A direct algorithm to compute rational solutions of first order linear q-difference systems

We present an algorithm to compute rational function solutions to a first order system of linear q-difference equations with rational coefficients. We make use of the fact that q-difference equations bear similarity to differential equations at the point 0 and to difference equations at other points. This allows the combining of known algorithms for the differential and the difference cases. This algorithm does not require preliminary uncoupling of the given system.

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