This repository contains a mix of Magma, Pari and SageMath code for calculating the endomorphism algebras and rings of Jacobian varieties of curves over number fields and finite fields.

An installation of both Magma and SageMath is required to run all of the code. To install the package in SageMath, first clone the repository via

git clone https://github.com/edgarcosta/endomorphisms.git

then go to the newly created directory and type

sage -pip install .

After that, a new package called endomorphisms will be available for import in SageMath.

The subdirectory endomorphisms/magma/ includes code that can be run purely within Magma. You can load all the Magma specific files by attaching the endomorphisms/magma/spec file with AttachSpec. For example, if you start your session of Magma inside the git directory, you can do this by typing

AttachSpec("endomorphisms/magma/spec");

A lot of examples, both in SageMath and purely in Magma, are given in the directory examples/. Interaction with databases in the LMFDB is described in the directory database/.

It is highly recommended to fix a Magma bug before using this package. In old version the file magma/package/Algebra/AlgQuat/interface.m had the following as line 145:

c := [Trace(theta), Norm(theta)];

This should be replaced by

cpol := MinimalPolynomial(theta);  
assert Degree(cpol) eq 2;  
c := [Coefficient(cpol,1), Coefficient(cpol, 0)];

For faster calculations of period matrices, you can install the new package

https://github.com/pascalmolin/hcperiods

In the examples you can then set the flag molin_neurohr to True. This will make the code run considerably faster, as well as making it more stable.

A description of the data structures used can be found in the files Dicts.md and Descs.md in the directory documentation/.