English

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 x2+ax+b=0x^2+ax+b=0, where a,ba, b are two quaternionic elements in H(α,β)\mathbb{H}(\alpha,\beta). 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 H(α,β)\mathbb{H}(\alpha,\beta).

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

R2 v1 2026-06-28T10:09:36.571Z