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Computing Riemann matrices of algebraic curves. (English) Zbl 1054.14079
Summary: A black-box program for the explicit calculation of Riemann matrices of arbitrary compact connected Riemann surfaces is presented. All such Riemann surfaces are represented as plane algebraic curves. These algebraic curves are allowed to have arbitrary singularities. The method of calculation of the Riemann matrix is essentially its definition: we numerically integrate the holomorphic differentials of the Riemann surface over the cycles of a canonical basis of the homology of the Riemann surface. Both the holomorphic differentials and the canonical basis of the homology of the Riemann surface are obtained exactly through symbolic calculations. This program is included in Maple 6, as part of the algcurves package.

MSC:
14Q05Computational aspects of algebraic curves
14H70Relationships of algebraic curves with integrable systems
30-04Machine computation, programs (functions of one complex variable)
30F30Differentials on Riemann surfaces
35B10Periodic solutions of PDE
Software:
Maple