多维整数三角学

Q3 Mathematics

Communications in Mathematics Pub Date : 2023-02-06 DOI:10.46298/cm.10919

J. Blackman, James Dolan, O. Karpenkov

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引用次数: 2

摘要

本文致力于介绍多维积分三角法。我们从2008年引入的二维整数三角函数的阐述开始，并用它将这些整数三角函数推广到任意维度。然后我们继续研究整数三角函数的基本性质。我们找到了转置和相邻单形锥以及生成相同单形的锥的整数三角关系。此外，我们还讨论了整数三角法、欧几里得算法和连续分数之间的关系。最后，我们使用相邻锥和转置锥引入了单锥最佳逼近的概念。在二维中，这种最佳近似的概念与实数的最佳近似的经典概念一致。

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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Multidimensional integer trigonometry

This paper is dedicated to providing an introduction into multidimensional integer trigonometry. We start with an exposition of integer trigonometry in two dimensions, which was introduced in 2008, and use this to generalise these integer trigonometric functions to arbitrary dimension. We then move on to study the basic properties of integer trigonometric functions. We find integer trigonometric relations for transpose and adjacent simplicial cones, and for the cones which generate the same simplices. Additionally, we discuss the relationship between integer trigonometry, the Euclidean algorithm, and continued fractions. Finally, we use adjacent and transpose cones to introduce a notion of best approximations of simplicial cones. In two dimensions, this notion of best approximation coincides with the classical notion of the best approximations of real numbers.

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来源期刊

Communications in Mathematics Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

45 weeks

期刊介绍： Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.