Now I have to thank Vaughan for an intense discussion on nondeterminism, which
emerged a week ago, when I spontaneously brought the symbolic Newton method. I
suppose, that it has exponential complexity - without regarding it's
termination condition, which could a) be a fixed number of steps or b) some
algebraic criteria. I learnt a lot from the discussion about computer science as
well as philosophy.

I also taught my software to do 4 steps of the Newton method symbolically and
was astonished of the growth of the function. The result, which might not be
perfect, can found at

http://cococo.de/products/windows/Columbo/sample4.html

The only method to reduce the expression I know, is to use Groebner bases. Does
anyone here know a proper criteria for the termination?
How do I know from symbolic values, if the root has been found?

Jens