Efficient multivariate factorization over finite fields
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We describe the Maple  implementation of multivariate factorization over general finite fields. Our first 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 efficiency. 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,..., x v ]. We also needed an efficient implementation of our algorithms in ℤ p [y][x] because any multivariate factorization may depend on several bivariate factorizations.
The efficiency of our implementation is illustrated by the ability to factor bivariate polynomials with over a million monomials over a small prime field.
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