title: How to perform a complicated change of variables for a polynomial (in Mathematica)
body: <p>I have an integer polynomial in four variables (w, x, y, and z) that I know can be written as an integer polynomial in these six variables:</p>
  
  <ul>
  <li>a = w z</li>
  <li>b = x y</li>
  <li>c = w^3 + z^3</li>
  <li>d = x + y</li>
  <li>e = w^3 x + y z^3</li>
  <li>f = w^3 y + x z^3</li>
  </ul>
  
  <p>How can I use Mathematica (or maybe Java) to easily do this change of variables?</p>