Involutive directions and new involutive divisions

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	Involutive directions and new involutive divisions
	Chen, YF; Gao, XS
	2001-04-01
发表期刊	COMPUTERS & MATHEMATICS WITH APPLICATIONS
ISSN	0898-1221
卷号	41 期号:7-8 页码:945-956
摘要	In this paper, we propose the concept of involutive direction as a vector representation for the concept of involutive division proposed by Gerdt and his co-workers. With this representation, most of the properties of involutive divisions such as Noetherity, Artinity, and constructivity, can be greatly simplified. A new algorithm to compute the involutive completion is also given. Based on the vector representation, two new types of involutive divisions are found and proved to be Noetherian, Artinian, and constructive. These new divisions may lead to new methods of finding integrability conditions of partial differential equations and computing Grobner bases of polynomial ideals. (C) 2001 Elsevier Science Ltd. All rights reserved.
关键词	involutive divisions involutive directions Grobner bases nonmultiplier prolongation involutive completion
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000167575900012
出版者	PERGAMON-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/15848
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, YF
作者单位	Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Chen, YF,Gao, XS. Involutive directions and new involutive divisions[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2001,41(7-8):945-956.
APA	Chen, YF,&Gao, XS.(2001).Involutive directions and new involutive divisions.COMPUTERS & MATHEMATICS WITH APPLICATIONS,41(7-8),945-956.
MLA	Chen, YF,et al."Involutive directions and new involutive divisions".COMPUTERS & MATHEMATICS WITH APPLICATIONS 41.7-8(2001):945-956.