  We calculate the ground states of a dipolar Bose gas confined in an infinite
tube potential. We use the extended Gross-Pitaevskii equation theory and
present a novel numerical method to efficiently obtain solutions. A key feature
of this method is an analytic result for a truncated dipole-dipole interaction
potential that enables the long-ranged interactions to be accurately evaluated
within a unit cell. Our focus is on the transition of the ground state to a
crystal driven by dipole-dipole interactions as the short ranged interaction
strength is varied. We find that the transition is continuous or discontinuous
depending upon average system density. These results give deeper insight into
the supersolid phase transition observed in recent experiments, and validate
the utility of the reduced three-dimensional theory developed in [Phys. Rev.
Res. 2, 043318 (2020)] for making qualitatively accurate predictions.
