A parallel Buchberger algorithm for multigraded ideals

TL;DR

This paper introduces a parallel algorithm for computing Gröbner bases of multigraded ideals, leveraging lattice anti-chains to identify independent S-polynomials for efficient reduction.

Contribution

It presents a novel parallelization technique for Gröbner basis computation in multigraded polynomial rings using lattice anti-chains.

Findings

Achieves parallel computation of Gröbner bases for multigraded ideals.

Uses lattice anti-chains to identify independent S-polynomials.

Improves efficiency of Gröbner basis algorithms in multigraded settings.

Abstract

We demonstrate a method to parallelize the computation of a Gr\"obner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice $\mathbb N^k$ to separate mutually independent S-polynomials for reduction.