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On valuations of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients

Algorithms for computing lower bounds on valuations (e.g., orders of the poles) of the components of meromorphic solutions of arbitrary-order linear difference systems with polynomial coefficients are considered. In addition to algorithms based on ideas which have been already utilized in computer algebra for treating normal first-order systems, a new algorithm using tropical calculations is proposed. It is shown that the latter algorithm is rather fast, and produces the bounds with good accuracy.