2016/01/12 by Anders Jensen, Anders Nedergaard Jensen, Jensen, Anders Nedergaard · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO
paper · pdf · doi:10.48550/arxiv.1601.02818
arxiv created 2016/01/12 · openalex publication_date 2016/01/12 · arxiv updated 2016/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.