QCohX

QCohX is an open-source software library for computational algebraic geometry, designed to assist mathematicians and computer scientists in working with quasi-coherent sheaves on schemes and related geometric structures. The project aims to provide a practical toolkit for representing schemes, morphisms, and sheaves, and for performing standard functorial operations and cohomology computations.

Core capabilities include data structures for schemes, morphisms, and quasi-coherent sheaves, as well as implementations of pullback and pushforward along morphisms, tensor products, Hom sheaves, and internal Hom. It supports computation of sheaf cohomology, global sections, and derived functors, with optional use of spectral sequences to organize computations. The library emphasizes modularity and numerical stability, enabling computations over common base fields and finite-type situations.

Implementation and usage: QCohX is written primarily in C++ with Python bindings, offering an accessible API for scripting and interactive work. It is designed to be extensible through plugin modules and provides interfaces for interoperability with other mathematical software systems.

Applications and community: The project targets research in algebraic geometry, representation theory, and related areas, as well as teaching and pedagogy. It can be used within notebook environments and integrates with established ecosystems such as SageMath and Jupyter for exploratory work. The project follows a collaborative development model with open documentation and example-driven tutorials.

License and availability: QCohX is distributed under an open-source license and maintained on a public repository. Contributions from researchers and developers are welcome, and the project maintains issue trackers, release notes, and a user mailing list.