\Titre{Calcul de déterminants}

\def\det{\renewenvironment{pmatrix}{\begin{vmatrix}}{\end{vmatrix}}}

\definecolor{gris}{rgb}{0.6,0.6,0.6}
\lstset{xleftmargin=0mm,frame=shadowbox,rulesepcolor=\color{gris}}
\lstinputlisting[language=maxima]{cdet.mc}

.m load("cdet.mc")$

.m cdet([1,1,1],[a,b,c],[a^2,b^2,c^2]);

.m cdet([1,x,x],[x,1,x],[x,x,1]);

.m cdet([a,b,c],[b,c,a],[c,a,b]);

.m cdet([(b-c)^2,b^2,c^2],[a^2,(c-a)^2,c^2],[a^2,b^2,(a-b)^2]);

.m cdet([x,2,3],[3,x,2],[2,3,x]);

.m cdet([1+x,1,1],[1,1+x,1],[1,1,1+x]);

.m cdet([0,c,-b],[-c,0,a],[b,-a,0]);

.m cdet([0,m,m^2],[1/m,0,m],[1/m^2,1/m,0]);

.m cdet([0,sin(phi),sin(2*phi)],[sin(phi),0,sin(2*phi)],[sin(2*phi),sin(phi),0]);

.m cdet([1,alpha,alpha^2],[beta,1,alpha],[beta^2,beta,1]);

.m cdet([-m,m-1,m],[2*m-1,m-1,-m],[-2,-4,2*m]);

.m cdet([1,1,1],[a,b,c],[a^3,b^3,c^3]);

.m cdet([a+b,a*b,a^2+b^2],[b+c,b*c,b^2+c^2],[c+a,c*a,c^2+a^2]);

.m cdet([2*b,b-c-a,2*b],[a-b-c,2*a,2*a],[2*c,2*c,c-a-b]);