Hilbert series of symplectic quotients by the 2-torus.

We compute the Hilbert series of the graded algebra of real regular functions on a linear symplectic quotient by the 2-torus as well as the first four coefficients of the Laurent expansion of this Hilbert series at t = 1 . We describe an algorithm to compute the Hilbert series as well as the Laurent coefficients in explicit examples. [ABSTRACT FROM AUTHOR]