Computing the bound of an Ore polynomial. Applications to factorization

We develop two algorithms for computing a bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a factorization algorithm. The asymptotic time complexity in the degree of the given Ore polynomial is studied. (C) 2018 Elsevier Ltd. All rights reserved.