KhovanskiiHomotopy

This repository contains Macaulay2 files for the examples appearing in "Numerical homotopies from Khovanskii bases"

The preprint of the paper is available at: https://arxiv.org/pdf/2008.13055.pdf

Examples 10 and 17 are motivated by a Bott-Samelson variety example given in Dave Anderson's 2012 paper.

Example 23 involves the algebra of planar cubics through four fixed points. This example is motivated by and example of Duff, Hein, and Sottile's 2018 preprint.

A word on the code:

All examples use the functions in Procedures.m2. This file loads the Macaulay2 packages NumericalAlgebraicGeometry, SubalgebraBases, Bertini, and PHCpack. Links for all of the packages is provided in Procedures.m2. The SubalgebraBases package - as of summer 2020 - is not published and is difficult to read and perhaps to install. Only Example 23 requires the SubalgebraBases package, however. This means the remaining examples can be run without necessitating the installation of SubalgebraBases.