Decomposition

 

In Mathematica

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Reduce

inputs outputs

• finding of polynomial substitution which transforms a polynomial into another polynomial in further polynomials

      Decompose[ x^6 + 9x^5 + 52x^4 + 177x^3 + 435x^2
                 + 630x + 593 ]
  

                         2    3
      {593 + 210 x + 25 x  + x , x (3 + x)}

  
      Decompose[ x^4 + 2x^3 y + 3x^2 y^2 + 2x y^3 +
                 y^4 + 2x^2 y + 2x y^2 + 2y^3 + 5x^2 +
                 5 x y + 6y^2 + 5y + 9, x ]
  

                  2                    2        2      3
      {9 + 5 x + x  + 5 y + 2 x y + 6 y  + 2 x y  + 2 y  +
  
         4
        y , x (x + y)}