Computational Approach to Riemann Surfaces

Volume 2013 of the series Lecture Notes in Mathematics pp 67-123


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

  • Bernard DeconinckAffiliated withDepartment of Applied Mathematics, University of Washington Email author 
  • , Matthew S. PattersonAffiliated withBoeing Research and Technology

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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.