  Homotopy continuation provides a numerical tool for computing the equivalence
of a smooth variety in an intersection product. Intersection theory provides a
theoretical tool for relating the equivalence of a smooth variety in an
intersection product to the degrees of the Chern classes of the variety. A
combination of these tools leads to a numerical method for computing the
degrees of Chern classes of smooth projective varieties in P^n. We illustrate
the approach through several worked examples.
