A characteristic set method for ordinary difference polynomial systems

doi:10.1016/j.jsc.2007.05.005

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	A characteristic set method for ordinary difference polynomial systems
	Gao, Xiao-Shan; Luo, Yong; Yuan, Chunming
	2009-03-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	44 期号:3 页码:242-260
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.
关键词	Difference polynomial Ascending chain Characteristic set Coherence Irreducibility Zero decomposition theorem Automated theorem proving
DOI	10.1016/j.jsc.2007.05.005
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000264447000004
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7354
专题	系统科学研究所
通讯作者	Gao, Xiao-Shan
作者单位	Acad Sinica, AMSS, Inst Syst Sci, Key Lab Math Mech, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Gao, Xiao-Shan,Luo, Yong,Yuan, Chunming. A characteristic set method for ordinary difference polynomial systems[J]. JOURNAL OF SYMBOLIC COMPUTATION,2009,44(3):242-260.
APA	Gao, Xiao-Shan,Luo, Yong,&Yuan, Chunming.(2009).A characteristic set method for ordinary difference polynomial systems.JOURNAL OF SYMBOLIC COMPUTATION,44(3),242-260.
MLA	Gao, Xiao-Shan,et al."A characteristic set method for ordinary difference polynomial systems".JOURNAL OF SYMBOLIC COMPUTATION 44.3(2009):242-260.