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 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模的自同态特征多项式及同源范数。这些算法适用于定义在任意基曲线上的任意秩的Drinfeld模。当基曲线为$\mathbb P^1_{\mathbb F_q}$时，我们对其复杂度进行了详尽研究，证明我们的算法在许多情况下具有渐近最优性能。第一类算法基于Drinfeld模与Anderson motive之间的对应关系，将计算归结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，基于将Frobenius特征多项式表示为中心单代数中约化范数的公式。