Details:

Title	Minimal involutive bases
Author(s)	Yuri A. Blinkov, Vladimir P. Gerdt
Type	Article in Journal
Abstract	In this paper, we present an algorithm for construction of minimal involutive polynomial bases which are Grobner bases of the special form. The most general involutive algorithms are based on the concept of involutive monomial division which leads to partition of variables into multiplicative and non-multiplicative. This partition 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 define two new ones. These two divisions, as well as Thomas division, do not depend on the order of variables. We prove noetherity, continuity and constructivity of the new divisions that provides correctness and termination of involutive algorithms for any finite set of input polynomials and any admissible monomial ordering. We show that, given an admissible monomial ordering, a monic minimal involutive basis is uniquely defined and thereby can be considered as canonical much like the reduced Grobner basis.
Keywords	Computer algebra, polynomial ideals, Grobner bases, involutive monomial division, minimal involutive bases, involutive algorithm
Length	18
ISSN	0378-4754
File
URL	dx.doi.org/10.1016/S0378-4754(97)00128-6
Language	English
Journal	Mathematics and Computers in Simulation
Volume	45
Number	5-6
Pages	543-560
Publisher	Elsevier Science Publishers B. V.
Address	Amsterdam, The Netherlands, The Netherlands
Year	1998
Month	March
Translation	No
Refereed	No