Generic Characteristic-Zero Equivalence Between Derivative Bézout Inversion and Multipoint Evaluation

Let $a_1,\ldots,a_m$ be distinct elements of a field $K$, and let $Z(X)=\prod_{i=1}^m (X-a_i)$. We study the arithmetic complexity of computing the unique normalized Bezout pair $s,t$ satisfying $sZ+tZ'=1$, with $°t<m$ and $°s<m-1$. The classical product-tree approach requires $O(M_K(m)\log m)$ fiel