Solving Systems of Polynomial Equations via Multidimensional p-adic Newton iteration

Mark Watkins (Penn State)

Thursday, January 15, 2004, in K9509 at 4pm.

The most common methods to solve systems of polynomial equations are
(multi)resultants and Groebner bases. Both of these quickly become tedious.
Solving systems of equations can be done with a multidimensional Newton
method, though the region of convergence is poor, partially due to the
norm. I shall describe how to find rational and algebraic solutions to
polynomial systems using p-adic techniques, and explain a few motivating
problems (suggested by Noam Elkies) that led to my investigation of this