  We numerically evaluate the density distribution of a spin-1 bosonic
condensate in its ground state within a modifed Gross-Pitaevskii theory, which
is obtained by the combination of the exact solution of the corresponding
integrable model with the local density approximation. Our study reveals that
atoms in the m_F = 0 state are almost completely suppressed for the
anti-ferromagnetic interactions in both weakly and strongly interacting
regimes, whereas all three components remain non-vanishing for ferromagnetic
interactions. Specially, when the system is in the Tonks-Girardeau (TG) regime,
obvious Fermi-like distribution emerges for each component. We also discuss the
possible deviation of the spatial distribution from the Fermi-like distribution
when the spin-spin interaction is strong enough.
