Alternative Ways of Solving Polynomial Systems

Ilias Kotsireas

We present some ways to solve polynomial systems using differential elimination
algorithms (e.g. RIF) and the notion of normal set which arises in the
interpretation of polynomial system solving as a matrix eigenproblem.  These
ideas apply to zero-dimensional systems, as well as to systems with
parameters.  These ideas are illustrated with two zero-dimensional polynomial
systems that arise in the study of central configurations in the N-body problem
of Celestial Mechanics and an inverse kinematics example from Robotics.  The
computations have been performed in Maple 6.  This is joint work with Greg
Reid. The normal set notion we use is borrowed from an article by Rob Corless.