论文标题
牛顿多面体和数值代数几何形状
Newton polytopes and numerical algebraic geometry
论文作者
论文摘要
我们开发了数值算法的集合，这些算法将多面体几何形状和代数几何形状连接起来。我们开发的第一种算法是Hypersurface的牛顿多层人物的数值甲骨文，并基于Hauenstein和Sottile的思想。此外，我们构建了一种数值热带成员算法，该算法将前算法用作子例程。基于埃斯特罗夫（Esterov）的最新结果，我们给出了一种算法，当该系统的支持是脱落或三角形时，该算法递归解决了稀疏的多项式系统。在解释这些结果之前，我们提供了关于多面体，代数几何形状，分支覆盖物单组和数值代数几何形状的必要背景。
We develop a collection of numerical algorithms which connect ideas from polyhedral geometry and algebraic geometry. The first algorithm we develop functions as a numerical oracle for the Newton polytope of a hypersurface and is based on ideas of Hauenstein and Sottile. Additionally, we construct a numerical tropical membership algorithm which uses the former algorithm as a subroutine. Based on recent results of Esterov, we give an algorithm which recursively solves a sparse polynomial system when the support of that system is either lacunary or triangular. Prior to explaining these results, we give necessary background on polytopes, algebraic geometry, monodromy groups of branched covers, and numerical algebraic geometry.
