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 by providing a new probabilistic complexity analysis for the Plantinga-Vegter algorithm is polynomial in the degree for random sparse (alas a restricted sparseness structure) polynomials and random Gaussian polynomials.