Numerically intersecting algebraic varieties via witness sets

@article{Hauenstein2013NumericallyIA,
title={Numerically intersecting algebraic varieties via witness sets},
author={Jonathan D. Hauenstein and Charles W. Wampler},
journal={Applied Mathematics and Computation},
year={2013},
volume={219},
pages={5730-5742}
}

The fundamental construct of numerical algebraic geometry is the representation of an irreducible algebraic set, A, by a witness set, which consists of a polynomial system, F , for which A is an irreducible component of V(F ), a generic linear space L of complementary dimension to A, and a numerical approximation to the set of witness points, L ∩A. Given F , methods exist for computing a numerical irreducible decomposition, which consists of a collection of witness sets, one for each… CONTINUE READING