On decomposition of tame polynomials and rational functions

TL;DR

This paper investigates the algebraic structure of tame polynomials and rational functions, providing algorithms and theoretical insights into their group decompositions and relations.

Contribution

It introduces new theoretical results and algorithms for understanding the group structure of tame polynomials and rational functions, extending previous work.

Findings

Proves relations between group orders for tame polynomials.

Extends analysis to rational functions.

Provides algorithmic considerations for decomposition.

Abstract

In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial, proving it for arbitrary tame polynomials, and considering the case of rational functions.