论文标题
稀疏的痕量测试
Sparse trace tests
论文作者
论文摘要
我们确定稀疏多项式系统的系数如何影响其零的总和（或轨迹）。作为应用程序，我们开发了数值测试，以验证稀疏系统的一组解决方案是否完成。这些算法以数值代数几何形状扩展了经典的痕量测试。我们的结果既取决于稀疏产生剂的结构的分析，又取决于埃斯特罗夫（Esterov）对稀疏系统单组的结果的扩展。
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a set of solutions to a sparse system is complete. These algorithms extend the classical trace test in numerical algebraic geometry. Our results rely on both the analysis of the structure of sparse resultants as well as an extension of Esterov's results on monodromy groups of sparse systems.
