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Directed evaluation

机译：定向评估

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摘要

Let K be a fixed effective field. The most straightforward approach to compute with an element in the algebraic closure of 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 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 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. (C) 2020 Elsevier Inc. All rights reserved.
机译：让K成为一个固定的有效领域。用K的代数闭合中的元件计算的最直接的方法是计算模型其最小多项式。从任意anihilator确定最小多项式的多项式需要一种在K的多项式分解算法。不幸的是，这种算法不存在于通用有效领域。它们确实存在于在其主要子字段上明确生成的字段，但它们通常是昂贵的。八十年代中杜瓦尔和合作者引入的动态评估范例提供了一种替代算法解决方案的计算。该方法不需要用于多项式分子的算法，但它仍然存在非琐碎的开销到次优的重新计算。我们首次设计了另一个范式，称为定向评估，它将动态评估的概念优势与良好的最坏情况复杂合并。 （c）2020 Elsevier Inc.保留所有权利。

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