Tropical Homotopy Continuation
Combinatorics
2016-01-13 v1 Algebraic Geometry
Abstract
Inspired by numerical homotopy methods we propose a combinatorial homotopy algorithm for finding all isolated solutions to a tropical polynomial systems of n tropical polynomials in n variables. In particular, a tropicalisation of the numerical "regeneration" technique leads to a new method for enumerating the mixed cells of a mixed subdivision. This tropical approach shares some ideas with the recent algorithm by Malajovich. However, our algorithm has several advantages. It is memoryless, parallelisable as a tree traversal, exact and relies on symbolic perturbations. Our computational experiments show that the method is competitive and especially fast on the Katsura class of examples.
Cite
@article{arxiv.1601.02818,
title = {Tropical Homotopy Continuation},
author = {Anders Nedergaard Jensen},
journal= {arXiv preprint arXiv:1601.02818},
year = {2016}
}