Cellular sheaves for F#.
This project is currently in very early development and should not be used.
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.
Look at the Jupyter Notebooks in the examples folder.
For simplicity and performance, faisceau works with coefficients in the binary field F2.
- XPlot.Plotly is needed for plotting.
- FsCheck is needed for testing.
[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
- Many more examples.
- Six operations.
- Integrate FSharpPlus categorical abstractions.
- Implement 'Scythe' algorithm from Curry/Ghrist/Nanda.
- Improve performance overall.
MIT License. Copyright (c) 2019 Nasos Evangelou-Oost.