"The Kapur-Saxena-Yang Dixon Resultant with Maple and Mathematica" Janet McShane, George Nakos and Robert M. Williams gcn@sma.usna.navy.mil Prof. George Nakos Mathematics Department, M/S 9E U.S. Naval Academy Annapolis, MD 21402-5002 USA gcn@sma.usna.navy.mil Dr. Robert M. Williams Code 505A Naval Air Warfare Center Warminster, PA 18974--5000 USA bobw@nadc.navy.mil Prof. Janet McShane Northern Arizona University Department of Mathematics Box 5717 Flagstaff, AZ 86011-5717 USA mcshane@odin.math.nau.edu The Dixon resultant is primarily an elimination method that can be also used to solve systems of polynomial equations. Dixon proved that the vanishing of his resultant is a necessary condition for a system of n+1 equations with n unknowns, to have an solution. Unfortunately, when the Dixon resultant vanishes identically (which is not uncommon) there is no information on the roots of the system. This question was addressed by Kapur, Saxena and Yang. By adding a technical condition they succeed in offering an necessary condition on the existence of common roots even when the Dixon resultant is identically zero. In this talk we discuss our implementation in Maple and Mathematica of the Kapur, Saxena and Yang variant of the Dixon resultant.