Substitutions over unit cube faces (Rauzy fractals)

[videlec]

This patch introduces unit cube faces and substitutions over them, as defined in the article 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).

CC: @sagetrac-sage-combinat @seblabbe @sagetrac-abmasse @sagetrac-tmonteil

Component: combinatorics

Keywords: word morphism unit face generalized substitution rauzy fractal

Author: Vincent Delecroix, Timo Jolivet, Franco Saliola, Štěpán Starosta

Reviewer: Sébastien Labbé, Alexandre Blondin Massé

Merged: sage-4.6.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/8431

[videlec]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
 Thinking about it for a long time and motivated by [#8423](https://github.com/sagemath/sage/issues/8423&usg=AFQjCNG8_y-UlT3ON3unoD3utIEHQfTYbQ) this ticket stands for
 * the creation of WordMorphismExtension and WordMorphismExtensionDual (from [an article of Sano-Arnoux-Ito](http://iml.univ-mrs.fr/~arnoux/AISrev.pdf))
-* Have easy to use function for plotting Rauzy fractals using those algebraic tools
+* think about easy to use functions for plotting Rauzy fractals using those algebraic tools
 

[videlec]

Description changed:

--- 
+++ 
@@ -1,4 +1,28 @@
 Thinking about it for a long time and motivated by [#8423](https://github.com/sagemath/sage/issues/8423&usg=AFQjCNG8_y-UlT3ON3unoD3utIEHQfTYbQ) this ticket stands for
 * the creation of WordMorphismExtension and WordMorphismExtensionDual (from [an article of Sano-Arnoux-Ito](http://iml.univ-mrs.fr/~arnoux/AISrev.pdf))
-* think about easy to use functions for plotting Rauzy fractals using those algebraic tools
+* think about easy to use functions for plotting Rauzy fractals using those algebraic tools. The broken lines and their projection for WordMorphismExtension and discrete planes approximation from WordMorphismExtensionDual.
 
+We could be able to access the extensions as a method of morphisms
+
+```
+sage: s = WordMorphism('a->ab,b->ac,c->a')
+sage: s.extension()
+Word morphism Extension [...]
+sage: s.extension_dual()
+Word morphism dual extension [...]
+```
+
+And plot them easily from fractals.
+
+```
+sage: s = WordMorphism('a->ab,b->ac,c->a')
+sage: fractals.RauzyFractal(morphism=s, format='broken_line')
+sage: fractals.RauzyFractal(morphism=s, format='discrete_plane')
+```
+
+The algebra requires the creation of few other classes which
+* Face and Patch (which is union of faces)
+* WordMorphismExtension and its dual
+* WordMorphismExtensionIterations for plotting approximations of the limit fractal from the extension or its dual
+
+TODO: think about cython for having fast data structure for Face and Patch (which heritates from tuple and set) !

[seblabbe]

comment:3

I add myself in cc because I am interested.

[seblabbe]

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 Thinking about it for a long time and motivated by [#8423](https://github.com/sagemath/sage/issues/8423&usg=AFQjCNG8_y-UlT3ON3unoD3utIEHQfTYbQ) this ticket stands for
-* the creation of WordMorphismExtension and WordMorphismExtensionDual (from [an article of Sano-Arnoux-Ito](http://iml.univ-mrs.fr/~arnoux/AISrev.pdf))
-* think about easy to use functions for plotting Rauzy fractals using those algebraic tools. The broken lines and their projection for WordMorphismExtension and discrete planes approximation from WordMorphismExtensionDual.
+* the creation of `WordMorphismExtension` and `WordMorphismExtensionDual` (from [an article of Sano-Arnoux-Ito](http://iml.univ-mrs.fr/~arnoux/AISrev.pdf))
+* think about easy to use functions for plotting Rauzy fractals using those algebraic tools. The broken lines and their projection for `WordMorphismExtension` and discrete planes approximation from `WordMorphismExtensionDual`.
 
 We could be able to access the extensions as a method of morphisms
 
@@ -22,7 +22,7 @@
 
 The algebra requires the creation of few other classes which
 * Face and Patch (which is union of faces)
-* WordMorphismExtension and its dual
-* WordMorphismExtensionIterations for plotting approximations of the limit fractal from the extension or its dual
+* `WordMorphismExtension` and its dual
+* `WordMorphismExtensionIterations` for plotting approximations of the limit fractal from the extension or its dual
 
 TODO: think about cython for having fast data structure for Face and Patch (which heritates from tuple and set) !

[sagetrac-tjolivet]

Changed keywords from word morphism to word morphism unit face generalized substitution rauzy fractal

[sagetrac-tjolivet]

Description changed:

--- 
+++ 
@@ -1,28 +1,11 @@
-Thinking about it for a long time and motivated by [#8423](https://github.com/sagemath/sage/issues/8423&usg=AFQjCNG8_y-UlT3ON3unoD3utIEHQfTYbQ) this ticket stands for
-* the creation of `WordMorphismExtension` and `WordMorphismExtensionDual` (from [an article of Sano-Arnoux-Ito](http://iml.univ-mrs.fr/~arnoux/AISrev.pdf))
-* think about easy to use functions for plotting Rauzy fractals using those algebraic tools. The broken lines and their projection for `WordMorphismExtension` and discrete planes approximation from `WordMorphismExtensionDual`.
+This patch  introduces unit cube faces and substitutions over them, as defined in the article [Pisot substitutions and Rauzy fractals](http://iml.univ-mrs.fr/%7Earnoux/ArnouxIto.pdf) by Arnoux and Ito.
 
-We could be able to access the extensions as a method of morphisms
+Three new classes are defined:
 
-```
-sage: s = WordMorphism('a->ab,b->ac,c->a')
-sage: s.extension()
-Word morphism Extension [...]
-sage: s.extension_dual()
-Word morphism dual extension [...]
-```
+* `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`
 
-And plot them easily from fractals.
+The plotting features enable us draw approximations of Rauzy fractals, or to generate patches of discrete planes.
 
-```
-sage: s = WordMorphism('a->ab,b->ac,c->a')
-sage: fractals.RauzyFractal(morphism=s, format='broken_line')
-sage: fractals.RauzyFractal(morphism=s, format='discrete_plane')
-```
-
-The algebra requires the creation of few other classes which
-* Face and Patch (which is union of faces)
-* `WordMorphismExtension` and its dual
-* `WordMorphismExtensionIterations` for plotting approximations of the limit fractal from the extension or its dual
-
-TODO: think about cython for having fast data structure for Face and Patch (which heritates from tuple and set) !
+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).

[sagetrac-tjolivet]

comment:4

Attachment: trac_8431_E1Star.patch.gz

[sagetrac-tjolivet]

Changed author from vdelecroix, sstarosta to vdelecroix, tjolivet, sstarosta