Practical Groebner Basis Computation

TL;DR

This paper explores practical aspects of Groebner basis computation, focusing on signature-based algorithms, introducing new data structures and techniques, and validating them through experiments with an open-source C++ library.

Contribution

It introduces new practical data structures and computational techniques for Groebner basis algorithms, enhancing efficiency and applicability.

Findings

Signature-based algorithms are effective in practice.

New data structures improve computational performance.

Experimental results validate the proposed methods.

Abstract

We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature based Groebner basis algorithms and more traditional variations of the classic Buchberger algorithm. Our conclusions are based on experiments using our new freely available open source standalone C++ library.