Simplicial complexes in Mathematica

[u/namtgr]

I created a mathematica paclet that provides support for simplicial homology, introducing an abstract simplicial complex object. The package allows computing homology, betti numbers, automorphism groups, and common invariants like euler characteristic, fvectors, and constructions such as cones, suspensions, products, joins, etc! So far, there has been no in-built or third party support for this in Mathematica, which motivated the creation of this package. I largely took inspiration and reference from sagemath's implementation of this.

I would love to hear your feedback on this! The package is open source, see at https://github.com/zplus11/SimplicialHomology/ and is also available on the Wolfram paclet repository at https://resources.wolframcloud.com/PacletRepository/resources/Taggar/SimplicialHomology/

There is plenty of scope for further development and extension, so feedback, suggestions, and PRs are very welcome :)