A-Tint: A polymake extension for algorithmic tropical intersection theory

TL;DR

This paper introduces A-Tint, a polymake extension that enhances the computation of tropical intersection theory, especially for moduli spaces, by leveraging polyhedral geometry for more efficient algorithms.

Contribution

It presents new algorithms for computing tropical cycles and intersection products, implemented as a polymake extension, improving efficiency for moduli space computations.

Findings

Algorithms enable faster tropical intersection computations

Implementation in polymake facilitates practical applications

Efficient handling of moduli space combinatorics

Abstract

In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of computing certain tropical cycles. The algorithms discussed here have been implemented in an extension for polymake, a software for polyhedral computations.