swMATH ID: 41771
Software Authors: N. Bruin, J. Sijsling, A. Zotine
Description: Riemann matrices and endomorphism rings of algebraic Riemann surfaces: This module provides a class, RiemannSurface, to model the Riemann surface determined by a plane algebraic curve over a subfield of the complex numbers. A homology basis is derived from the edges of a Voronoi cell decomposition based on the branch locus. The pull-back of these edges to the Riemann surface provides a graph on it that contains a homology basis. The class provides methods for computing the Riemann period matrix of the surface numerically, using a certified homotopy continuation method due to [Kr2016]. The class also provides facilities for computing the endomorphism ring of the period lattice numerically, by determining integer (near) solutions to the relevant approximate linear equations.
Homepage: https://doc.sagemath.org/html/en/reference/curves/sage/schemes/riemann_surfaces/riemann_surface.html
Dependencies: sagemath
Related Software: SageMath; Theta.jl; Julia
Cited in: 1 Document

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