Mathematica Homological Toolbox for the Quantum Mechanic
License: MIT
Description
This is a set of Mathematica packages built to compute the cohomology of the chain complexes introduced in the paper 'Homological Tools for the Quantum Mechanic' (arXiv:1901.02011).
For software that can compute ranks of cohomology components in Octave/Matlab, see: https://github.com/tmainiero/homological-tools-4QM-octave.
Unlike the Octave software, these packages are written in a functional style, and also allow one to output explicit representatives of generators of cohomology components.
An interactive quick start guide/minimal documentation is included in quick_start.nb.
Most functions are documented. (If we are interested in a function functionOfInterest, a description can be found by evaluating ??functionOfInterest.)
The package BasicStable.wl provides useful quantum mechanical operations and can be used independently of the remainder of the packages.
How to Download
Git
git clone https://github.com/tmainiero/homological-tools-4QM-mathematica.git
From the Github web interface
Click that fancy green "Clone or download" button on the top right! Then "Download ZIP".
File by File
From the Github web interface:
- Go to the file you want to download and click it to view the contents
- Locate the "Raw" button (On the top right at the time of writing) and right click.
- Save as...
Make sure that all files are located in the $Path of your Mathematica directory, if not the same folder!
Caveat
Unfortunately, this software was written before the GNS and commutant cochain complexes were fully understood. The techniques used to compute cohomology, present in CechOpsStable, are meant to compute Cech homology of a co-presheaves, rather than Cech cohomology of presheaves---the latter being the technique used in the paper. One can, however, recover the appropriate cohomology after some degree shifting (and sign corrections) in the form of some wrapper functions present in StateHomologyStable. A solution to this confusion would be a rewrite of the functions in the intermediate package CechOpsStable; this might be planned for future versions of this software.