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Computing Curves Bounding Trigonometric Planar Maps: Symbolic and Hybrid Methods

Daniel Lichtblau
Organization: Wolfram Research, Inc.

ADG 2004
Conference location

Gainesville, Florida

Presented at ADG 2004, Gainesville, FL, September 2004


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" 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.

*Mathematics > Algebra > Field and Ring Theory
*Mathematics > Algebra > Polynomials
*Mathematics > Geometry > Trigonometry
*Mathematics > Number Theory
*Wolfram Technology > Kernel > Numerics

implicitization, hybrid symbolic-numeric methods
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ADG2004_talk.pdf (422.5 KB) - PDF Document
ADG2004_paper.nb (1.6 MB) - Mathematica Notebook
ADG2004_talk.nb (1 MB) - Mathematica Notebook