An abstract simplicial complex is a family of finite sets closed under the operation of taking subsets. In this package, the finite set consists of variables in a polynomial ring and each subset is represented as a product of the corresponding variables. In other words, we exploit the natural bijection between abstract simplicial complexes and Stanley-Reisner ideals.
This package is designed to explore applications of abstract simplicial complexes within combinatorial commutative algebra. Introductions to this theory can be found in the following textbooks:
The following people have generously contributed code, improved existing code, or enhanced the documentation: Janko Böhm, Sorin Popescu, Mike Stillman, and Lorenzo Venturello.
This package is not intended to handle abstract simplicial complexes with a very large number of vertices, because computations in the corresponding polynomial ring are typically prohibitive.
Version 2.0 of this package was accepted for publication in volume 13 of Journal of Software for Algebra and Geometry on 2023-03-21, in the article Simplicial complexes in Macaulay2 (DOI: 10.2140/jsag.2023.13.53). That version can be obtained from the journal.
This documentation describes version 2.0 of SimplicialComplexes.
If you have used this package in your research, please cite it as follows:
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The object SimplicialComplexes is a package, defined in SimplicialComplexes.m2, with auxiliary files in SimplicialComplexes/.
The source of this document is in SimplicialComplexes/Documentation.m2:83:0.