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TitleMinimal involutive bases
Author(s) Yuri A. Blinkov, Vladimir P. Gerdt
TypeArticle in Journal
AbstractIn 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.
KeywordsComputer algebra, polynomial ideals, Grobner bases, involutive monomial division, minimal involutive bases, involutive algorithm
URL dx.doi.org/10.1016/S0378-4754(97)00128-6
JournalMathematics and Computers in Simulation
PublisherElsevier Science Publishers B. V.
AddressAmsterdam, The Netherlands, The Netherlands
Translation No
Refereed No