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.