**Numerical Irreducible Decomposition**

** using PHCpack **

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

#### Abstract:

Homotopy continuation methods have proven to be reliable and
efficient to approximate all isolated solutions of polynomial systems.
In this paper we show how we can use this capability as a blackbox device
to solve systems which have positive dimensional components of solutions.
We indicate how the software package PHCpack can be used in conjunction
with Maple and programs written in C.
We describe a numerically stable algorithm for decomposing positive
dimensional solution sets of polynomial systems into irreducible components.
**2000 Mathematics Subject Classification:**
Primary 65H10; Secondary 13P05, 14Q99, 68N30, 68W30.

**keywords:**
homotopy continuation, interfaces,
numerical algebraic geometry, polynomial system, software.

In *Algebra, Geometry and Software Systems*,
edited by M. Joswig and N. Takayama, pages 109-130, Springer-Verlag 2003.