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