  We apply to the $CP^9$ model two recently proposed numerical techniques for
simulation of systems with a theta term. The algorithms, successfully tested in
the strong coupling limit, are applied to the weak coupling region. The results
agree and errors have been evaluated and are at % level. The results scale well
with the renormalization group equation and show that, for $CP^9$ in presence
of a theta term, CP symmetry is spontaneously broken at $\theta=\pi$ in the
continuum limit.
