A Method for Solving quadratic Equations in Real Quaternion Algebra by using Scilab software
Rings and Algebras
2023-07-18 v3
Abstract
In this paper, we present some numerical applications for the equation , where are two quaternionic elements in . Based on well-known solving methods, we have developed a new numerical algorithm that solves the equation for any quaternions a and b in any algebra .
Keywords
Cite
@article{arxiv.2304.08930,
title = {A Method for Solving quadratic Equations in Real Quaternion Algebra by using Scilab software},
author = {Geanina Zaharia and Diana-Rodica Munteanu},
journal= {arXiv preprint arXiv:2304.08930},
year = {2023}
}
Comments
In this article, we have provided an algorithm in Scilab which allows us to find solutions for the monic quadratic equation $x^2+bx+c=0$, with $b,c \in \mathbb{H}(\alpha, \beta)$. By feeding the algorithm with the quaternions b and c and using the formulas, we compute A, B, and C, determine the case, and find the two solutions of the monic quadratic equation