Mathematica Tools for Quaternionic Polynomials

Abstract

In this paper we revisit the ring of (left) one-sided quaternionic polynomials with special focus on its zero structure. This area of research has attracted the attention of several authors and therefore it is natural to develop computational tools for working in this setting. The main contribution of this paper is a Mathematica collection of functions QPolynomial for solving polynomial problems that we frequently find in applications.

A Two-Step Quaternionic Root-Finding Method

“…Remark 3. Observe that the polynomials R i in ( 16) used to obtain the roots are the same polynomials presented in (8) to obtain the factor terms.…”

“…For the first two experiments we have used the Mathematica add-on application QuaternionAnalysis [17] specially designed for symbolic manipulation of quaternion valued functions together with the collection of functions QPolynomial [8,10] for solving polynomial problems in H[x].…”

“…is given by (8). To obtain estimates for ρ, the local order of convergence of the method, we used the following computational estimate (see e.g.…”