This repository contains Magma code for determining parts of Prym varieties cut out by intermediate Jacobians.
You can enable the functionality of this code in Magma by attaching the spec file with AttachSpec. To make this independent of the directory in which you find yourself, and to active this on startup by default, you may want to indicate the relative path in your ~/.magmarc file, by adding a line such as
AttachSpec("~/Programs/prym_decomposition/spec");
Examples are given in the directory examples/. The file ranks.m gives examples of calculations with the Chevalley--Weil decomposition, while test-tools.m runs our algorithms on an example.
Verbose comments are enabled by
SetVerbose("FindCovs", n)
where n is either 1, 2 or 3. A higher value gives more feedback.
This package includes algorithms by Paulhus and before her Breuer that can be found at jenpaulhus/breuer-modified and without which none of this work would have been possible. An explanation of this work can be found here.
If this code has been helpful in your research, then please cite the GitHub repository by Paulhus, as well as the book where Breuer explains these techniques:
Thomas Breuer Characters and automorphism groups of compact Riemann surfaces. London Mathematical Society Lecture Note Series, volume 280. Cambridge University Press, Cambridge, 2000.
Please also cite our preprint:
Davide Lombardo, Elisa Lorenzo García, Christophe Ritzenthaler, and Jeroen Sijsling Decomposing Jacobians via Galois covers
Preprint available at TBA