Involutive Algorithms for Computing Groebner Bases

TL;DR

This paper introduces an efficient involutive algorithm for computing Groebner bases that leverages involutive monomial division, offering potential computational advantages over traditional methods like Buchberger's algorithm.

Contribution

The paper presents a novel involutive algorithm for Groebner basis computation based on involutive monomial division, improving efficiency and reducing computational costs.

Findings

The involutive algorithm can compute Groebner bases more efficiently than Buchberger's algorithm.

Reduced Groebner bases are obtained as fixed subsets of involutive bases without extra costs.

Experimental results indicate the involutive algorithm's superiority in certain cases.

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.