Before revision:  We demonstrate its capabilities by providing a new probabilistic complexity analysis for the Plantinga-Vegter algorithm , which covers both random sparse (alas a restricted sparseness structure) polynomials and random Gaussian polynomials.
After revision:  We demonstrate its capabilities in two problems, under very mild probabilistic assumptions. On the one hand, we show that the average run-time of the Plantinga-Vegter algorithm , which covers both random sparse (alas a restricted sparseness structure) polynomials and random Gaussian polynomials.