DECOMPOSE _ _ _ _ _ _ _ _ _ _ _ _ operator

The decompose operator takes a multivariate polynomial as argument, and returns an expression and a list of equations from which the original polynomial can be found by composition.

syntax:

examples:

decompose(x^8-88*x^7+2924*x^6-43912*x^5+263431*x^4-
          218900*x^3+65690*x^2-7700*x+234)

 

   2                  2            2
  U  + 35*U + 234, U=V  + 10*V, V=X  - 22*X 


     decompose(u^2+v^2+2u*v+1) 

   2
  W   + 1, W=U + V

Unlike factorization, this decomposition is not unique. Further details can be found in V.S. Alagar, M.Tanh, <Fast Polynomial Decomposition>, Proc. EUROCAL 1985, pp 150-153 (Springer) and J. von zur Gathen, <Functional> <Decomposition of Polynomials: the Tame Case>, J. Symbolic Computation (1990) 9, 281-299.