We design a fast algorithm that computes, for a given linear differential operator with coefficients in $Z[x ]$, all the characteristic polynomials of its p-curvatures, for all primes $p < N$ , in asymptotically quasi-linear bit complexity in N. We discuss implementations and applications of our algorithm. We shall see in particular that the good performances of our algorithm are quickly visible.

翻译：我们设计了一个快速算法,用来计算一个具有Z[x]美元系数的给定线性差操作员,计算其曲线特性中所有典型的多数值,计算所有质素,计算出美元 < N$,在N.,我们讨论算法的实施和应用。我们特别可以看到,我们算法的良好性能很快可见。