/faisceau

Cellular sheaves for F#

Primary LanguageF#MIT LicenseMIT

faisceau

Cellular sheaves for F#.


Warning

This project is currently in very early development and should not be used.

About

faisceau is an experimental toolkit for computing with cellular sheaves in F#, inspired by Michael Robinson's PySheaf.

We are presently in very early development and most of the intended functionality is not implemented.

Usage

Look at the Jupyter Notebooks in the examples folder.

For simplicity and performance, faisceau works with coefficients in the binary field F2.

Dependencies

References

[1] CURRY, Justin. Sheaves, cosheaves and applications. arXiv preprint arXiv:1303.3255, 2013. https://arxiv.org/abs/1303.3255

[2] GHRIST, Robert W. Elementary applied topology. Seattle: Createspace, 2014. https://www.math.upenn.edu/~ghrist/notes.html

[3] CURRY, Justin; GHRIST, Robert; NANDA, Vidit. Discrete Morse theory for computing cellular sheaf cohomology. Foundations of Computational Mathematics, 2016, 16.4: 875-897. https://arxiv.org/abs/1312.6454v2

[4] HANSEN, Jakob; GHRIST, Robert. Toward a Spectral Theory of Cellular Sheaves. arXiv preprint arXiv:1808.01513, 2018. https://arxiv.org/abs/1808.01513


Roadmap

Features

Optimisations

  • Implement 'Scythe' algorithm from Curry/Ghrist/Nanda.
  • Improve performance overall.

License

MIT License. Copyright (c) 2019 Nasos Evangelou-Oost.