RiemannSurface 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 Cited by 2 Authors 1 Agostini, Daniele 1 Chua, Lynn Cited in 1 Serial 1 The Journal of Software for Algebra and Geometry Cited in 3 Fields 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Numerical analysis (65-XX) Citations by Year