  Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using
the variational ansatz for the generalized one-body density-matrix in the
Valatin form. It is shown that the projected-energy functional can be
completely expressed in terms of the HFB density-matrix and the pairing-tensor.
The variation of this projected-energy is shown to result in HFB equations with
modified expressions for the pairing-potential and the Hartree-Fock field. The
expressions for these quantities are explicitly derived for the case of
particle number-projection. The numerical applicability of this projection
method is studied in an exactly soluble model of a deformed single-j shell.
