  The main purpose of this article is to extend some of the ideas from Schubert
calculus to the more general setting of Hamiltonian torus actions on compact
symplectic manifolds with isolated fixed points. Given a generic component of
the moment map, we define a canonical class \alpha_p in the equivariant
cohomology of the manifold M for each fixed point p of M. When they exist,
canonical classes form a natural basis of the equivariant cohomology of M; in
particular, when M is a flag variety, these classes are the equivariant
Schubert classes. We show that the restriction of a canonical class \alpha_p to
a fixed point q can be calculated by a rational function which depends only on
the value of the moment map, and the restriction of other canonical classes to
points of index exactly two higher. Therefore, the structure constants can be
calculated by a similar rational function. Our restriction formula is
manifestly positive in many cases, including when M is a flag manifold.
Finally, we prove the existence of integral canonical classes in the case that
M is a GKM manifold the moment map component is index increasing. In this case,
our restriction formula specializes to an easily computable rational sum which
depends only on the GKM graph.
