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 nonmultiplicative. This partition gives thereby the selfconsistent computational procedure for constructing an involutive basis by performing nonmultiplicative 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  03784754 
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 URL 
dx.doi.org/10.1016/S03784754(97)001286 
Language  English  Journal  Mathematics and Computers in Simulation  Volume  45  Number  56  Pages  543560  Publisher  Elsevier Science Publishers B. V.  Address  Amsterdam, The Netherlands, The Netherlands  Year  1998  Month  March  Translation 
No  Refereed 
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