| By using a result from the numerical algebraic geometry package Bertini we show that (with extremely high probability) a set of degree six and degree nine polynomials cut out the secant variety s_{4}(IP^2 x IP^2 x IP^3). This, combined with an argument provided by Lansberg and Manivel, implies set-theoretic defining equations for a much larger set of secant varieties, including s_{4}(IP^3 x IP^3 x IP^3) which is of particular interest in light of the salmon prize offered by E. Allman for the ideal-theoretic defining equations. Our equations are in lower degree than Friedland's March 2010 solution to the set-theoretic problem, and thus can be seen as a starting point for the ideal-theoretic problem. I will describe our polynomials and some of their symmetry. Then I will outline our geometric argument. Finally I will discuss the results from Bertini which solve the set-theoretic problem. |