A Variant of the Gr\"obner Basis Algorithm for Computing Hilbert Bases

TL;DR

This paper introduces a modified Gr"obner basis algorithm tailored for efficiently computing Hilbert bases of numerical submonoids and subspaces over finite fields, enhancing computational algebra techniques.

Contribution

It presents a novel variant of the Gr"obner basis algorithm specifically designed for calculating Hilbert bases in finite-dimensional vector spaces over finite prime fields.

Findings

Algorithm effectively computes Hilbert bases for numerical submonoids.

Demonstrates improved computational efficiency over existing methods.

Applicable to subspace kernel computations over finite fields.

Abstract

Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field given as a matrix kernel.