Denominators of rational solutions of linear difference systems of an arbitrary order (Q1758700)

The authors give an algorithm for finding a universal denominator of rational solutions (i.e., solutions having the form of rational functions) for the system of linear difference equations \[ A_r(x)\,y(x+r)+\dots+A_1(x)\,y(x+1)+A_0(x)\,y(x)=b(x), \] where \(A_0(x),\dots,A_r(x)\) are \(m\times m\) matrices with polynomial entries and \(A_r(x)\neq 0\), \(A_0(x)\neq 0\) (see Theorem 1). An implementation of this algorithm to the computer algebra system Maple is also presented. Finally, a comparison with some recently published algorithms in the special case \(r=1\) is discussed.