An open problem from symbolic-numeric computation asks to decide whether there exists in the neighborhood of a given multivariate polynomial a factorizable polynomial with complex coefficients. In a related problem we compute of a polynomial system with approximate complex coefficients the decomposition of its solution set into irreducible components of various dimensions and degrees. We will discuss how symbolic information - polynomial equations describing the irreducible solution components - is generated from numerical data. This is joint work with Andrew Sommese and Charles Wampler.
UIC MSCS Department Colloquium, 2 April 2001.