As far as I can see, there is no method available to compute the companion matrix of a polynomial. May I suggest the addition of a method along these lines?:
// Creates the Companion matrix for a given polynomial
GiNaC::matrix CreateCompanion(const GiNaC::ex &poly, const GiNaC::ex &symbol)
{
if(poly.is_polynomial(symbol))
{
int rank = poly.degree(symbol);
GiNaC::matrix mat(rank, rank);
GiNaC::ex majorCoeff = poly.coeff(symbol, rank);
for(int i = 0; i < rank; ++i)
{
for(int j = 0; j < rank; ++j)
{
if(i - j == 1)
{
mat(i, j) = 1;
}
else if(i == 0)
{
mat(i, j) = -1 * poly.coeff(symbol, rank - j - 1) / majorCoeff;
}
}
}
return mat;
}
else
{
// Throw exception or return empty matrix
}
}