Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case

  • Authors:

  • Xiaoliang Li;Chenqi Mou;Dongming Wang

  • Affiliations:

  • LMIB-SKLSDE-School of Mathematics and Systems Science, Beihang University, Beijing 100191, China;LMIB-SKLSDE-School of Mathematics and Systems Science, Beihang University, Beijing 100191, China and Laboratoire d'Informatique de Paris 6, Université Pierre et Marie Curie-CNRS, 104 avenue d ...;Laboratoire d'Informatique de Paris 6, Université Pierre et Marie Curie-CNRS, 104 avenue du Président Kennedy, F-75016 Paris, France

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product determined by a simple set. As a subprocedure of the generalized squarefree decomposition approach, a method is proposed to extract the pth root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms.