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The homalg project is a multi-author multi-package open source software project for constructive homological algebra.
Mainly written in GAP4 it allows the use of external programs and other computer algebra systems (CASs) for specific time critical tasks. Although the central part of the source code is the formalization of abstract notions like Abelian categories, our focus lies on concrete applications ranging from linear control theory to commutative algebra and algebraic geometry.
A big part of the project is already distributed with GAP. The yet undeposited packages and the tested development versions of all packages can be downloaded from the project GitHub homepage.
The core part of the project is the homalg package. It provides an abstract structure and algorithms for abelian categories up to spectral sequences of multigraded complexes.
The other packages of the homalg project implement data structures and algorithms for several mathematical objects, like modules over graded rings. For more packages based on the homalg project see the table on this page.
This slideshow visualizes the interdependency of most of the packages in this repository:
Packages of homalg_project:
| Name | Description | Documentation |
|---|---|---|
| homalg | A homological algebra meta-package for computable Abelian categories |   |
| 4ti2Interface | A link to 4ti2 | |
| ExamplesForHomalg | Examples for the GAP Package homalg | |
| Gauss | Extended Gauss functionality for GAP | |
| GaussForHomalg | Gauss functionality for the homalg project | |
| GradedModules | A homalg based package for the Abelian category of finitely presented graded modules over computable graded rings | |
| GradedRingForHomalg | Endow Commutative Rings with an Abelian Grading | |
| HomalgToCAS | A window to the outer world | |
| IO_ForHomalg | IO capabilities for the homalg project | |
| LocalizeRingForHomalg | A Package for Localization of Polynomial Rings | |
| MatricesForHomalg | Matrices for the homalg project | |
| Modules | A homalg based package for the Abelian category of finitely presented modules over computable rings | |
| RingsForHomalg | Dictionaries of external rings | |
| SCO | SCO - Simplicial Cohomology of Orbifolds | |
| ToolsForHomalg | Special methods and knowledge propagation tools | |