compute a functional decomposition of a polynomial
FunctionalDecomposition(f, v, inert)
name or list or set of names
This function computes a functional decomposition of the polynomial f. That is, it computes g(x) and h and rewrites the output as a composition f=gx=h|gx=h and the process is repeated on g and h until they can not be functionally decomposed further. This decomposition is not unique.
This function currently just calls compoly repeatedly and constructs the decomposition as a single unexpanded polynomial. If no decomposition is found, f is returned unaltered.
If f is not of type polynom then frontend is used before performing polynomial calculations.
The inert option adds ``() calls around x so that the linear part of the polynomial and pure monomial substitutions will not be expanded by automatic simplification. The output will look like a polynomial, but will not be true polynomial unless expand is called to remove the ``() similar to the output of ifactor.
f ≔ expand⁡x2+2⁢x−1x=x3−x|x2+2⁢x−1x=x3−xx=x2+3⁢x|x2+2⁢x−1x=x3−x|x2+2⁢x−1x=x3−xx=x2+3⁢x
f1 ≔ expand⁡x2+x⁢ⅇa−1x=x2−x|x2+x⁢ⅇa−1x=x2−x
f2 ≔ expand⁡−x3−2⁢x2−x+1x=−y2+x−1|−x3−2⁢x2−x+1x=−y2+x−1
The PolynomialTools[FunctionalDecomposition] command was introduced in Maple 2022.
For more information on Maple 2022 changes, see Updates in Maple 2022.
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