Click here to grab the Maple/Bertini implementation of our algorithms.

In the directory, you will find a relatively self-explanatory README file that explains how to run the code.

To make a long story short, we use Bertini to find approximations of generic points on algebraic sets, then use LLL (or PSLQ) applied to various Veronese embeddings of the points to find low-degree equations that vanish on each irreducible component. Applications in both the paper and the code include finding equations for secant varieties (or joins) and finding equations for the desingularization of a curve.