Searching for laurent solutions of truncated systems of linear differential equations with the use of EG-eliminations

Laurent solutions of systems of linear ordinary differential equations with the truncated power series coefficients are considered. The Laurent series in the solutions are also truncated. We use induced recurrent systems for constructing the solutions and have previously proposed an algorithm for the case when the induced system has a non-singular leading matrix. The algorithm finds the maximum possible number of terms of the series in the solutions that are invariant with respect to any prolongation of the original system. Below we present advances in extending our algorithm to the case when the leading matrix is singular using algorithm EG as an auxiliary tool. The implementation of the algorithm as a Maple procedure and examples of its usage are presented.