cient Multivariate Factorization Over

We describe the Maple 23] implementation of multivariate factorization over general nite elds. Our rst implementation is available in Maple V Release 3. We give selected details of the algorithms and show several ideas that were used to improve its eeciency. Most of the improvements presented here are incorporated in Maple V Release 4. In particular, we show that we needed a general tool for implementing computations in GF (p k))x1; x2; : : : ; xv ]. We also needed an eecient implementation of our algorithms in Zpy]]x] because any multivariate factorization may depend on several bivariate factorizations. The eeciency of our implementation is illustrated by the ability to factor bivariate polynomials with over a million monomials over a small prime eld.