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Algorithms for computing rational generating functions of solutions ofone-dimensional difference equations are well-known and easy to implement. Wepropose an algorithm for computing rational generating functions of solutionsof two-dimensional difference equations in terms of initial data of thecorresponding initial value problems. The crucial part of the algorithm is thereconstruction of infinite one-dimensional initial data on the basis of finiteinput data. The proposed technique can be used for the development of similaralgorithms in higher dimensions. We furnish examples of the implementation ofthe proposed algorithm.

Computing Rational Generating Function of a Solution to the Initial Value Problem of Two-dimensional Difference Equation with Constant Coefficients