#8431: Substitutions over unit cube faces (Rauzy fractals)
--------------------------------------------------------------------------------+
Reporter: vdelecroix
| Owner: tjolivet
Type: task
| Status: needs_review
Priority: major
| Milestone: sage-4.6
Component: combinatorics
| Keywords: word morphism unit face generalized substitution rauzy fractal
Author: Vincent Delecroix, Timo Jolivet, Franco Saliola, Stepan Starosta
| Upstream: N/A
Reviewer:
| Merged:
Work_issues:
|
--------------------------------------------------------------------------------+
Changes (by newvalueoldvalue):
* status: needs_work => needs_review
* author: Vincent Delecroix, Timo Jolivet, Stepan Starosta, Franco
Saliola => Vincent Delecroix, Timo Jolivet,
Franco Saliola, Stepan Starosta
Old description:
> This patch introduces unit cube faces and substitutions over them, as
> defined in the article [http://iml.univ-mrs.fr/%7Earnoux/ArnouxIto.pdf
> Pisot substitutions and Rauzy fractals] by Arnoux and Ito.
>
> Three new classes are defined:
>
> * `Face` -- models a unit cube face
> * `Patch` -- models a finite collection of faces
> * `E1Star` -- models the the ''E_1!^*(sigma)'' substitution (over faces)
> defined by a unimodular substitution `sigma`
>
> The plotting features enable us draw approximations of Rauzy fractals, or
> to generate patches of discrete planes.
>
> The dimension of the faces can be of any dimension (and the substitutions
> work accordingly), but the plotting features work only in dimension three
> (with three-letter alphabet substitutions).
New description:
This patch introduces unit cube faces and substitutions over them, as
defined in the article [http://iml.univ-mrs.fr/%7Earnoux/ArnouxIto.pdf
Pisot substitutions and Rauzy fractals] by Arnoux and Ito.
Three new classes are defined:
* `Face` -- models a unit cube face
* `Patch` -- models a finite collection of faces
* `E1Star` -- models the the ''E_1!^*(sigma)'' substitution (over faces)
defined by a unimodular substitution `sigma`
The plotting features enable us draw approximations of Rauzy fractals, or
to generate patches of discrete planes.
The dimension of the faces can be of any dimension (and the substitutions
work accordingly), but the plotting features work only in dimension three
(with three-letter alphabet substitutions).
'''EDIT (2010-09-19):''' a new version of the patch is attached
(`trac_8431_e_one_star.patch`), taking into account the suggestions given
in the comments. Documentation compiles fine, except for the following
warning, which I don't think comes from an error in `e_one_star.py`:
`/home/timo/sage-4.5.3/local/lib/python2.6/site-
packages/sage/combinat/e_one_star.py:docstring of
sage.combinat.e_one_star:56: (WARNING/2) Literal block expected; none
found.`
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8431#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
