The NumericalCertification package in Macaulay2

The package $\mathtt{\text{NumericalCertification}}$ implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale’s $\alpha$-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 $\mathtt{\text{Macaulay2}}$.