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Decompose

Decompose
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.
Represent a polynomial as a composition of polynomials:
Represent a polynomial as a composition of polynomials:
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A composition of more than two polynomials:
No decomposition:
A polynomial with symbolic coefficients:
Decompose a polynomial over integers modulo 2:
Solve some polynomial equations of degrees higher than 4 in terms of radicals:
Solve by solving and then etc:
Check that these indeed are the roots of :
Mathematica solvers use Decompose automatically:
Composition of polynomials given by Decompose gives the original polynomial:
Use Fold to compose the polynomials:
Use Expand to show that the result is equal to :
Use Factor to represent a polynomial as a product of irreducible factors:
can be factored but not decomposed; can be decomposed but not factored:
Decompose ignores possible decompositions with inner polynomials that are linear:
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