#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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Comment(by abmasse):
Hi, Timo and Sébastien !
Replying to [comment:25 tjolivet]:
> Hi Sébastien and the others,
>
> '''Now, a last and important remark'''. Writing
>
> {{{
> sigma = WordMorphism('1->12,2->13,3->1')
> }}}
> is less painful than writing
>
> {{{
> sigma = WordMorphism({1:[1,2], 2:[1,3], 3:[1]})
> }}}
I agree with you on that one. This is something I've noticed too when
using `WordMorphism`'s. The thing is: the problem comes from the object
WordMorphism, and it's where it should be solved, in my opinion, and not
in the class `E1Star`.
> Since all the face types are integers and the
[http://trac.sagemath.org/sage_trac/search/opensearch?q=wiki%3AWordMorphism
WordMorphism] defining an `E1Star` must be on integers, we are supposed to
use the latter way to define `sigma`. However, I find it very
inconvenient, so we allow the user to give a `sigma` defined on an
'''arbitrary''' alphabet. When `E1Star` is defined, it is converted and
stored as a substitution on the alphabet `[1, ..., d]` (so that there is a
correspondence between the types of the faces and the alphabet of the
substitutions). It really makes the definitions much more convenient and I
don't think that it harms `sage` so much.
>
> Also, I don't think that it would be useful to allow the user to specify
an arbitrary alphabet for the faces, since they are not used as the
letters of a word, but as three-dimensional objects, which we ''call'' of
type `1`, `2` or `3`. (This is why all the types are represented by
integers.) It corresponds to the mathematical definition of the object.
>
I disagree. If I'm not mistaken, the integer meaning of 1, 2, 3 is never
used in the construction of patches and discrete plane. I mean, we could
use a,b,c and everything would work the same, there is no gain from
encoding it with integers, since no additive group structure is used
(correct me if I'm wrong, though, that could be a good argument).
In fact, I think it's quite the opposite. It would be better to allow the
user to have any alphabet, so that he can use any structure he wants
(additive group, for instance, or any other operation that might encode
interesting discrete plane construction).
> I strongly insist on this last remark!
What I propose you is that either Sébastien or I work on the improvement
of the construction of `WordMorphism` in order to offer something like
{{{
sigma = WordMorphism('1->12,2->13,3->1', type='integer')
}}}
Does that seem reasonable?
P.S. I'm following your discussion and I see the progress... Keep the good
work!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8431#comment:26>
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