"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.