Dear sage developers,

some people, including myself, believe that Sage should contain more
tools for topology. E.g., there was a thread
http://groups.google.com/group/sage-devel/browse_thread/thread/5bd11c7e9fe08e4c/6ba64c41dd86770e?lnk=gst&q=simplicial+complexes#6ba64c41dd86770e
about simplicial complexes and their homology.

John Palmieri has sent a post to some algebraic topology list (https://
lists.lehigh.edu/mailman/listinfo/algtop-l), pointed the people to
Sage and asked for contribution. Thank you, John!

Being subscriber of that list, I added that one way to contribute is
to point us to existing software packages. So far, there was one
answer (concerning "plex", see below).

My question: How should the work on inclusion of topology software be
organized? Should one open a single trac ticket (essentially
complaining that there is not enough topology around), on which
suggestions for inclusions are collected? Or should the collection be
on this thread, with one separate ticket for each suggestion?

Here are three suggestions:
 1. Simplicial complexes / Homology (see thread above)
I asked Frank Lutz, and he said that Polymake had a module 'topaz'
that can compute homology. However, in a recent Polymake upgrade,
topaz was removed from the distribution, due to some compiler problem.
So, it might make sense to wait for on upgrade of topaz.

 2. SnapPea
SnapPea is a program for creating and studying hyperbolic 3-manifolds
(http://www.geometrygames.org/SnapPea-old/index.html). It seems to be
widely used by computational topologists. AFAIK it can deal with ideal
triangulations, compute volume, has a census of hyperbolic manifolds,
can also work with hyperbolic knots, etc.
If I understand correctly, it is under GNU GPL and may be used as a
Python module.

3. Plex (suggestion of Ryan Lewis from the above-mentioned topology
list)
Plex is a software package for computing persistent homology of finite
simplicial complexes, often generated from point cloud data (http://
comptop.stanford.edu/programs/jplex/index.html).

4. I found a link to a list of topology related software:
http://www.math.uiuc.edu/~nmd/computop/
Some of these might be interesting.

I am not sure if Plex really is an option for Sage. Previous versions
were written for Matlab. The current version is written in Java and
can also run in a standalone mode, using an integrated Java
interpreter, called Beanshell. Dunno if that works for Sage.

Cheers,
     Simon

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