The PolynomialNormalForm(F,x) function constructs the polynomial normal form for F, where F is a rational function in x over a field of characteristic .

A sequence of four elements , where z is an element in K and  are monic polynomials over K such that the following three conditions are satisfied, is returned:    

Note: E is the automorphism of K(x) defined by {E(f(x)) = f(x+1)}.

This function is part of the RationalNormalForms package, and so it can be used in the form PolynomialNormalForm(..) only after executing the command with(RationalNormalForms). However, it can always be accessed through the long form of the command by using RationalNormalForms[PolynomialNormalForm](..).

Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.