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.

中文翻译：

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计算有限域上的无平方极化阿贝尔变体

我们给出算法来计算定义在有限域 $\mathbb{F}_q$ 上的普通阿贝尔变体的同构类，其特征多项式（Frobenius 的）是无平方的，以及定义在素域 $\mathbb{F} 上的阿贝尔变体_p$ 的特征多项式是无平方的并且没有实数根。在普通情况下，我们还可以计算极化和自同构群（极化种类），以及当极化为主时，周期矩阵。