Hyperexponential solutions of finite-rank ideals in orthogonal ore rings

An orthogonal Ore ring is an abstraction of common properties of linear partial differential, shift and q-shift operators. Using orthogonal Ore rings, we present an algorithm for finding hyperexponential solutions of a system of linear differential, shift and q-shift operators, or any mixture thereof, whose solution space is finite-dimensional. The algorithm is applicable to factoring modules over an orthogonal Ore ring when the modules are also finite-dimensional vector spaces over the field of rational functions.

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