Computing tropical points and tropical links

Abstract

We present an algorithm for computing zero-dimensional tropical varieties based on triangular decomposition and Newton polygon methods. From it, we derive algorithms for computing points on and links of higher-dimensional tropical varieties, using intersections with affine hyperplanes to reduce the dimension to zero. We use the algorithms to show that the tropical Grassmannians ${\mathcal{G}}_{3,8}$ and ${\mathcal{G}}_{4,8}$ are not simplicial.

20 pages, 6 figures; open access link: https://rdcu.be/4bPZ

References in corpus (3)

• Stable Intersections of Tropical Varieties
• Dressians, Tropical Grassmannians, and Their Rays
• Combinatorial simplex algorithms can solve mean payoff games

Cited by in corpus (1)

• Detecting tropical defects of polynomial equations