I have been experimenting with GiNaC, and I found that on page 46, section 5.5.2, of the manual (version 1.0.6) that degree() works reliably also on non-expanded polynomials. But the following program seems to prove that it is not the case.
#include <iostream> #include <ginac/ginac.h>
using namespace std; using namespace GiNaC;
typedef GiNaC::ex GExpr; typedef GiNaC::symbol GSymbol;
int main() { GSymbol x("x");
GExpr h_a = numeric(1,2) * x * (x-1); GExpr h_b = - (x+1) * (x-1); GExpr h_c = numeric(1,2) * x * (x+1);
GExpr p = h_a + h_b + h_c; std::cout << "p = " << p << " degree " << p.degree(x) << std::endl; p = p.expand(); std::cout << "p = " << p << " degree " << p.degree(x) << std::endl; return 0; }
This is the output that I obtained (from version 1.0.5):
p = 1/2*(1+x)*x+1/2*(-1+x)*x+(-1+x)*(-1-x) degree 2 p = 1 degree 0
Best wishes
Alessandro Zaccagnini The purrs developers team at the University of Parma