# The NumericalCertification package in Macaulay2

@article{Lee2022TheNP, title={The NumericalCertification package in Macaulay2}, author={Kisun Lee}, journal={ArXiv}, year={2022}, volume={abs/2208.01784} }

The package 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 Macaulay2 .

## 2 Citations

### Homotopy techniques for analytic combinatorics in several variables

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We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the asymptotics of…

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