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 subject.