Factorization of bivariate polynomials over all supported rings is now accomplished by a new algorithm which extends van Hoeij's knapsack ideas for Z[x] to solve the hard combination problem for GF(q)[x, y]. The new algorithm runs in polynomial time and performs extremely well in practice. General multivariate factorization is reduced to this new bivariate algorithm, so a combination problem never arises for any number of variables. Shoup's tree Hensel lifting algorithm has also been adapted for power series, making the lifting stages of all kinds of bivariate/multivariate factorization much faster than previously.
Most of the algorithms for multivariate GCD and resultant computation have also been rewritten from scratch. In particular, a faster interpolation algorithm is used for resultants, and there are several new heuristics.
New Features: