Arithmetical structures on dominated polynomials

TL;DR

This paper introduces an algorithm for computing arithmetical structures on dominated polynomials, extending previous matrix-based methods to a new class of multivariate polynomials.

Contribution

It adapts existing matrix algorithms to handle dominated polynomials, providing a novel computational approach for this polynomial class.

Findings

Developed an algorithm for dominated polynomial arithmetical structures

Extended matrix-based methods to multivariate polynomials

Demonstrated the algorithm's effectiveness on examples

Abstract

In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmetical structures over dominated polynomials. A dominated polynomial is an integer multivariate polynomial such that contains a monomial which is divided by all its monomials.