# Asymptotic Solutions of Polynomial Equations with Exp-Log Coefficients

## TL;DR

This paper introduces an algorithm to compute asymptotic approximations of roots for polynomials with exp-log coefficients, providing explicit expressions and a method to identify real roots, supported by implementation and empirical data.

## Contribution

It presents a novel algorithm for asymptotic root approximation of polynomials with exp-log coefficients, including a real root identification method.

## Key findings

- Algorithm successfully computes asymptotic roots with explicit exp-log expressions.
- Method effectively distinguishes real roots among approximations.
- Empirical data demonstrates the algorithm's practical performance.

## Abstract

We present an algorithm for computing asymptotic approximations of roots of polynomials with exp-log function coefficients. The real and imaginary parts of the approximations are given as explicit exp-log expressions. We provide a method for deciding which approximations correspond to real roots. We report on implementation of the algorithm and present empirical data.