  Let $G$ be a compact connected Lie group and $T$ be its maximal torus. The
homogeneous space $G/T$ is called the (complete) flag manifold. One of the main
goals of the {\em equivariant Schubert calculus} is to study the
$T$-equivariant cohomology $H^*_T(G/T)$ with regard to the $T$-action on $G/T$
by multiplication. There are three presentations known for $H^*_T(G/T)$; (1)
the free $H^*(BT)$-module generated by the Schubert varieties (2) (with the
rational coefficients) the {\em double coinvariant ring} of the Weyl group (3)
the {\em GKM ring} associated to the Hasse graph of the Weyl group. Each
presentation has both advantages and disadvantages. In this paper, we describe
how to convert an element in one presentation to another by giving an explicit
algorithm, which can then be used to compute the equivariant structure
constants for the product of Schubert classes. The algorithm is implemented in
Maple.
