  We give an algorithm to compute representatives of the conjugacy classes of
semisimple square integral matrices with given minimal and characteristic
polynomials. We also give an algorithm to compute the
$\mathbb{F}_q$-isomorphism classes of abelian varieties over a finite field
$\mathbb{F}_q$ which belong to an isogeny class determined by a characteristic
polynomial $h$ of Frobenius when $h$ is ordinary, or $q$ is prime and $h$ has
no real roots.
