**Is the attained solution isolated?**

*T.Y. Li
(Michigan State University)*
#### Abstract:

A numerical solution of a polynomial system is normally classified
as an isolated nonsingular solution if its Jacobian does not allow
very small singular values. However, when the Jacobian does have very
small singular values, the solution could still be isolated with a
multiple multiplicity or may belong to a solution component with
positive dimension. An algorithm is proposed
to differentiate those cases.