Computing Border Bases without using a Term Ordering

TL;DR

This paper extends the border basis algorithm to compute border bases that are not tied to any specific term ordering, broadening their applicability beyond traditional Gröbner basis methods.

Contribution

It introduces a novel extension of the border basis algorithm enabling the computation of border bases independent of term orderings.

Findings

Algorithm successfully computes non-term-ordering border bases

Broadens applicability of border bases in industrial problems

Enhances flexibility over traditional Gröbner basis methods

Abstract

Border bases, a generalization of Groebner bases, have actively been researched during recent years due to their applicability to industrial problems. A. Kehrein and M. Kreuzer formulated the so called Border Basis Algorithm, an algorithm which allows the computation of border bases that relate to a degree compatible term ordering. In this paper we extend the original Border Basis Algorithm in such a way that also border bases that do not relate to any term ordering can be computed by it.