Using Numerical Insights to Improve Symbolic Computations

Numerical algebraic geometry provides a toolbox of numerical methods for performing computations involving systems of polynomial equations. Even though some of the computations which are performed on a computer using floating-point arithmetic are not certified, they can often be made very reliable using adaptive precision computations. Moreover, there is a wealth of information regarding the original problem which can be extracted from various numerical computation that can be used to improve subsequent symbolic computations to certify the result. This paper highlights two applications of such hybrid numeric-symbolic methods in algebraic geometry.

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