  We give algorithms to compute isomorphism classes of ordinary abelian
varieties defined over a finite field $\mathbb{F}_q$ whose characteristic
polynomial (of Frobenius) is square-free and of abelian varieties defined over
the prime field $\mathbb{F}_p$ whose characteristic polynomial is square-free
and does not have real roots. In the ordinary case we are also able to compute
the polarizations and the group of automorphisms (of the polarized variety)
and, when the polarization is principal, the period matrix.
