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Involutive directions and new involutive divisions

✍ Scribed by Yu-Fu Chen; Xiao-Shan Gao

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 959 KB
Volume: 41
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)00332-1

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✦ Synopsis

In this paper, we propose the concept of involutive direction ss a vector representation for the concept of involutive division proposed by Gerdt and hi 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.

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