Handbook of Automated Reasoning

4.3 Parametric zero-sets

In many applications of constraint solving one wants to study not only the zero sets of fixed polynomial systems, but also a whole class of such problems given by a polynomial system F = 0, where the coefficients of the polynomials in the system depend on (complex or real) parameters. Then the complex or real zero-set of F depends on these parameters and the goal is to describe this dependence on the parameters as uniformly as possible.

Another source of parametric zero-sets are polynomial systems F that are parameter-free but where V (F) has positive dimension and one wants to determine the zeros of F depending on ...