Numerical algorithms for detecting embedded components

Numerical algorithms for detecting embedded components and eliminating dual spaces

Robert Krone, Anton Leykin

Papers:

Numerical algorithms for detecting embedded components, arXiv:1405.7871, (with appendix by Jon Hauenstein).
Eliminating dual spaces, arXiv:1503.02038.

Code:

Examples for the paper:

example-cyclic4.m2
example-5lines-2planes.m2

These should work in future versions of Macaulay2.
At the moment (March 2015) to ensure that the examples run, one needs to have

Macaulay2 version 1.7 (current stable release),
source code fetched from github repository kroner/M2 (ect-eds branch):
git clone -b ect-eds https://github.com/kroner/M2.git
packages loading from the M2/Macaulay2/packages/ directory of the source code above.

Most functions in the file M2/Macaulay2/packages/NumericalAlgebraicGeometry/npd.m2 of the package NumericalAlgebraicGeometry were implemented specifically for this work. Several of these depend heavily on the NumericalHilbert package.