>
> Approximate GCD? That's a curious concept. What is it used for? I
> can't imagine defining a GCD in this context as divisibility is an
> exact phenomenon.

For example, in an inverse parametrization problem. Suppose that you
have a rational curve given by a parametrization with float
cofficients  (p(t), q(t)) and you have a point (a,b) with floats that
lies on the curve (up to a precission). Than point (a,b) could be
obtained by intersecting your parametric curve with another one, for
example.

If you need to compute tha parameter corresponding to (a,b). You need
to solve the system of equations a-p(t), b-q(t). This is an
approximate GCD problem.

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