  An analytical expression for the lower bound of the average number of
hyperfine component $\mu =0$ particles in the ground state of spin-1
condensates (denoted as $\overset{\_\_}{\rho _{0}}$) under a magnetic field has
been derived. In the derivation the total magnetization $M$ is kept rigorously
conserved. Numerical examples are given to show the applicability of the
analytical expression. It was found that, in a broad domain of parameters
specified in the paper, the lower bound is very close to the actual
$\overset{\_\_}{\rho _{0}}$. Thereby, in this domain, $\overset{\_\_}{% \rho
_{0}}$ can be directly evaluated simply by using the analytical expression.
