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SimplicialComplexes :: SimplicialComplexes

SimplicialComplexes -- exploring abstract simplicial complexes within commutative algebra


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.

See also



This documentation describes version 2.0 of SimplicialComplexes.

Source code

The source code from which this documentation is derived is in the file SimplicialComplexes.m2. The auxiliary files accompanying it are in the directory SimplicialComplexes/.


For the programmer

The object SimplicialComplexes is a package.