  Algorithms for computing rational generating functions of solutions of
one-dimensional difference equations are well-known and easy to implement. We
propose an algorithm for computing rational generating functions of solutions
of two-dimensional difference equations in terms of initial data of the
corresponding initial value problems. The crucial part of the algorithm is the
reconstruction of infinite one-dimensional initial data on the basis of finite
input data. The proposed technique can be used for the development of similar
algorithms in higher dimensions. We furnish examples of the implementation of
the proposed algorithm.
