Computing Explicit Isomorphisms with Full Matrix Algebras over Fq(x)

Ivanyos, Gábor and Kutas, Péter and Rónyai, Lajos (2018) Computing Explicit Isomorphisms with Full Matrix Algebras over Fq(x). FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, 18 (2). pp. 381-397. ISSN 1615-3375

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Abstract

We propose a polynomial time f-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over (Formula presented.)) for computing an isomorphism (if there is any) of a finite-dimensional (Formula presented.)-algebra (Formula presented.) given by structure constants with the algebra of n by n matrices with entries from (Formula presented.). The method is based on computing a finite (Formula presented.)-subalgebra of (Formula presented.) which is the intersection of a maximal (Formula presented.)-order and a maximal R-order, where R is the subring of (Formula presented.) consisting of fractions of polynomials with denominator having degree not less than that of the numerator. © 2017 SFoCM

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