\documentclass[12pt,a4paper]{article}
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\newcommand{\xcas}{{\bfseries\texttt{Xcas}}}

\title{Exemples d'utilisation de \texttt{Giac}}
\author{Jean-Michel Sarlat}


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\maketitle
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La plupart des exemples qui apparaissent ici sont tirés du
\emph{tutorial} de \xcas.

\section{Premiers calculs}

.g 1/3+1/4;
.g sqrt(2)^5;
.g solve(a*x^2+b*x+c,x);
.g 50!
.g 2*a+b;
.g a/2*b;
.g a/2/b;
.g a^2*b;

.g sqrt(2);
.g evalf(sqrt(2));
.g sqrt(2)-evalf(sqrt(2));
.g exact(evalf(sqrt(2)))*10^9;
.g exact(evalf(sqrt(2)*10^9));

.g evalf(sqrt(2),50);
.g evalf(pi,70);

.g Digits:=50;
.g evalf(pi);
.g evalf(exp(pi*sqrt(163)));

.g (1+2*i)^2;
.g (1+2*i)/(1-2*i);
.g e^(i*pi/3);

.g 1/0; (1/0)^2; -(1/0)^2;


\section{Manipulation des chaînes de caractères}

.g s:="azertyuiop";

.g size(s);

.g s[0]+s[3]+s[size(s)-1];

.g concat(s[0],concat(s[3],s[size(s)-1]));

.g head(s);

.g tail(s);

.g mid(s,3,2);

.g l:=asc(s);

.g ss:=char(l);

.g string(123);

.g expr(123);

.g expr(0123);

\section{Les variables}

.g a==b;

.g a:=b;

.g a==b;

.g solve(a=b,a);

.g solve(2*a=b+1,a);

.g sqrt(a^2);

.g assume(a<0);

.g sqrt(a^2);

.g assume(n,integer);

.g sin(n*pi);

.g subst(a^2+1,a=1);

.g subst(a^2+1,a=sqrt(b-1));

.g a^2+1;

\end{document}