Abstract
We describe the design and relationships of several Macaulay2 packages that use numerical polynomial homotopy continuation as their engine. Macaulay2 is a computer algebra system built around the classical symbolic computation tools such as Grobner bases. However, recent Macaulay2 versions include its own fast implementation of homotopy continuation, interfaces to external numerical algebraic geometry software (Bertini and PHCpack), and a unified data structures design that allows the use of the internal and external capabilities interchangeably. The resulting numerical and hybrid tools are of general interest to Macaulay2 users interested in computational experimentation.
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