English

Computing complex and real tropical curves using monodromy

Algebraic Geometry 2016-05-16 v1 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.1605.04203,
  title  = {Computing complex and real tropical curves using monodromy},
  author = {Daniel A. Brake and Jonathan D. Hauenstein and Cynthia Vinzant},
  journal= {arXiv preprint arXiv:1605.04203},
  year   = {2016}
}

Comments

23 pages, 5 figures

R2 v1 2026-06-22T14:00:13.803Z