Computing Riemann matrices of algebraic curves

The two authors have implemented an algorithm for computing the period matrix or Riemann matrix of an algebraic curve. The implementation is part of the algcurves package in Maple V Release 6, and is discussed in this paper.

To calculate the period matrix, one needs algorithms for the monodromy, homology, and holomorphic differentials. These algorithms are also discussed in this paper.

An implementation for Maple V release 5 is available here. View the paths around the branchpoints of the curve f = ((y^4-16)^2-2*x)*y^3 - x^12 that the algorithm follows to compute the monodromy.

Download this paper postscript file or pdf file.