Sheafhom 2.0

Sheafhom 2.0 is a freeware package for large sparse linear algebra computations over the integers and other exact number types. It provides efficient algorithms for the Smith normal form of sparse matrices, and dense algorithms for LLL and Hermite normal form. Graphs and windows are provided to show the progress of the computation in real time, which helps in tuning the algorithms for specific applications. The package is motivated by algebraic topology, and provides partial support for items from category theory as first-class objects: vector spaces, morphisms of vector spaces, and cochain complexes.

Download

Download the Java source code and documentation.

Download shh.jar, which contains the runtime Java classes.

Here are three ways to learn more about the package.

Download shh.jar and run the demo with
java -jar shh.jar
On Windows and some other operating systems, you can simply double-click on the shh.jar icon.
- By default, the demo sets up a 1000 × 2000 matrix in which only 0.3% of the entries are non-zero. About half the non-zeros are 1; the other half are -2. These defaults can be changed with the GUI that's provided.
- The demo computes the Smith normal form (the elementary divisors) of the matrix, with a window showing how the sparsity changes in real time. The top bar gives the pivot location, the sparsity (percentage of non-zeros), and the percentage of non-zeros represented by the arbitrary-precision integer data type.
- The biggest time constraint is not the computation, but painting the window. If you minimize (hide) the window, the computation will go much faster. If you close (kill) the window, the whole process stops.
Open the documentation at doc/index.html in a browser. Start with the articles on CSparse, MPDQ, and ExactCategoryMorphism.
If you prefer to read source code, start with the main methods in the following files.
- csparse/Test1.java runs a bare-bones Smith normal form computation on a small matrix.
- util/Demo.java runs Smith normal form on a large matrix.
- csparse/DenseMatrixZ.java illustrates LLL.
- csparse/TestHNF.java illustrates Hermite normal form.
- homolalg/QvspMorphism.java works with objects and arrows in the category of vector spaces over Q.