Abstract simplicial complexes in Macaulay2
Nathan Grieve · Journal of Software for Algebra and Geometry · 2025
AbstractSimplicialComplexes.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.