Linear programs and convex hulls over fields of Puiseux fractions

TL;DR

This paper presents an implementation of Puiseux series in polymake to solve parameter-dependent linear programs and convex hulls, with applications in tropical geometry, enabling advanced algebraic and geometric computations.

Contribution

It introduces a novel implementation of Puiseux series in polymake for parameter-dependent linear programming and convex hull computations, expanding computational tools in tropical geometry.

Findings

Enabled solving parameter-dependent linear programs.

Facilitated convex hull computations over Puiseux fields.

Applied approach to problems in tropical geometry.

Abstract

We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful for computations in tropical geometry.