Numerical Irreducible Decomposition Using PHCpack

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. Key words and phrases. homotopy continuation, interfaces, numerical algebraic geometry, polynomial system, software.

• Type: Conference
• Year: 2003
• Where: DAGSTUHL
• Authors: Andrew J. Sommese, Jan Verschelde, Charles W. Wampler
• Keywords: DAGSTUHL 2003, DAGSTUHL 2007, Homotopy Continuation, Homotopy Continuation Methods, Polynomial System