Date: 21 Dec 2010

Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package “Algcurves”

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Abstract

In this chapter, we present an overview of different algorithms for computing with compact connected Riemann surfaces, obtained from desingularized and compactified plane algebraic curves. As mentioned in Chap.1 [Bob11], all compact connected Riemann surfaces may be represented this way. The Maple package “algcurvess”, largely developed by the authors and Mark van Hoeij contains implementations of these algorithms. A few recent additions to the “algcurves” package are not due to the authors or Mark van Hoeij. The algorithm behind those commands are not discussed here as they have no bearing on anything associated with Riemann surfaces.