Complexity and Applications of Parametric Algorithms of Computational Algebraic Geometry

Wednesday, November 19, 1997 - 2:00pm - 2:20pm
Keller 3-180
Marek Rychlik (University of Arizona)
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.