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.

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  1. Agostini, Daniele; Chua, Lynn: Computing theta functions with Julia (2021)