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

Factorization and root-finding for polynomials over division quaternion algebras