Resultants of skew polynomials over division rings

TL;DR

This paper extends classical results on the resultant of univariate polynomials to skew polynomials over division rings within Ore extensions, providing algorithms and Magma implementations for practical computation.

Contribution

It generalizes the concept of resultants to skew polynomials over division rings and offers computational tools for their analysis.

Findings

Extended classical resultants to skew polynomials over division rings

Developed algorithms for computing resultants in Ore extensions

Provided Magma programs for practical applications

Abstract

Let $\mathbb{F}$ be a division ring. In this paper, we extent some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension $\mathbb{F}[x;\sigma,\delta]$. Finally, some algorithms and Magma programs are given as a numerical application of the main theoretical results of this paper.