Examples for the paper
    Numerical computation of endomorphism rings of jacobians
by
    Nils Bruin, Jeroen Sijsling, and Alexandre Zotine

Required:
    * Sage at least 8.3.beta0
    * (optional) the functionality at https://github.com/edgarcosta/endomorphisms for the algorithms in Magma

Contents:

For Example 5.1 (ANTS Version):
    * decomposition.sage -- Main computation
    * decomposition-endoring.sage -- Description of the numerical endomorphism ring
    * Decomposition-Factor-Num.m -- (optional) Magma script for numerically identifying genus 2 curves
    * Decomposition-Factor-Alg.m -- (optional) Magma script for determining curves in the decomposition
    * Decomposition-Factor-Hom.m -- (optional) Magma script for checking that no morphism can exist for one of the idempotents

For Example 5.2 (ANTS Version):
    * macbeath.sage -- Sage script for the computation

For Example 5.3 (ANTS Version):
    * genus4prym.sage -- Numerical check of a prym variety in genus 4

For Example 5.4 (ArXiv Version):
    * example4.sage -- Sage script for the computation