  A generalized summation by parts algorithm is presented for solving of
difference equations of the form $T^m(y)-a[u]y=b[u]$ where $T$ denotes the
shift $u_j\to u_{j+1}$. Solvability of such type of equations with respect to
coefficients of formal symmetry (or formal recursion operator) provides a
convenient integrability test for evolutionary differential-difference
equations $u_{,t}=f(u_{-m},\dots,u_m)$. The algorithm is implemented in {\em
Mathematica}.
