Involutive Algorithms for Computing Groebner Bases
Commutative Algebra
2007-05-23 v1 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0501111,
title = {Involutive Algorithms for Computing Groebner Bases},
author = {Vladimir P. Gerdt},
journal= {arXiv preprint arXiv:math/0501111},
year = {2007}
}
Comments
27 pages, Proceedings of the NATO Advanced Research Workshop "Computational commutative and non-commutative algebraic geometry" (Chishinau, June 6-11, 2004), IOS Press, to appear