#8431: Substitutions over unit cube faces (Rauzy fractals)
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Reporter: vdelecroix
| Owner: tjolivet
Type: task
| Status: needs_work
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:
|
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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).
>
> '''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.`
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).
--
Comment(by tjolivet):
Hello, I uploaded a new patch (that applies over !``e_one_star and !`` and
!``review-sl!``).
* It changes the `plot_tikz` function. There are no more `\newcommand`'s,
but only `\def`'s that are inside the `tikzpicture` environment. (No more
global annoyance, and it should work fine with `sagetex` now.) Also, RGB
colors a printed with two decimals only.
* In response to "the domain alphabet of the substitution used must
correspond to the type of faces": now, every substitution defining an
`E1Star` object is converted to an equivalent substitution on alphabet
`'1'`, ..., `'d'`. The type of a face can be specified by a positive
integer or a string representing a positive integer, and is converted to a
string when the `Face` object is created. This allows us to assume that
the type of a face in 3D is in {`'1'`, `'2'`, `'3'`}, which is very useful
for plotting functions.
* An option to color face according to their type has been added.
* It is possible to choose whether to (or not to) print the `tikzpicture`
environment definition, and the `\def` macros.
* Some other minor fixes, and small documentation fixes.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8431#comment:23>
Sage <http://www.sagemath.org>
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