The package
NumericalAlgebraicGeometry, also known as
NAG4M2 (Numerical Algebraic Geometry for Macaulay2), implements methods of polynomial homotopy continuation to solve systems of polynomial equations and describe positive-dimensional complex algebraic varieties.
Basic types (such as Point and WitnessSet) are defined in the package NAGtypes.
Basic functions:
Some of the basic computations can be outsourced to
Bertini and
PHCpack (look for
Software option).
Service functions:
Functions related to scheme analysis:
- isPointEmbedded -- determine if the point is an embedded component of the scheme
- isPointEmbeddedInCurve -- determine if the point is an embedded component of a 1-dimensional scheme
- colon -- colon of a (truncated) dual space
Functions related to Certified tracking:
References:
- A.J. Sommese, J. Verschelde, and C.W. Wampler, "Introduction to numerical algebraic geometry", in "Solving polynomial equations" (2005), 301--338
- A.J. Sommese and C.W. Wampler, "The numerical solution of systems of polynomials", World Scientific Publishing (2005)
- C. Beltran and A. Leykin, "Certified numerical homotopy tracking", Experimental Mathematics 21(1): 69-83 (2012)
- R. Krone and A. Leykin, "Numerical algorithms for detecting embedded components.", arXiv:1405.7871