Let F be a rational function of n over a field K of characteristic 0, q is a nonzero element of K which is not a root of unity. The QPolynomialNormalForm(F,q,n) command constructs the q-polynomial normal form for F.

The output is a sequence of 4 elements  where z is an element of K, and  are monic polynomials over K such that:     

Note: Q is the automorphism of K(n) defined by {Q(F(n)) = F(q*n)}.

Abramov, S.A., and Petkovsek, M. "Finding all q-hypergeometric solutions of q-difference equations." Proc. FPSAC '95, Univ.de Marne-la-Vall'ee, Noisy-le-Grand, pp. 1-10. 1995.

Koornwinder, T.H. "On Zeilberger's algorithm and its q-analogue: a rigorous description." J. Comput. Appl. Math. Vol. 48. (1993): 91-111.