通过热带几何学论单自由度平面连杆的属概念

arXiv - MATH - Metric Geometry Pub Date : 2024-08-01 DOI:arxiv-2408.00449

Josef Schicho, Ayush Kumar Tewari, Audie Warren

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引用次数: 0

摘要

本文主要研究在$\mathbb C^2$中实现的图的配置空间，这样的配置空间在归一化之后是一维的。如果是这种情况，那么一般来说，配置空间是一条光滑的复曲线，可以看作是黎曼曲面。本文感兴趣的属性是这条曲线的属。利用热带几何，我们给出了计算该属的算法。我们提供了一个 Python 实现，并给出了各种示例。

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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On the Genus of One Degree of Freedom Planar Linkages via Tropical Geometry

This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a smooth complex curve, and can be seen as a Riemann surface. The property of interest in this paper is the genus of this curve. Using tropical geometry, we give an algorithm to compute this genus. We provide an implementation in Python and give various examples.

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arXiv - MATH - Metric Geometry

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