Using monodromy to decompose solution sets of polynomial systems into irreducible components. (English) Zbl 0990.65051

Ciliberto, Ciro (ed.) et al., Applications of algebraic geometry to coding theory, physics and computation. Proceedings of the NATO advanced research workshop, Eilat, Israel, February 25-March 1, 2001. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 36, 297-315 (2001).
Summary: 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 text examples, this new method achieves a great increase in speed and accuracy, as well as improved numerical conditioning of the multivariate interpolation problem.
For the entire collection see [Zbl 0971.00013].


65H10 Numerical computation of solutions to systems of equations
13P05 Polynomials, factorization in commutative rings
14Q99 Computational aspects in algebraic geometry
68W30 Symbolic computation and algebraic computation