Abstract

The foundation of algebraic geometry is the solving of systems of polynomial equations. When the equations to be considered are defined over a subfield of the complex numbers, numerical methods can be used to perform algebraic geometric computations forming the area of numerical algebraic geometry. This article provides a short introduction to numerical algebraic geometry with the subsequent articles in this special issue considering three current research topics: solving structured systems, certifying the results of numerical computations, and performing algebraic computations numerically via Macaulay dual spaces.

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