The Comprehensive Groebner Basis algorithm of V.~Weispfenning can be applied to compute the maximal dimension of an algebraic variety depending on parameters and a variety of other problems which can be solved in the non-parametric case with the help of Groebner bases. The algorithm and its experimental implementation in Common Lisp will be described. A variety of examples from several areas of mathematics and science will be presented, including bifurcation theory, mechanics and chemistry. In particular, benchmarks on some scalable dynamical systems will be discussed.

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