The GeometricDecomposability package for Macaulay2

TL;DR

The paper introduces the Macaulay2 package GeometricDecomposability, enabling researchers to test and explore the geometric vertex decomposability property of ideals using recursive definitions.

Contribution

It provides a new software tool that automates the testing of geometric vertex decomposability in ideals, based on recent theoretical developments.

Findings

The package facilitates experimentation with geometric vertex decomposability.

It implements recursive algorithms for testing decomposability.

It supports research in algebraic geometry and combinatorics.

Abstract

Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein and Rajchgot. We introduce the Macaulay2 package GeometricDecomposability which provides a suite of tools to experiment and test the geometric vertex decomposability property of an ideal.