topoaccel: maxima scripts for evaluating topological acceleration

Copyright (C) 2009, 2021, 2022 Boud Roukema, GPL-2+ Copyright (C) 2021, 2022 Quentin Vigneron, GPL-2+

Scroll to the bottom for a GPL-2+ guideline.

As of December 2021, these scripts calculate topological acceleration for several of the S^3 quotient spaces that we call 'regular', in that they have a Platonic solid as one of their fundamental domain shapes, and are globally homogeneous. See Vigneron & Roukema, ArXiv:2201.09102 for details.

Testing

• 20 Jan 2022 - scripts run correctly in ten seconds or so with Maxima-5.44.0-3 and GNU Common Lisp 2.6.12.

How to run the files

Example command lines to run these Maxima scripts in a Unix-like shell:

maxima -b main_max_Mass.m

maxima < main_max_Mass.m

maxima < main_max_Mass.m > logfile

Computer algebra resources

• Maxima
  • https://tracker.debian.org/pkg/maxima
  • https://maxima.sourceforge.io/documentation.html
• SageMath
  • https://en.wikipedia.org/wiki/SageMath
• learn about shell redirection - the < and > symbols
  • https://en.wikipedia.org/wiki/Redirection_%28computing%29

TODO:

• Maxima needs help to learn how to handle sqrt{5} expressions from cos() and sin() of angles appropriate for the dodecahedral symmetries. The maxima library 'ntrig' would appear to be what is needed, but the scripts currently are not able to use this to simplify formulae enough. The current hack is to force numerical evaluation of square roots before the main Taylor series expansions, and also after the calculations. Please create a git branch and propose a merge if you find a solution.

• fixes for older/newer versions of maxima

• general tidying

Copyright

This program 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 2, or (at your option) any later version.

This program 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 this program; if not, see: http://www.gnu.org/licenses/gpl.html