Computing Tropical Linear Spaces
Combinatorics
2013-03-07 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1109.4130,
title = {Computing Tropical Linear Spaces},
author = {Felipe Rincón},
journal= {arXiv preprint arXiv:1109.4130},
year = {2013}
}
Comments
15 pages, 2 figures. Added a few examples and made some minor corrections