MINIMAL INVOLUTIVE BASES

In this papers we present an algorithm for construction of minimal inv olutive polynomial bases which are Grobner bases of the special form. The most general involutive algorithms are based on the concept of inv olutive monomial division which leads to partition of variables into m ultiplicative and non-multiplicative. This partition gives thereby the self-consistent computational procedure for constructing an involutiv e basis by performing non-multiplicative prolongations and multiplicat ive reductions. Every specific involutive division generates a particu lar form of involutive computational procedure. In addition to three i nvolutive divisions used by Thomas, Janet and Pommaret for analysis of partial differential equations we define two new ones. These two divi sions, as well as Thomas division, do not depend on the order of varia bles. We prove noetherity, continuity and constructivity of the new di visions that provides correctness and termination of involutive algori thms for any finite set of input polynomials and any admissible monomi al ordering. We show that, given an admissible monomial ordering, a mo nic minimal involutive basis is uniquely defined and thereby can be co nsidered as canonical much like the reduced Grobner basis. (C) 1998 IM ACS/Elsevier Science B.V.