摘要
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 coraputing the radicals of ideals over finite fields. Experiments show the efficiency of the algorithm.
出处
《系统科学与数学》
CSCD
北大核心
2012年第1期15-26,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金国际合作与交流项目(60911130369)资助
关键词
三角列
正则列
简单列
多项式集
简单分解.
Triangular set, regular set, simple set, polynomial set, simple decomposition
