Involutive Algorithms for Computing Groebner Bases

Details Involutive Algorithms for Computing Groebner Bases Involutive Algorithms for Computing Groebner Bases

2005-01-08

arxiv.org/abs/math/0501111v1

Mathematics

Commutative Algebra

27 pages, Proceedings of the NATO Advanced Research Workshop "Computational commutative and non-commutative algebraic geometry

Scientific paper

In this paper we describe an efficient involutive algorithm for constructing Groebner 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 Groebner 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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