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SimplicialComplexes -- exploring abstract simplicial complexes within commutative algebra

Description

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:

Contributors

The following people have generously contributed code, improved existing code, or enhanced the documentation: Janko Böhm, Sorin Popescu, Mike Stillman, and Lorenzo Venturello.

Caveat

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

Authors

Certification a gold star

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.

Version

This documentation describes version 2.0 of SimplicialComplexes, released 7 May 2022.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SimplicialComplexesSource,
  title = {{SimplicialComplexes: exploring abstract simplicial complexes within commutative algebra. Version~2.0}},
  author = {Gregory G. Smith and Ben Hersey and Sasha Zotine},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

@article{SimplicialComplexesArticle,
  title = {{Simplicial complexes in \emph{Macaulay2}}},
  author = {Gregory G. Smith and Ben Hersey and Sasha Zotine},
  journal = {Journal of Software for Algebra and Geometry},
  volume = {13},
  year = {2023},
}

Exports

For the programmer

The object SimplicialComplexes is a package, defined in SimplicialComplexes.m2, with auxiliary files in SimplicialComplexes/.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/SimplicialComplexes/Documentation.m2:83:0.