I'm doing a calculation which finds the characteristic polynomial of a matrix with rather complex entries and then determines the discriminant of that polynomial. For smaller matrices up to around 7x7 it finishes evaluating the Discriminant command within a few hours, but at a 10x10, which is what I need, it takes days to evaluate. Running in parallel won't work for the built in Discriminant command. I was wondering if there was a more efficient way to evaluate the discriminant of high-order polynomial, as I know my code is basic.
CPHH = Collect[CharacteristicPolynomial[HH, x],x]]; DD = Discriminant[CPHH, x, Method -> SylvesterMatrix]; Simplify[DD, TimeConstraint -> Infinity]
If the rest of the code would be useful in determining a solution I'd be happy to post it