Computation of Milnor numbers and critical values at infinity

We describe how to compute topological objects associated to a polynomial map of several complex variables with isolated singularities. These objects are the affine critical values, the affine Milnor numbers for all irregular fibers, the critical values at infinity, and the Milnor numbers at infinity for all irregular fibers. Then for a family of polynomials we detect parameters where the topology of the polynomials can change. Implementation and examples are given with the computer algebra system SINGULAR .