Computing Tropical Linear Spaces
arXiv:1109.4130 · doi:10.1016/j.jsc.2012.03.008
Abstract
We define and study the cyclic Bergman fan of a matroid M, which is a simplicial polyhedral fan supported on the tropical linear space T(M) of M and is amenable to computational purposes. It slightly refines the nested set structure on T(M), and its rays are in bijection with flats of M which are either cyclic flats or singletons. We give a fast algorithm for calculating it, making some computational applications of tropical geometry now viable. Our C++ implementation, called TropLi, and a tool for computing vertices of Newton polytopes of A-discriminants, are both available online.
15 pages, 2 figures. Added a few examples and made some minor corrections
References in corpus (4)
Cited by in corpus (9)
- Computing Tropical Resultants
- A-Tint: A polymake extension for algorithmic tropical intersection theory
- Algorithms for Tight Spans and Tropical Linear Spaces
- Local tropical linear spaces
- Perfect matroids over hyperfields
- Tropicalization of Del Pezzo Surfaces
- Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
- Bergman Complexes of Lattice Path Matroids
- Effective Results on non-Archimedean Tropical Discriminants