Tropical Newton-Puiseux polynomials II

TL;DR

This paper develops explicit formulas for tropical Newton-Puiseux polynomials, which are piece-wise linear functions with rational coefficients, serving as tropical algebraic functions, particularly focusing on their role as tropical zeroes of parametric univariate tropical polynomials.

Contribution

It introduces explicit formulas for tropical Newton-Puiseux polynomials as zeroes of univariate tropical polynomials with parametric coefficients.

Findings

Derived explicit formulas for tropical Newton-Puiseux polynomials

Characterized their role as tropical zeroes of parametric polynomials

Enhanced understanding of tropical algebraic functions

Abstract

Tropical Newton-Puiseux polynomials defined as piece-wise linear functions with rational coefficients at the variables, play a role of tropical algebraic functions. We provide explicit formulas for tropical Newton-Puiseux polynomials being the tropical zeroes of a univariate tropical polynomial with parametric coefficients.