** Using Monodromy to Decompose Solution Sets of **

** Polynomial Systems into Irreducible Components **

*Andrew J. Sommese*,
*Jan Verschelde*, and
*Charles W. Wampler*

#### Abstract:

To decompose solution sets of polynomial systems
into irreducible components, homotopy continuation methods
generate the action of a natural monodromy group which partially classifies
generic points onto their respective irreducible components.
As illustrated by the performance on several test
examples, this new method achieves a great increase in
speed and accuracy, as well as
improved numerical conditioning of the multivariate interpolation
problem.
**2000 Mathematics Subject Classification :**
Primary 65H10; Secondary 13P05, 14Q99, 68W30.

**keywords :**
Components of solutions,
embedding, generic points, homotopy continuation, irreducible components,
monodromy group,
numerical algebraic geometry, polynomial system, primary decomposition.

In *Application of Algebraic Geometry to Coding Theory, Physics,
and Computation*,
edited by C. Ciliberto, F. Hirzebruch, R. Miranda, and M. Teicher.
Proceedings of a NATO Conference, February 25 - March 1, 2001, Eilat,
Israel. Pages 297-315, Kluwer Academic Publishers.