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:
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.
This documentation describes version 2.0 of SimplicialComplexes.