  We give a comprehensive introduction into a diagrammatic method that allows
for the evaluation of Gutzwiller wave functions in finite spatial dimensions.
We discuss in detail some numerical schemes that turned out to be useful in the
real-space evaluation of the diagrams. The method is applied to the problem of
d-wave superconductivity in a two-dimensional single-band Hubbard model. Here,
we discuss in particular the role of long-range contributions in our
diagrammatic expansion. We further reconsider our previous analysis on the
kinetic energy gain in the superconducting state.
