QDifferenceEquations
QPolynomialNormalForm
construct the q-polynomial normal form of a rational function
Calling Sequence
Parameters
Description
Examples
References
QPolynomialNormalForm(F, q, n)
F
-
rational function of n
q
name used as the parameter q, usually q
n
variable
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)}.
Check the results.
Condition 1 is satisfied.
Condition 2 is satisfied.
Condition 3 is satisfied.
Condition 4 is satisfied.
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.
See Also
QDifferenceEquations[QDispersion]
QDifferenceEquations[QRationalCanonicalForm]
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