decomposes a polynomial, if possible, into a composition of simpler polynomials.
Details and Options
- Decompose gives a list of the polynomials Pi which can be composed as to give the original polynomial.
- The set of polynomials Pi is not necessarily unique.
- Decomposition is an operation which is independent of polynomial factorization.
Examplesopen allclose all
Basic Examples (3)
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 f:
Wolfram Language solvers use Decompose automatically:
Properties & Relations (2)
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 f:
Use Factor to represent a polynomial as a product of irreducible factors:
f can be factored but not decomposed; g can be decomposed but not factored:
Possible Issues (1)
Decompose ignores possible decompositions with inner polynomials that are linear:
Wolfram Research (1988), Decompose, Wolfram Language function, https://reference.wolfram.com/language/ref/Decompose.html.
Wolfram Language. 1988. "Decompose." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Decompose.html.
Wolfram Language. (1988). Decompose. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Decompose.html