Decomposing Polynomial Systems into Simple Systems
Decomposing Polynomial Systems into Simple Systems
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DOI：
10.1006/jsco.1997.0177
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发表时间：
1998-03
期刊：
影响因子：
--
通讯作者：
Dongming Wang
中科院分区：
文献类型：
--
作者：
Dongming Wang
一个简单的系统是一对多元多项式集合（一个集合用于方程，另一个集合用于不等式）以三角形形式排序，其中每个多项式是无平方的，并且关于其前导变量具有非零前导系数。本文提出了一种将任意一对多项式组分解为多个简单系统并进行零分解的方法。该方法采用自顶向下的分裂消元和子结式正则子链的形成作为基本操作。
A simple system is a pair of multivariate polynomial sets (one set for equations and the other for inequations) ordered in triangular form, in which every polynomial is squarefree and has non-vanishing leading coefficient with respect to its leading variable. This paper presents a method that decomposes any pair of polynomial sets into finitely many simple systems with an associated zero decomposition. The method employs top-down elimination with splitting and the formation of subresultant regular subchains as basic operation.