Numerical algebraic geometry. (English) Zbl 1311.14057

Leykin, Anton

J. Softw. Algebra Geom. 3, 5-10 (2011).

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

Software:

Macaulay2; NumericalAlgebraicGeometry