Abstract simplicial complexes in Macaulay2
Abstract
AbstractSimplicialComplexes.m2 is a computer algebra package written for the computer algebra system Macaulay2 M2. 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 non-reduced simplicial chain complexes. Further, it facilitates construction of random simplicial complexes. The approach that we employ here builds on the Macaulay2 package Complexes.m2 Stillman:Smith:Complexes.m2. It complements and is entirely different from the existing Macaulay2 simplicial complexes framework that is made possible by the package SimplicialComplexes.m2 Smith:et:al:SimplicialComplexes.m2:jsag.
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