Computing explicit isomorphisms with full matrix algebras over $\mathbb{F}_q(x)$

We propose a polynomial time f -algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over Fq) for computing an isomorphism (if there is any) of a finite dimensional Fq(x)-algebra A given by structure constants with the algebra of n by n matrices with entries from Fq(x). The method is based on computing a finite Fq-subalgebra of A which is the intersection of a maximal Fq[x]-order and a maximal R-order, where R is the subring of Fq(x) consisting of fractions of polynomials with denominator having degree not less than that of the numerator.