Involutive Directions and New Involutive Divisions
نویسنده
چکیده
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. @ 2001 Elsevier Science Ltd. All rights reserved. Keywords-Involutive divisions, Involutive directions, Grijbner bases, Nonmultiplier prolongation, Involutive completion.
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