Some formal invariants of linear difference systems and their computations (Q2710292)

The properties of some formal invariants involving the function \(\Gamma\) of general invertible linear difference systems without any restrictions are considered. The authors give a method to compute the \(\Gamma\)-order of an invertible linear difference system by using an ``irreducible'' form of the system. This yields an efficient algorithm for computing the irregular part involving the function \(\Gamma\) in a fundamental matrix of formal solutions. Together with earlier papers of the authors it gives a complete algorithm for an effective computation of the irregular part in the fundamental matrix of formal solutions for a general class of linear difference systems.