Tropical Implicitization and Mixed Fiber Polytopes

TL;DR

This paper introduces TrIm, a software tool that performs tropical implicitization and elimination, enabling computation of tropical varieties and mixed fiber polytopes for polynomial maps with generic coefficients.

Contribution

The paper presents TrIm, a novel software implementation for tropical implicitization and elimination, extending the computational capabilities in tropical geometry.

Findings

TrIm efficiently computes tropical varieties of polynomial map images.

It can determine Newton polytopes of hypersurface images.

Supports computation of mixed fiber and secondary polytopes.

Abstract

The software TrIm offers implementations of tropical implicitization and tropical elimination, as developed by Tevelev and the authors. Given a polynomial map with generic coefficients, TrIm computes the tropical variety of the image. When the image is a hypersurface, the output is the Newton polytope of the defining polynomial. TrIm can thus be used to compute mixed fiber polytopes, including secondary polytopes.