Groebner.jl: A package for Gr\"obner bases computations in Julia

TL;DR

Groebner.jl is an efficient, extensible Julia package for computing Groebner bases using the F4 algorithm, supporting multiple fields, multi-threading, and various symbolic techniques, outperforming existing tools in many cases.

Contribution

This paper introduces Groebner.jl, a Julia package that enhances Groebner basis computations with improved performance, extensibility, and support for multiple algebraic structures.

Findings

Outperforms existing Groebner basis software in many instances

Supports computations over integers modulo a prime and rationals

Leverages Julia's type system for extensibility

Abstract

We present Groebner.jl, a Julia package for computing Groebner bases with the F4 algorithm. Groebner.jl is an efficient, portable, and open-source software. Groebner.jl works over integers modulo a prime and over the rationals, supports basic multi-threading, and specializes in computation in the degree reverse lexicographical monomial ordering. The implementation incorporates various symbolic computation techniques and leverages the Julia type system and tooling, which allows Groebner.jl to compete with the existing state of the art, in many instances outperform it, and exceed them in extensibility. Groebner.jl is freely available at https://github.com/sumiya11/Groebner.jl.