Improving incremental signature-based Groebner basis algorithms

TL;DR

This paper enhances incremental signature-based Groebner basis algorithms by combining existing optimizations, significantly improving their efficiency, and compares the effects on the F5 and G2V algorithms from both theoretical and practical perspectives.

Contribution

It introduces a novel combination of known optimizations to improve the performance of Groebner basis algorithms and provides a comparative analysis of F5 and G2V.

Findings

Optimizations significantly boost algorithm efficiency

Different effects observed on F5 and G2V algorithms

Theoretical and practical improvements demonstrated

Abstract

In this paper we describe a combination of ideas to improve incremental signature-based Groebner basis algorithms having a big impact on their performance. Besides explaining how to combine already known optimizations to achieve more efficient algorithms, we compare the quite different effects on the two best-known algorithms in this area, F5 and G2V, both from a theoretical and a practical point of view.