A new symbolic-numerical local dimension test.
One of the sticky problems in numerical algebraic geometry over the years has been determining the local dimension of a solution p of a polynomial system F. The local dimension is just the maximum dimension of the irreducible components on which p sits. This new is a hybrid symbolic-numerical method that detects the dimension of _all_ components containing p by computing ranks of various matrices (formed from taking higher and higher partial derivatives of the system, more or less).

This is joint work with J. Hauenstein, C. Peterson, and A. Sommese.