# 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.