Homological Shift Ideals: Macaulay2 Package

TL;DR

This paper presents a Macaulay2 package for computing and analyzing homological shift ideals of monomial ideals, facilitating the study of their algebraic properties such as linear resolutions and polymatroidality.

Contribution

The paper introduces a new Macaulay2 package that automates the computation and analysis of homological shift ideals, expanding tools available for algebraic and combinatorial research.

Findings

Package enables efficient computation of homological shift ideals.

Supports checking properties like linear resolution and polymatroidality.

Enhances research capabilities in algebraic combinatorics.

Abstract

We introduce the Macaulay2 package HomologicalShiftIdeals. It allows to compute the homological shift ideals of a monomial ideal, and to check the homological shift properties, including having linear resolution, having linear quotients, or being polymatroidal. The theory behind these concepts is explained and the main features of the package are presented.