Macaulay2中的NumericalCertification包
The NumericalCertification package in Macaulay2
摘要：
软件包\texttt{NumericalCertification}实现了用于证明给定多项式方程系统的解的数值逼近的方法。为了证明正则解，该软件包实现了Smale的$α$理论和Krawczyk方法。对于一个奇异解，我们使用迭代收缩方法实现软验证。我们展示了该软件包的功能，重点是与当前的数值求解器在\texttt{Macaulay2}的互动。
英文摘要：
The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $α$-theory and Krawczyk method. For a singular solution, we implement soft verification using the iterative deflation method. We demonstrate the functionalities of the package focusing on interaction with current numerical solvers in \texttt{Macaulay2}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
