xorshift-period.gp

\\ determine that order of g equals to n
isprimitive(g, n, e=1) = {
  my(factors, p);
  if (g^n != e, return(0));
  factors = factor(n);
  for (i = 1, matsize(factors)[1],
    p = factors[i, 1];
    if (g^(n/p) == e, return(0)));
  return(1);
}
\\ identity matrix
E = matid;
\\ right & left shift matrix
R(n, k) = { return(matrix(n, n, i, j, i + k == j)); }
L(n, k) = { return(R(n, -k)); }
\\ convert to matrix on F_2
to_f2(mat) = { return(matrix(matsize(mat)[1], matsize(mat)[2], i, j, Mod(mat[i, j], 2))); }

n = 64;
T = to_f2((E(n) + L(n, 17)) * (E(n) + R(n, 7)) * (E(n) + L(n, 13)));
print(isprimitive(Mod(x, charpoly(T, x)), 2^n - 1));

In the function isprimitive(), you'd better to use my() rather than local(). It's a bit difficult to explain how these are different... my() declares statically scoped local variables, while local() declares dynamically scoped local variables. See the reference manual of pari-gp, or type ??my in a pari-gp session. Example:
? x=0; f()={x}
%1 = ()->x
? g()={my(x=1); f()}
%2 = ()->my(x=1);f()
? h()={local(x=1); f()}
%3 = ()->local(x=1);f()
? g()
%4 = 0
? h()
%5 = 1

Thanks. I understood. I fixed it :)