Computations in intersection rings of flag bundles
  Intersection rings of flag varieties and of isotropic flag varieties are generated by Chern classes of the tautological bundles modulo the relations coming from multiplicativity of total Chern classes. In this paper we describe the Groebner bases of the ideals of relations and give applications to computation of intersections, as implemented in Macaulay2. 
Daniel R. Grayson, Alexandra Seceleanu, and Michael E. Stillman
math.AG math.AC