DESC is a DErived Sheaf Calculator: a tool for working with (co)chains in derived categories of sheaves over finite posets. The supported operations include computing the minimal injective resolution of a constant sheaf and star/shriek pushforwards/pullbacks of injective (co)chains through monotonic maps. The code is based on [1], where you can find all necessary theory as well as detailed description of the algorithms used.
The main code is in the file src/desc.py. The main() method contains a sample code showing how to compute part of the examples presented in [1], so it can be ran directly from terminal with python3 src/desc.py, but the recommended use is to create a jupyter notebook, and import desc.py in it.
Currently all computations are done over the two element field Z_2.
To learn more about how to use DESC, see the jupyter notebook examples.ipynb. It contains several use-cases and interesting examples that can be computed with the tool -- it serves both as a user guide and as a demonstration of what can be computed with DESC.
The numpy library is needed only for class Sheaf in src/desc.py, which is only needed to explicitly define a generic sheaf (rather than just starting with a constant sheaf and using pushforward/pullback vectors).
The networkx library is needed to work with generic posets (rather than just, e.g., simplicial complexes), and general sheaves. The import can dropped if the following classed are also dropped:
- class
PosetDAGinsrc/posets.py - class
Sheafinsrc/desc.py
[1] Adam Brown and Ondřej Draganov. Discrete Microlocal Morse Theory. 2022. https://arxiv.org/abs/2209.14993
Copyright ©2022. Institute of Science and Technology Austria (IST Austria). All Rights Reserved.
This file is part of DESC: Derived Sheaf Calculator, which is free software: you can redistribute it and/or modify it under the terms of the MIT License.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the MIT License for more details.
You should have received a copy of the MIT License along with this program. If not, see https://opensource.org/licenses/.