\section{Calcul de déterminant}


Un calcul de déterminant sans factorisation~:

\begin{detmat}
detmat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[])
\end{detmat}

\begin{lstlisting}
\begin{detmat}
detmat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],[])
\end{detmat}

\end{lstlisting}

Un autre calcul avec résultat factorisé~:

\begin{detmat}
detmat([[1-t,2,0],[1,2-t,0],[0,0,1-t]],[factor])
\end{detmat}

\begin{lstlisting}
\begin{detmat}
detmat([[1-t,2,0],[1,2-t,0],[0,0,1-t]],[factor])
\end{detmat}
\end{lstlisting}

\section{Inverse d'une matrice}


Des calculs d'inverse :

\begin{invmat}
 invmat([[1,-2,3],[1,0,0],[0,0,1]])
\end{invmat}

\begin{lstlisting}
\begin{invmat}
 invmat([[1,-2,3],[1,0,0],[0,0,1]])
\end{invmat}
\end{lstlisting}


\begin{invmat}
 invmat([[a,-b,3],[1,0,0],[0,0,1]])
\end{invmat}



\begin{lstlisting}
\begin{invmat}
 invmat([[a,-b,3],[1,0,0],[0,0,1]])
\end{invmat}
\end{lstlisting}


\section{Puissance d'une matrice}


\begin{puimat}
puimat([[1,1,1],[1,1,1],[1,1,1]],5,[])
\end{puimat}

\begin{lstlisting}
\begin{puimat}
puimat([[1,1,1],[1,1,1],[1,1,1]],5,[])
\end{puimat}
\end{lstlisting}


\begin{puimat}
puimat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],3,[trigo])
\end{puimat}

\begin{lstlisting}
\begin{puimat}
puimat([[cos(theta),-sin(theta),0],[sin(theta),cos(theta),0],[0,0,1]],3,[trigo])
\end{puimat}
\end{lstlisting}

\end{document}