Minimal Involutive Bases
Date: July 17th (Wednesday)
Time: 11:30-12:00
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.
