Finite Quadratic Modules and Simple Lattices

Implementation of several algorithms, tools and supplementary material for the article "Lattices with many Borcherds products" by Jan H. Bruinier, S. Ehlen and E. Freitag.

Installation

• A) On your own computer which has sage and git installed: We expect that a current version of sage is installed on your system (see dependencies).

  Go to the directory where you would like to download the repository to.

  You should be able to simply run:

  $ git clone https://github.com/sehlen/sfqm.git
  $ sage setup.py install
  

  Then start sage and try the following:

  sage: from sfqm.fqm.genus_symbol import *
  sage: s = GenusSymbol('3^+1')
  sage: s
  Genus symbol 3^+1
  sage: s.dimension_cusp_forms(3)
  0
  

• B) In the sage math cloud (SMC), http://cloud.sagemath.com: This is a nice possibility to try out the programs if you don't have sage installed.

  You only have to modify A) a little bit. Instead of the first command you can (in a project of your choice) click on the "+ New" button whcih you use to create a new file.

  Then you insert the url https://github.com/sehlen/sfqm.git in the input field (filename) and click on "From Internet".

  Now open a new terminal ("+New" and then "Terminal") and type:

  $ cd sfqm
  $ sage setup.py install --user
  

  Now you can test the installation as in A), either on the command line or in a sage worksheet (you may have to restart the worksheet server in your project). If this does not work, try the following command:

  $ sage setup.py develop --user
  

Dependencies

• sage: A current version of sage (the implementation has been updated to work with sage 7.2)

• git: if you do not have git installed, you can download the tarball version.

The library dependencies have been included into the release files.

The following modules are required and can also be obtained separately from my (sehlen) psage fork (use the devel branch).

• psage.modules.finite_quadratic_module (N.-P. Skoruppa et. al.)
• psage.modform.weilrep_tools (S. Ehlen)
• psage.modules.weil_invariants (S. Ehlen and N.-P. Skoruppa)

EXAMPLES

Todo.