Schubert2 -- characteristic classes for varieties without equations
SegreClasses -- test containment of varieties and computes algebraic multiplicity of subvarieties and Fulton-MacPherson intersection products, via a very general Segre class computation
ToricInvariants -- Euclidean distance degrees, polar degrees, degree and codimension of the dual, and Chern-Mather classes of toric varieties X_A from the polytope conv(A) or from its Gale dual