Work

Abstract simplicial complexes in Macaulay2

Year: 2025

Type: conference-abstract

Abstract: SimplicialComplexes.m2 is a package written for Macaulay2.It provides new infrastructure to work with abstract simplicial complexes and related homological constructions.Its key novel feature is to implement each given abstract simplicial complex as a certain graded list in the form of a hash table with integer keys.Among other features, this allows for a direct implementation of the associated reduced and nonreduced simplicial chain complexes.Further, it facilitates construction of random simplicial complexes.The approach that we employ here builds on Stillman and Smith's Macaulay2 package Complexes.m2;It complements and is entirely different from the simplicial complexes framework made possible by the Macaulay2 package SimplicialComplexes.m2 of Smith, Hersey and Zotine.

Source: Journal of Software for Algebra and Geometry

DOI: 10.2140/jsag.2025.15.29

Author: Nathan Grieve

Institutions: University of Waterloo, Université du Québec à Montréal, Carleton University, Acadia University

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: Natural Sciences and Engineering Research Council of Canada

Awards: Methods for arithmetic distance, distribution and complexity of rational points, Methods for arithmetic distance, distribution and complexity of rational points