---------- Forwarded message ---------- From: Dmitriy Morozov <dmit...@mrzv.org> Date: Thu, Feb 4, 2010 at 11:48 AM Subject: Re: [sage-devel] Rips complex in Sage? To: Mike Hansen <mhan...@gmail.com> Cc: sage-devel <sage-devel@googlegroups.com>
Excerpts from Mike Hansen's message of Thu Feb 04 14:24:54 -0500 2010: >On Thu, Feb 4, 2010 at 6:10 AM, Simon King <simon.k...@nuigalway.ie> wrote: >> Hi! >> >> At >> http://groups.google.com/group/sage-support/browse_thread/thread/edcd7dc0e8be9aa5 >> Eli posed a problem that -- as much as I understand -- can be tackled >> using the Rips complex. A quick search suggests that it is not >> provided by Sage. >> >> Is there a sufficiently free (licence-wise etc) piece of software that >> can compute Rips complex? Do people think that -- if it exists -- it >> would be worth the effort to interface/link Sage with it? > >I found this: http://www.mrzv.org/software/dionysus/ , but I was not >able to find anything on licensing. > >I've cc'd Dmitriy, the author, on this. Hi, Mike, I've always intended Dionysus to be GPL (at some point I stated so in the README file, but the note seems to be no longer there). Perhaps, I should make it clear on the front page of the documentation. In any case, it's GPL. On a less direct note, from scanning the conversation Simon links to, the construction he describes is not the Rips complex, but rather the Cech complex (which is defined as the nerve of the collection of discs). In persistent homology Rips complex is used more commonly since it's much easier to compute and in a certain (precise) sense approximates the Cech complex, but the two are not the same. Now, Cech complex is in turn homotopy equivalent to an alpha shape, which is a subset of the Delaunay triangulation. This fact makes the alpha shape nicely realizable geometrically, and I suspect that that's the actual construction Simon has in mind. Dionysus can compute alpha shapes, but it uses CGAL's Delaunay triangulation for the computation. I do not pretend to understand Eli's original problem, so I don't know if this indeed is the best solution, but that's a quick survey of the various complexes that may be useful for Sage. Best, Dmitriy -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
