Detecting Nonexistence of Rational Solutions of Linear Difference Equations in Early Stages of Computation

Abstract

We discuss some changes of the traditional scheme for finding rational solutions of linear difference equations (homogeneous or inhomogeneous) with rational coefficients. These changes in some cases allow one to detect the absence of rational solutions in an early stage of computation and to stop the work. The corresponding strategy may be useful for the algorithms based on finding rational solutions of equations of considered form, e.g., for some symbolic summation algorithms.