  We present a computational approach to general hyperelliptic Riemann surfaces
in Weierstrass normal form. The surface is either given by a list of the branch
points, the coefficients of the defining polynomial or a system of cuts for the
curve. A canonical basis of the homology is introduced algorithmically for this
curve. The periods of the holomorphic differentials and the Abel map are
computed with the Clenshaw-Curtis method in order to achieve spectral accuracy.
The code can handle almost degenerate Riemann surfaces. This work generalizes
previous work on real hyperelliptic surfaces with prescribed cuts to arbitrary
hyperelliptic surfaces. As an example, solutions to the sine-Gordon equation in
terms of multi-dimensional theta functions are studied, also in the solitonic
limit of these solutions.
