  In [GT], Goldin and the second author extend some ideas from Schubert
calculus to the more general setting of Hamiltonian torus actions on compact
symplectic manifolds with isolated fixed points. (See also [Kn99] and [Kn08].)
The main goal of this paper is to build on this work by finding more effective
formulas. More explicitly, given a generic component of the moment map, they
define a canonical class $\alpha_p$ in the equivariant cohomology of the
manifold $M$ for each fixed point $p \in M$. 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. It
is a long standing problem in combinatorics to find positive integral formulas
for the equivariant structure constants associated to this basis. Since
computing the restriction of the canonical classes to the fixed points
determines these structure constants, it is important to find effective
formulas for these restrictions. In this paper, we introduce new techniques for
calculating the restrictions of a canonical class $\alpha_p$ to a fixed point
$q$. Our formulas are nearly always simpler, in the sense that they count the
contributions over fewer paths. Moreover, our formula is manifestly positive
and integral in certain important special cases.
