Factoring Ore polynomials over ${\mathbb{F}}_q(t)$ is difficult

Abstract

We show that the effective factorization of Ore polynomials over ${\mathbb{F}}_q(t)$ is still an open problem. This is so because the known algorithm in [1] presents two gaps, and therefore it does not cover all the examples. We amend one of the gaps, and we discuss what kind of partial factorizations can be then computed by using [1].