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We develop a fast algorithm for computing the bound of an Ore polynomial overa skew field, under mild conditions. As an application, we state a criterionfor deciding whether a bounded Ore polynomial is irreducible, and we discuss afactorization algorithm. The asymptotic time complexity in the degree of thegiven Ore polynomial is studied. In the class of Ore polynomials over a finitefield, our algorithm is an alternative to Giesbretch's one that reduces thecomplexity in the degree of the polynomial.

Computing the bound of an Ore polynomial. Applications to factorization