Some improvements of a lemma of Rosenfeld

François Boulier

Date: July 17th (Wednesday)
Time: 09:20-09:50
Abstract
In this paper we study of the uniqueness properties of involutive polynomial bases which are redundant Gröobner bases of the special form. The most general involutive algorithmic techniques is based on the concept of involutive monomial division which allows one to separate all the variables into multiplicative and non-multiplicative subsets. The separation gives thereby the self-consistent computational procedure for constructing an involutive basis by performing non-multiplicative prolongations and multiplicative reductions. Every specific involutive division generates a particular form of involutive computational procedure. In addition to three involutive divisions used by Thomas, Janet and Pommaret for analysis of partial differential equations we introduce two new ones. These two divisions much as Thomas division do not depend on the order of variables. We prove noetherity and continuity of the new divisions. Given noetherian and continuous division, we present an algorithm for constructing of the minimal involutive basis for a polynomial ideal. This minimal basis is uniquely defined for any admissible monomial ordering.

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