This repository consists of Python 2.7 libraries for manipulating cell complexes and data structures on them:

1. Local and relative homology of abstract simplicial complexes¹
2. Sheaves of sets or vector spaces on cell complexes²,³,⁴,⁵,⁶,⁷

Full documentation is at http://kb1dds.github.io/pysheaf/

You can install by cloning this repo (there is no PyPI package). For Linux, you can do:

$ git clone https://github.com/kb1dds/pysheaf.git
$ pip install pysheaf

See the documentation for full details!

The general plan of usage is

1. First (usually on paper!) lay out the cell complex that will serve as the base for your sheaf. Label each cell with a unique index, starting from zero.
2. Determine all of the stalks over each cell, and the restriction maps from lower dimension to higher. Restriction maps can be a mixture of numpy matrices or instances of LinearMorphism, SetMorphism, or SheafMorphism.
3. Construct a Sheaf instance from a list of SheafCell instances, all at once using the information from the previous two steps.
4. Analyze the resulting sheaf:
   1. If you have data, you can build Section instances whose list of SectionCell instances refer to your sheaf.
   2. You can compute cohomology of the Sheaf instance as well.

Have a look at the pysheaf/tests folder for some examples!

The pysheaf.py module should be able to duplicate the functionality of simplicialHomology.py, albeit somewhat more slowly because the base space constructions are more general and less efficient.

Finally, this code is under active development, so not everything works as it should. Stay away from Sheaf.localSectional() and Cell.localPairComplex() as these don't currently work correctly! If you find anything that you can correct, feel free to send me suggestions!