Experience with FORMAC algorithm design

2) and its derivative R' are polynomials which arose naturally in a recent application of PM, where it was desired to find whether R has any multiple factors. Both pairs of polynomials turn out to be relatively prime. Using the old algorithm, the computation (1) required 0.64 seconds; using the new algorithm, it required 0.22 seconds. The advantage of the new algorithm increases rapidly with the complexity of the polynomials to which it is applied. It did the computation (2) in 0.30 minutes, while the old algorithm required 21.11 minutes!