Nowadays, asymptotically fast algorithms are widely used in computer algebra for computations in towers of algebraic field extensions of small height. Yet it is still unknown how to reach softly linear time for products and inversions in towers of arbitrary height. In this paper we design the first algorithm for general ground fields with a complexity exponent that can be made arbitrarily close to one from the asymptotic point of view. We deduce new faster algorithms for changes of tower representations, including the computation of primitive element representations in subquadratic time.

中文翻译：

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加速塔算术

如今，渐近快速算法已广泛用于计算机代数中，用于计算小高度的代数场扩展的塔。然而，如何达到任意高度的塔中的乘积和反演的软线性时间仍然未知。在本文中，我们设计了第一个具有复杂度指数的通用地面场算法，该算法可以从渐近的角度任意接近一个。我们推导了新的更快的塔表示更改算法，包括在二次时间内计算原始元素表示。