Computing complex and real tropical curves using monodromy

Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients. These algorithms rely on homotop...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2019-12, Vol.223 (12), p.5232-5250
Main Authors: Brake, Danielle A., Hauenstein, Jonathan D., Vinzant, Cynthia
Format: Article
Language:English
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Summary:Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays of a complex and real tropical curve defined by polynomials with constant coefficients. These algorithms rely on homotopy continuation, monodromy loops, and Cauchy integrals. Several examples are presented which are computed using an implementation that builds on the numerical algebraic geometry software Bertini.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2019.03.019