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 Documentation / Mathematica / Built-in Functions / Algebraic Computation / Polynomial Functions  /
Decompose

  • Decompose[ poly , x ] decomposes a polynomial, if possible, into a composition of simpler polynomials.
  • Decompose gives a list of the polynomials which can be composed as to give the original polynomial.
  • The set of polynomials is not necessarily unique.
  • Decomposition is an operation which is independent of polynomial factorization.
  • See the Mathematica book: Section 3.3.4.
  • See also: FactorList, Solve.

    Further Examples

    This polynomial can be rewritten in a variable that is a polynomial in the original variable.

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    Here is a more complicated example. We first set up a triple composition.

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    The functions in the decomposition are different from the three we started with, although in this case the degrees are the same.

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    Recomposing the three new polynomials brings us back to the original composition.

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