Some improvements of a lemma of Rosenfeld
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.
