Signature-Based Gr\"obner Basis Algorithms --- Extended MMM Algorithm for computing Gr\"obner bases

TL;DR

This paper presents a perspective that views signature-based Gr"obner basis algorithms as an extension of the MMM algorithm, offering a simpler understanding without introducing new algorithms or proofs.

Contribution

It provides a new conceptual framework relating signature-based algorithms to the MMM algorithm, simplifying their understanding.

Findings

Signature-based algorithms can be viewed as extended MMM algorithms.

This perspective simplifies the understanding of signature-based Gr"obner basis algorithms.

No new algorithms or proofs are introduced.

Abstract

Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a view of signature-based algorithms is given, that is, signature-based algorithms can be regarded as an extended version of the famous MMM algorithm. By this view, this paper aims to give an easier way to understand signature-based Gr\"obner basis algorithms.