  We describe a method of solving the nuclear Skyrme-Hartree-Fock problem by
using a deformed Cartesian harmonic oscillator basis. The complete list of
expressions required to calculate local densities, total energy, and
self-consistent fields is presented, and an implementation of the
self-consistent symmetries is discussed. Formulas to calculate matrix elements
in the Cartesian harmonic oscillator basis are derived for the nuclear and
Coulomb interactions.
