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有限域上多项式集的简单分解

李晓亮1,王东明2   

  1. 1. 北京航空航天大学数学与系统科学学院, 北京 100191; 2.法国国家科学研究中心巴黎六大计算机科学实验室,  巴黎75252
  • 收稿日期:2011-02-22 出版日期:2012-01-25 发布日期:2012-04-01

李晓亮,王东明. 有限域上多项式集的简单分解[J]. 系统科学与数学, 2012, 32(1): 15-26.

LI Xiaoliang; WANG Dongming. SIMPLE DECOMPOSITION OF POLYNOMIAL SETS OVER  FINITE FIELDS[J]. Journal of Systems Science and Mathematical Sciences, 2012, 32(1): 15-26.

SIMPLE DECOMPOSITION OF POLYNOMIAL SETS OVER  FINITE FIELDS

LI Xiaoliang1; WANG Dongming2   

  1. 1.School of Mathematics and Systems Science, Beihang University; 2.Laboratoire d'Informatique de Paris , UPMC--CNRS, Paris
  • Received:2011-02-22 Online:2012-01-25 Published:2012-04-01
研究如何将任意有限域上的多项式集分解为有限多个简单列.为了解决这一问题, 首先研究简单列和根理想之间的关系, 然后基于已有的正则分解算法和有限域上理想的根的两种计算方法设计一个有限域上多项式集的简单分解算法.计算试验表明, 文章给出的算法是有效的.
This paper addresses the problem of decomposing an arbitrary set of multivariate polynomials over an arbitrary finite field into simple sets. We first study the
relationship between simple sets and radical ideals and then present an algorithm for simple decomposition of polynomial sets over finite fields based on existing regular decomposition algorithms and two methods for computing the radicals of ideals over finite fields. Experiments show the efficiency of the algorithm.

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