Abstract Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called “ amplituhedronBoundaries ” for calculating the boundary structures of three positive geometries: the amplituhedron, the momentum amplituhedron and the hypersimplex. The first two geometries are relevant for scattering amplitudes in planar N = 4 supersymmetric Yang–Mills theory, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to the m = 2 momentum amplituhedron. The package includes an array of useful tools for the study of these positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians. Program summary Program title: amplituhedronBoundaries CPC Library link to program files: http://dx.doi.org/10.17632/fhcnzn3z96.1 Developer’s repository link: https://github.com/mrmrob003/amplituhedronBoundaries Licensing provisions: GNU General Public License 3 Programming language: Wolfram Mathematica 11.0 Nature of problem: The package facilitates the determination and study of the boundary stratifications for three positive geometries: the amplituhedron, the momentum amplituhedron, and the hypersimplex. The first two geometries are relevant for scattering amplitudes in planar N = 4 sYM, while the last one is a well-studied polytope appearing in many important contexts in mathematics. Solution method: The package includes an array of useful tools for exploring the three aforementioned positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians. Restrictions: Wolfram Mathematica 11.0 or above

中文翻译：

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与 amplituhedronBoundaries 的 amplituhedron 的边界

摘要 正几何为计算各种物理模型中的散射幅度提供了一种现代方法。为了便于探索这些新的几何方法，我们引入了一个名为“amplituhedronBoundaries”的 Mathematica 包，用于计算三个正几何的边界结构：amplituhedron、momentum amplituhedron 和 hypersimplex。前两个几何与平面 N = 4 超对称杨-米尔斯理论中的散射幅度相关，而最后一个几何是在数学中的许多上下文中出现的经过充分研究的多面体，并且与 m = 2 动量幅面体密切相关。该软件包包括一系列用于研究这些正几何的有用工具，包括它们的边界分层、绘制它们的边界偏序、以及用于操纵对正 Grassmannians 有用的组合结构的其他工具。程序摘要 程序名称：amplituhedronBoundaries CPC 库程序文件链接：http://dx.doi.org/10.17632/fhcnzn3z96.1 开发者存储库链接：https://github.com/mrmrob003/amplituhedronBoundaries 许可条款：GNU General Public License 3 编程语言：Wolfram Mathematica 11.0 问题性质：该包有助于确定和研究三个正几何体的边界分层：幅度面体、动量幅度面体和超单纯形。前两个几何形状与平面 N = 4 sYM 中的散射幅度有关，而最后一个几何形状是在数学中的许多重要环境中出现的经过充分研究的多面体。解决方法：该软件包包括一系列用于探索上述三种正几何的有用工具，包括它们的边界分层、绘制它们的边界偏序，以及用于操纵对正 Grassmannians 有用的组合结构的其他工具。限制条件：Wolfram Mathematica 11.0 或更高版本