Exact calculation of the condensate fraction in multi-dimensional
inhomogeneous interacting Bose systems which do not possess continuous
symmetries is a difficult computational problem. We have developed an iterative
procedure which allows to calculate the condensate fraction as well as the
corresponding eigenfunction of the one-body density matrix. We successfully
validate this procedure in diffusion Monte Carlo simulations of a Bose gas in
an optical lattice at zero temperature. We also discuss relation between
different criteria used for testing coherence in cold Bose systems, such as
fraction of particles that are superfluid, condensed or are in the
zero-momentum state.Comment: 4 pages, 2 figure