Computing the bound of an Ore polynomial. Applications to factorization

TL;DR

This paper introduces a fast algorithm for computing bounds of Ore polynomials over skew fields, with applications to irreducibility testing and factorization, improving efficiency over existing methods especially over finite fields.

Contribution

The authors present a novel, efficient algorithm for bounding Ore polynomials and apply it to irreducibility criteria and factorization, reducing complexity in finite field cases.

Findings

Algorithm computes bounds efficiently under mild conditions.

Provides a criterion for irreducibility of bounded Ore polynomials.

Offers an alternative factorization method with lower complexity over finite fields.

Abstract

We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a factorization algorithm. The asymptotic time complexity in the degree of the given Ore polynomial is studied. In the class of Ore polynomials over a finite field, our algorithm is an alternative to Giesbretch's one that reduces the complexity in the degree of the polynomial.