Linear recurrence operators in characteristic $p$ are classified by their $p$-curvature. For a recurrence operator $L$, denote by $\chi(L)$ the characteristic polynomial of its $p$-curvature. We can obtain information about the factorization of $L$ by factoring $\chi(L)$. The main theorem of this paper gives an unexpected relation between $\chi(L)$ and the true singularities of $L$. An application is to speed up a fast algorithm for computing $\chi(L)$ by desingularizing $L$ first. Another contribution of this paper is faster desingularization.
翻译:以美元为特质的线性重现操作员按美元-曲率分类。对于重现操作员,用美元/美元(L)表示其美元-曲率的特性多元值。我们可以通过乘以美元/chi(L)来获得关于美元乘数的信息。本文的主要理论提供了美元/chi(L)美元与真正奇数(L美元)之间的意外关系。一个应用是先用美元/chi(L)来加速计算美元/奇(L)的快速算法,先用美元去配值。本文的另一个贡献是更快的脱值。