使用复嵌入时改进数域上多项式根的计算

Journal of Computational Algebra Pub Date : 2024-10-21 DOI:10.1016/j.jaca.2024.100026

Andrea Lesavourey , Thomas Plantard , Willy Susilo

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引用次数: 0

摘要

我们探索了一种相当通用的方法，通过复嵌入计算数域上多项式的根。我们的主要贡献在于展示了如何利用相对扩展结构在子字段中解码。此外，我们还介绍了几种启发式方案，以提高实际效率。我们提供了实现过程中的实验数据，并将我们的方法与在 Pari/Gp 中实现的最先进算法进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Improved computation of polynomial roots over number fields when using complex embeddings

We explore a fairly generic method to compute roots of polynomials over number fields through complex embeddings. Our main contribution is to show how to use a structure of a relative extension to decode in a subfield. Additionally we describe several heuristic options to improve practical efficiency. We provide experimental data from our implementation and compare our methods to the state of the art algorithm implemented in Pari/Gp.

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Journal of Computational Algebra

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