Let $\mathbb{K}$ be a fixed effective field. The most straightforward approach to compute with an element in the algebraic closure of $\mathbb{K}$ is to compute modulo its minimal polynomial. The determination of a minimal polynomial from an arbitrary annihilator requires an algorithm for polynomial factorization over $\mathbb{K}$. Unfortunately, such algorithms do not exist over generic effective fields. They do exist over fields that are explicitly generated over their prime sub-field, but they are often expensive. The dynamic evaluation paradigm, introduced by Duval and collaborators in the eighties, offers an alternative algorithmic solution for computations in the algebraic closure of $\mathbb{K}$. This approach does not require an algorithm for polynomial factorization, but it still suffers from a non-trivial overhead due to suboptimal recomputations. For the first time, we design another paradigm, called directed evaluation, which combines the conceptual advantages of dynamic evaluation with a good worst case complexity bound.

让 $\mathbb{ķ}$成为固定的有效领域。使用元素的代数闭包进行计算的最直接方法$\mathbb{ķ}$是对它的最小多项式取模。从任意an灭器确定最小多项式需要一个用于多项式因式分解的算法$\mathbb{ķ}$。不幸的是，这种算法在通用有效域上并不存在。它们确实存在于在其主要子字段上显式生成的字段上，但是它们通常很昂贵。由Duval和合作者在80年代提出的动态评估范式，为计算代数闭包提供了一种替代算法解决方案。$\mathbb{ķ}$。这种方法不需要用于多项式因式分解的算法，但是由于次优的重新计算，它仍然遭受不小的开销。首次，我们设计了另一个范式，称为定向评估，将动态评估的概念优势与良好的最坏情况复杂度界限相结合。