turkmath.org

The long-term goal of our project is to successfully implement algorithms in Magma in order to integrate differential form on Riemann Surfaces. In this talk, we will take a closer look at the first homology group of a given compact Riemann surface and the computation of a homology basis. Naturally, its elements, 1-cycles, are the objects along which differential forms are integrated. An important part of this is the computation of the monodromy group, for which we implemented an algorithm similar to the one used in the Maple package algcurves.