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Numerical algebraic geometry. (English) Zbl 1311.14057

Summary: Numerical algebraic geometry uses numerical data to describe algebraic varieties. It is based on numerical polynomial homotopy continuation, which is an alternative to the classical symbolic approaches of computational algebraic geometry. We present a package, whose primary purpose is to interlink the existing symbolic methods of Macaulay2 and the powerful engine of numerical approximate computations. The core procedures of the package exhibit performance competitive with the other homotopy continuation software.

MSC:

14Q99 Computational aspects in algebraic geometry
68N01 General topics in the theory of software
13P15 Solving polynomial systems; resultants
65D99 Numerical approximation and computational geometry (primarily algorithms)
65Y15 Packaged methods for numerical algorithms
68W30 Symbolic computation and algebraic computation
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