Hi Dima, Is the default choice of the algorithm the right one? > One can see that > sage: A.determinant(algorithm="hessenberg") > 16801.7979988558 > is quite good... >
The PARI documentation of the function charpoly() says: "If flag=2, uses the Hessenberg form. Assumes that the base ring is a field. Uses $O(n^3)$ scalar operations, but suffers from coefficient explosion unless the base field is finite or $\R$." Since the determinant is just the constant term of the characteristic polynomial, this looks safe for the determinant as well. I guess the question whether we should use Sage's built-in Hessenberg algorithm or PARI's matdet() comes down to which of the two is faster. Peter -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
