Hybrid numerical/symbolical algorithms for algebraic geometry
Adrian Koch (kocha at rhrk.uni-kl.de)
In this library you'll find implementations of some of the algorithms presented
in the paper listed below: Bertini is used to compute a witness set of a given
ideal I. Then a lattice basis reduction algorithm is used to recover exact
results from the inexact numerical data. More precisely, we obtain elements
of prime components of I, the radical of I, or an elimination ideal of I.
NOTE that Bertini may create quite a lot of files in the current directory
(or overwrite files which have the same names as the files it wants to create).
It also prints information to the screen.
The usefulness of the results of the exactness recovery algorithms heavily
depends on the quality of the witness set and the quality of the lattice basis
The procedures requiring a witness set as part of their input use a simple,
unsofisticated version of the LLL algorithm.
Daniel Bates, Jonathan Hauenstein, Timothy McCoy, Chris Peterson, and Andrew Sommese;
Recovering exact results from inexact numerical data in algebraic geometry;
Published in Experimental Mathematics 22(1) on pages 38-50 in 2013