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Involutive Algorithms for Computing Gröbner Bases
Vladimir P. Gerdt
199 - 225
NATO Science Series, III: Computer and Systems Sciences
Volume 196: Computational Commutative and Non-Commutative Algebraic Geometry
Abstract

In this paper we describe an efficient involutive algorithm for constructing Gröbner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Gröbner basis is the internally fixed subset of an involutive basis, and having computed the later, the former can be output without any extra computational costs. We also discuss some accounts of experimental superiority of the involutive algorithm over Buchberger's algorithm.

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