Efficient multivariate factorization over finite fields

  • Laurent Bernardin
  • Michael B. Monagan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1255)


We describe the Maple [23] 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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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Laurent Bernardin
    • 1
  • Michael B. Monagan
    • 2
  1. 1.Institut für Wissenschaftliches RechnenETHZürichSwitzerland
  2. 2.Center for Experimental and Constructive Mathematics Department of Mathematics and StatisticsSimon Fraser UniversityCanada

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