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

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Computational Approach to Riemann Surfaces

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2013))

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.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195-2420, USA

    Bernard Deconinck

  2. Boeing Research and Technology, 2760 160th Ave SE, Bellevue, WA, 98008, USA

    Matthew S. Patterson

Authors
  1. Bernard Deconinck
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  2. Matthew S. Patterson
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Corresponding author

Correspondence to Bernard Deconinck .

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Technical University of Berlin, Straße des 17.Juni 136, Berlin, 10623, Germany

    Alexander I. Bobenko

  2. Institut de Mathématiques, Université de Bourgogne, av. Alain Savary 9, Dijon Cedex, 21078, France

    Christian Klein

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Deconinck, B., Patterson, M.S. (2011). Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package “Algcurves”. In: Bobenko, A., Klein, C. (eds) Computational Approach to Riemann Surfaces. Lecture Notes in Mathematics(), vol 2013. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17413-1_2

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