These files take care of the positive dominance
tests used in the proofs of the Symmetrization
Lemma 1 and the Symmetrization Lemma 2.
You compile the code with the command javac *.java
and you run the code with the command java Main.
The program has documentation which explains how
to run the tests.  The tests take about 3 minutes
all together.

There are 3 auxiliary subdirectories:

ZDebug:  This contains mathematica files which also
construct the polynomials used in the tests.  One
can print out the polynomials used in the java program
and see that, one by one, they match the polynomials
created by the more transparent Mathematica code.

ZExperiment: This lets you numerically test
what the symmetrization operation(s) do to randomly
chosen configurations in the domain(s) of interest.
You can also customize the domains to do your
own experimenting.  This program is not part of
the formal proof, but I used it to find the
right statements for what I was trying to prove.

ZPure: This directory contains just the code which goes into
the tests, with all the graphical interface stripped off.
These files are much easier to inspect.