A characteristic set method for ordinary difference polynomial systems

被引：24

作者：

Gao, Xiao-Shan ^{[1
]}

Luo, Yong ^{[1
]}

Yuan, Chunming ^{[1
]}

机构：

[1] Acad Sinica, AMSS, Inst Syst Sci, Key Lab Math Mech, Beijing 100080, Peoples R China

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2009年 / 44卷 / 03期

关键词：

Difference polynomial; Ascending chain; Characteristic set; Coherence; Irreducibility; Zero decomposition theorem; Automated theorem proving; DECOMPOSITION;

D O I：

10.1016/j.jsc.2007.05.005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove several basic properties for difference ascending chains, including a necessary and sufficient condition for an ascending chain to be the characteristic set of its saturation ideal and a necessary and sufficient condition for an ascending chain to be the characteristic set of a reflexive prime ideal. Based on these properties, we propose an algorithm to decompose the zero set of a finite set of difference polynomials into the union of zero sets of certain ascending chains. This decomposition algorithm is implemented and used to solve the perfect ideal membership problem, and to prove certain difference identities automatically. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：242 / 260

页数：19

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