Wikipeida explains how to come up with the parametrization (I think I've seen the term "generating functions" for this, but really that term means something entirely different).

Wikipedia explains how to come up with the parametrization (I think I've seen the term "generating functions" for this, but really that term means something entirely different).

Update: Ha! apparently you can also use Hilbert's theorem 90 to obtain the parametrization (Elkies' note).