ELECTRON CHAMP
by Rich Schwartz
10 Jan 2010.

This program contains the code for the proof that the triangular
bi-pyramid is the energy minimizer for the Coulomb potential,
and also for the 1/r^2 potential.   Aside for the graphical
display, all the code for the proof is contained in the files
beginning with Interval.  The file Proof.java contains the main
algorithm.  

There are many things you can do with the interface, such
as manually move the electron configurations around on the
picture window.  However,  I will just explain how to get
to the proof.   Right now,  a rudimentary
"Program Documentation" window pops up, but this
documentation is far from being complete.
I hope to complete this documentation window in the
coming months.

******

Here is a step-by-step guide to running the proof
for the Coulomb potential.

1.  Compile the code using the command 

javac *.java

You need a Java compiler to run the code.

2. Run the program by typing 

java Main.

3. On the main control panel, use the arrow keys to set the
 confine diameter to 13.   Setting this parameter to k runs
the code until it eliminates all configurations that are more
than 2^{-k} from the triangular bi-pyramid, as discussed
in the paper.

4. On the "action" control panel, select the proof option.  This brings
up an auxilliary control panel.

5. The auxilliary control panel is initially set to run the program without
interval arithmetic.  Click the box near the words "interval arithmetic"
if you want to run the proof with interval arithmetic.

6. Push the green go button.  If you are not using the interval
arithmetic, go out and have lunch. The program will terminate
in about an hour.  If you are using interval arithmetic, go to dinner
and see a movie and then come back.  The code takes about 6
hours to run.

7.  At the bottom left of the control panel, there is a pair of
boxes that says "select energy".  This lets you select the exponent
for the power law.    Set this to 2/1 if you want to see the
1/r^2 potential.   If you use an exponent other than 1 or 2,
you cannot run the interval arithmetic.

8. The picture window shows a graphical display of the configurations
that are considered in the proof.   If you want to see these displayed
as the proof runs, turn on the "update proof" option.



