We provide two families of algorithms to compute characteristic polynomials of endomorphisms and norms of isogenies of Drinfeld modules. Our algorithms work for Drinfeld modules of any rank, defined over any base curve. When the base curve is $\mathbb P^1_{\mathbb F_q}$, we do a thorough study of the complexity, demonstrating that our algorithms are, in many cases, the most asymptotically performant. The first family of algorithms relies on the correspondence between Drinfeld modules and Anderson motives, reducing the computation to linear algebra over a polynomial ring. The second family, available only for the Frobenius endomorphism, is based on a new formula expressing the characteristic polynomial of the Frobenius as a reduced norm in a central simple algebra.

翻译：我们提出了两类算法，用于计算Drinfeld模自同态的特征多项式以及同源映射的范数。这些算法适用于任意秩的Drinfeld模，且可定义于任意基曲线上。当基曲线为$\mathbb P^1_{\mathbb F_q}$时，我们进行了充分的复杂度分析，证明这些算法在多数情形下具有渐近最优性能。第一类算法基于Drinfeld模与Anderson动机之间的对应关系，将计算归约为多项式环上的线性代数问题。第二类算法仅适用于Frobenius自同态，其核心是一个新公式：通过中心单代数中的约化范数来表达Frobenius特征多项式。