Numerical Software to Compute Newton polytopes and Tropical Membership
Numerical Software to Compute Newton polytopes and Tropical Membership
复制标题
计算牛顿多面体和热带隶属度的数值软件
DOI：
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发表时间：
2018
期刊：
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通讯作者：
Taylor Brysiewicz
中科院分区：
文献类型：
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作者：
Taylor Brysiewicz
我们提出了一种算法的实现，该算法充当超曲面牛顿多面体的数值预言机。此外，我们基于 Hept 和 Theobald 的想法提出了一种算法，该算法可作为更高维维品种的热带隶属度测试。这种热带隶属度算法依赖于数值预言机，我们分析了一些涉及的收敛速度。我们的实现被编写为名为 NumericalNP.m2 的Macaulay2 包。为了展示这个包，我们研究了来自代数视觉的超曲面和 Lüroth 不变量的牛顿多面体。
We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface. Additionally, we propose an algorithm which functions as a tropical membership test for higher codimension varieties based on ideas from Hept and Theobald. This tropical membership algorithm relies on a numerical oracle and we analyze some of the convergence rates involved. Our implementation is written as a Macaulay2 package called NumericalNP.m2. To showcase this package, we investigate the Newton polytope of both a hypersurface coming from algebraic vision and the Lüroth invariant.