Computing Curves Bounding Trigonometric Planar Maps: Symbolic and Hybrid Methods

  • Daniel Lichtblau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3763)


A few years ago S-H Kim investigated some problems at the boundary of number theory, optimization, and geometry. One question regarded an optimal packing of certain “triangular oval” planar curves and another looked at some related transformations of ℝ2 to ℝ2. These were investigated primarily using tools from calculus but it turns out that computational algebra methods may instead be employed to particular advantage. Moreover, generalizations that are beyond the reach of such methods are still amenable to hybrid approaches using numeric and symbolic methods in tandem. We introduce some of the specific problems and generalizations, and show by detailed example how such techniques may be implemented and deployed.


Lagrange Multiplier Symbolic Computation Null Vector Polynomial System Level Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Daniel Lichtblau
    • 1
  1. 1.Wolfram Research, Inc.ChampaignUSA

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