Hi, On Wed, 6 Mar 2002, Alessandro Zaccagnini wrote:
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
Thanks for pointing this out. Our documentation is wrong and will be changed. There is no way to cleverly find out the degree() or ldegree() of unexpanded/uncollected expressions because there might be cancellations of the highest/lowest terms. (x-1)^2-x^2 is a simple example, where x^2 is cancelled in the expanded polynomial. Thus, degree() and ldegree() only give upper/lower bounds. This has always been the intent of degree() and ldegree() -- sorry for the confusion. I just checked against Maple and there it is the same. Their documentation honors this, though: : The polynomial a must be in collected form in order for degree/ldegree to : return an accurate result. For example, given (x+1)*(x+2) - x^2, degree : would not detect the cancellation of the leading term, and would incorrectly : return a result of 2. Applying the function collect or expand to the : polynomial before calling degree avoids this problem. Regards -richy. -- Richard B. Kreckel <Richard.Kreckel@Uni-Mainz.DE> <http://wwwthep.physik.uni-mainz.de/~kreckel/>