  We use a symmetry-constrained variational procedure to construct a
generalization of BCS to include Cooper pairs with non-zero momentum and
angular momentum. The resulting gap equations are solved at zero and finite
temperature, and the doping-dependent solutions are used to construct gap and
phase diagrams. We find a pseudogap terminating at a critical doping that may
be interpreted in terms of both competing order and preformed pairs. The strong
similarity between observation and predicted gap and phase structure suggests
that this approach may provide a unified description of the complex structure
observed for cuprate superconductors.
