Using examples of interest from real problems, we will discuss the Dixon-EDF resultant as a method of solving parametric polynomial systems.  We will briefly describe the method itself, then discuss problems arising in Nash equilibria, geometric computing, flexibility of molecules, chemical reactions, global positioning systems, operations research, and others.  We will compare Dixon-EDF to several implementations of Grobner bases algorithms on several systems.  We find that Dixon-EDF is greatly superior.

Keywords: polynomial system, resultant, Dixon, determinant, symbolic computing, Grobner basis.