################################################## /**

•                                                         *

• scabble - interactive 3d scl ball explorer *
• Copyright Danny Calegari and *
• Alden Walker 2010 *
• Uses code from exlp by Masashi Kiyomi *
• and calls glpk and gmp by the GNU project *
• Released under the GPL license *
• • **/ ##################################################

Current version: 1.0 -- February 3, 2011

Theory:

See Chapter 4 of:

Danny Calegari, scl, MSJ Memoirs 20. Mathematical Society of Japan, Tokyo, 2009

Installation:

Just type "make". You will need gmp, gtk, gtkglext, and opengl. If you're using linux or fink, you can probably just install the packages for these things using the default settings, and everything should work.

Usage:

Try the following: Note there are some chains provided by default

• press "run"
• after a few seconds, press "pause"
• press "step" a bunch of times
• enter something like "0.2" in the tolerance box
• press "run" and wait for it to finish
• delete the tolerance and press "run" again

License:

scabble3d is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

scabble3d is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with scallop. If not, see http://www.gnu.org/licenses/.

Because scabble uses the same strategy to compute scl as scallop, the same comments on rigor are appropriate (and the same fix applicable):

Rigour:

The algorithm that scallop uses to compute scl is rigorous for (finite linear combinations of) (cyclically) alternating words: those where a generator never appears twice (or more) in a row. Hence: abAB is alternating, aaab is not, a is not.

For nonalternating input, scallop rigorously computes upper bounds on scl. Moreover, the output is "statistically" correct on most input, especially if the value of scl is small.