Polynomial factorization and root finding are among the most standard themes of computational mathematics. Yet still, little has been done for polynomials over quaternion algebras, with the single exception of Hamiltonian quaternions for which there are known numerical methods for polynomial root approximation. The sole purpose of the present paper is to present a polynomial factorization algorithm for division quaternion algebras over number fields, together with its adaptation for root finding.

翻译：多项式因式分解和求根是计算数学中最经典的主题之一。然而，对于四元数代数上的多项式，除了哈密顿四元数这一特例——已有数值方法可近似求其多项式根——相关研究仍十分有限。本文的唯一目的在于提出一种适用于数域上四元数除环的多项式因式分解算法，并在此基础上改进得到求根方法。