Let F be a rational function of n over a field K of characteristic 0. The PolynomialNormalForm(F,n) command constructs the 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: E is the automorphism of K(n) defined by {E(F(n)) = F(n+1)}.

Gosper, R.W., Jr. "Decision procedure for indefinite hypergeometric summation." Proc. Natl. Acad. Sci. USA. Vol. 75. (1977): 40-42.

Petkovsek, M. "Hypergeometric solutions of linear recurrences with polynomial coefficients." J. Symb. Comput. Vol. 14. (1992): 243-264.