  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.
