The MorseResolutions package for Macaulay2
Trung Chau, Selvi Kara, Augustine O'Keefe
TL;DR
The paper introduces the MorseResolutions package for Macaulay2, enabling computation of Morse resolutions of monomial ideals, including Lyubeznik and Barile-Macchia types, and procedures for minimal resolutions.
Contribution
It provides a new software tool for computing and analyzing Morse resolutions of monomial ideals within Macaulay2, focusing on Lyubeznik and Barile-Macchia resolutions.
Findings
Implemented procedures for Lyubeznik and Barile-Macchia resolutions
Includes methods to find minimal Barile-Macchia resolutions
Enhances computational capabilities for monomial ideal resolutions
Abstract
Using discrete Morse theory, Batzies and Welker introduced Morse resolutions of monomial ideals. In this note, we present the {\it Macaulay2} package {\tt MorseResolutions} for working with two important classes of Morse resolutions: Lyubeznik and Barile-Macchia resolutions. This package also contains procedures to search for a minimal Barile-Macchia resolution of a given monomial ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Algebraic Geometry and Number Theory