File: introExample37bis.tex

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\begin{center}\begin{minipage}{15cm}\begin{Verbatim}[frame=single]
> ChebPolynomials = proc(n) {
    var i, res;
    if (n<0) then res = [||]
    else if (n==0) then res = [|1|]
    else {
       res = [|1, _x_|];
       for i from 2 to n do res[i] = horner(2*_x_*res[i-1]-res[i-2]);
    };
    return res;
  };
> 
> f = sin(x);
> T = ChebPolynomials(4);
> canonical = on!;
> for i from 0 to 4 do T[i];
1
x
-1 + 2 * x^2
-3 * x + 4 * x^3
1 - 8 * x^2 + 8 * x^4
\end{Verbatim}
\end{minipage}\end{center}