README

sdp.py is a python script intended to study the nodal structure of
quintic spectrahedra.  Spectrahedra are the feasible set of
semidefinite programs, a broad category to which many types of convex
optimization problems can be reduced.  Because optimal values are
often nodes, understanding their properties can provide useful
information on the likely results of these optimization problems.

The main script, sdp.py, is intended to generate random spectrahedra,
compute the positions of nodes, and run a large number of optimization
problems with random linear objectives, correlating the results with
the locations of nodes.  Other included python scripts are various
ways of driving this code and processing the results.

While the goal is to write the code in a manner compatible with
Python3, it is currently only compatible with Python2.7, due to the
requirements of cvxpy.

Requirements:

* Singular: http://www.singular.uni-kl.de/
* Macaulay2: http://www.math.uiuc.edu/Macaulay2/
* Bertini: https://bertini.nd.edu/
* cvxpy: https://github.com/cvxgrp/cvxpy/
* numpy and scipy: http://scipy.org/