稀疏迹测试

摘要：

我们建立了稀疏多项式系统的系数如何影响其零点的和（或迹）。作为一个应用程序，我们开发的数值测试验证是否一组解决方案的稀疏系统是完整的。这些算法扩展了数值代数几何中的经典迹检验。我们的研究结果依赖于稀疏结式的结构分析，以及扩展的Esterov的结果单值组的稀疏系统。

英文摘要：

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.

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