Linear q-difference equations depending on a parameter

We consider linear q-difference equations with polynomial coefficients depending on a parameter. We discuss an algorithm recognizing the existence of numerical values of the parameter for which a given equation has a non-zero rational function solution. If such values exist, then the algorithm finds them as well as the corresponding solutions. In addition, we propose parametric versions of the q-accurate summation, and q-Zeilberger algorithms. An implementation in Maple of all proposed algorithms is described.