Vector Bundles

This is a Sagemath package implementing algorithms for creating and manipulating Vector Bundles over algebraic curves on finite field (some features should work on infinite field and most algorithms are valid, but there is no guarantee for the implementation). All manipulations are done using algebra on function fields. This implements algorithms from this work.

This package was developped and tested using Sage version 10.3. There is no guarantee that it will work with an older version of Sage. For instance, structural differences in the function_field package of sage prevents vector_bundle from working with Sage version 9.2 and earlier. Please let me know wheter vector_bundle works for you if you use a version of Sage between 9.2 and 10.3.

Installation

If sage is built from source

Download the source from the git repository:

$ git clone https://git.disroot.org/montessiel/vector-bundles-sagemath.git

Run the following from the root directory of the cloned repository:

$ sage -pip install --upgrade --no-index -v .

For convenience this package contains a makefile with this and other often used commands. Should you wish too, you can use the shorthand:

$ make install

Using the package without installation

If you did not build Sage from sources, you can use this package without installing it. Download the source using.

$ git clone https://git.disroot.org/montessiel/vector-bundles-sagemath.git

Reun the following from the root directory:

$ sage -python setup.py build_ext --inplace

Add the vector_bundle directory to your Python sys.path

Usage

Once the package is installed, you can use it in Sage with:

sage: from vector_bundle import *

See also the demo notebook demo.ipynb> and the documentation.

Documentation

The documentation of the package can be generated using Sage's Sphinx installation::

$ cd docs
$ sage -sh -c "make html"

You may also find an online version of the documentation here.

Warning

This project is still young, and does not fully use the features of Sage. As these are integrated later on, they may come with breaking changes.