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