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Zbl 1054.14079
Deconinck, Bernard; van Hoeij, Mark
Computing Riemann matrices of algebraic curves. (English)
[J] Physica D 152-153, 28-46 (2001). ISSN 0167-2789

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 {\tt algcurves} package.

MSC 2000:: *14Q05 Curves
14H70 Automorphisms of curves
30-04 Machine computation, programs (functions of a complex variable)
30F30 Differentials on Riemann surfaces
35B10 Periodic solutions of PDE

Keywords: period matrix; Riemann surface; effective methods; Maple 6

Cited in: Zbl 1092.33018

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