f4ncgb: High Performance Gr\"obner Basis Computations in Free Algebras

TL;DR

f4ncgb is an open-source C++ library that advances noncommutative Gr"obner basis computations by adapting recent commutative algorithms, achieving state-of-the-art performance.

Contribution

It introduces a novel software library that transfers recent commutative Gr"obner basis techniques to the noncommutative setting, improving computational efficiency.

Findings

f4ncgb achieves new state-of-the-art performance in noncommutative Gr"obner basis computations.

The library demonstrates effective implementation of advanced algorithms.

Experimental results validate the efficiency of the proposed methods.

Abstract

We present f4ncgb, a new open-source C++ library for Gr\"obner basis computations in free algebras, which transfers recent advancements in commutative Gr\"obner basis software to the noncommutative setting. As our experiments show, f4ncgb establishes a new state-of-the-art for noncommutative Gr\"obner basis computations. We also discuss implementation details and design choices.