#20154: train-tracks
-------------------------------------+-------------------------------------
Reporter: dbenielli | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-7.1
Component: combinatorics | Resolution:
Keywords: free-group | Merged in:
automorphism | Reviewers:
Authors: Dominique | Work issues:
Benielli and Thierry Coulbois | Commit:
Report Upstream: N/A | 8e7f6300f59a3eca9d69233a52fc09b025cb33a2
Branch: | Stopgaps:
u/dbenielli/train_tracks |
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by jhpalmieri):
This is in response to http://ask.sagemath.org/question/33238/unable-to-
build-the-doc-reference-html/. There are a lot of problems with the
formatting of the docstrings. Here are a few fixes as illustrations. See
also http://www.sphinx-doc.org/en/stable/rest.html and
http://docutils.sourceforge.net/rst.html for the basics of
reStructuredText, and
http://doc.sagemath.org/html/en/developer/coding_basics.html
#documentation-strings for Sage-specific instructions.
{{{
#!diff
diff --git a/src/sage/combinat/words/convex_core.py
b/src/sage/combinat/words/convex_core.py
index 0183e0f..a3c873a 100644
--- a/src/sage/combinat/words/convex_core.py
+++ b/src/sage/combinat/words/convex_core.py
@@ -6,8 +6,8 @@ AUTHORS:
- Thierry COULBOIS (2013-01-01) : initial version
- Dominique BENIELLI (2016-02_15) :
-AMU University <[email protected]>,
-Integration in SageMath
+ AMU University <[email protected]>,
+ Integration in SageMath
EXAMPLES::
@@ -46,13 +46,15 @@ class ConvexCore():
Guirardel's convex core of two simplicial
trees with an action of a free group.
- Let T1 and T2 be trees with actions of the free group FN. G1=T1/FN
- and G2=T2/FN are MarkedGraph.
+ Let `T_1` and `T_`2` be trees with actions of the free group `FN`.
`G_1=T_1/FN`
+ and `G_2=T_2/FN` are MarkedGraph.
A ConvexCore is a CW-complex of dimension 2. 2-cells are
squares. 1-cells are edges labeled by edges of G1 or G2. A square
is of the form
+ ::
+
e
----->
| |
@@ -89,20 +91,20 @@ class ConvexCore():
EXAMPLES::
- sage: phi=FreeGroupAutomorphism("a->ab,b->ac,c->a")
- sage: phi=phi*phi
- sage: C=ConvexCore(phi)
- sage: print C.slice('c',0)
- Looped multi-digraph on 2 vertices
+ sage: phi=FreeGroupAutomorphism("a->ab,b->ac,c->a")
+ sage: phi=phi*phi
+ sage: C=ConvexCore(phi)
+ sage: print C.slice('c',0)
+ Looped multi-digraph on 2 vertices
- sage: C.vertices()
- [0, 1, 2, 3]
+ sage: C.vertices()
+ [0, 1, 2, 3]
- sage: C.squares()
- [[3, 0, 2, 1, 'c', 'a']]
+ sage: C.squares()
+ [[3, 0, 2, 1, 'c', 'a']]
- sage: C.twice_light_squares()
- [[1, 4, 0, 5, 'a', 'c']]
+ sage: C.twice_light_squares()
+ [[1, 4, 0, 5, 'a', 'c']]
AUTHORS:
@@ -686,7 +688,7 @@ class ConvexCore():
- a homotopy equivalence
- that maps the root v0 of ``G0.spanning_tree()`` to the root v1
of
- ``G1.spanning_tree()``
+ ``G1.spanning_tree()``
- the image of each vertex has at least two gates.
@@ -771,27 +773,27 @@ class ConvexCore():
- The boundary of a square is a list [e0,e1,e2,e3] of edges such
that
- e0=(w,v,(a,0)) and e2 are edges with a positive letter
- a, and e1=(w,v,(b,1)) and e3 are edges with b a
- positive letter.
+ e0=(w,v,(a,0)) and e2 are edges with a positive letter
+ a, and e1=(w,v,(b,1)) and e3 are edges with b a
+ positive letter.
- The boundary of an edge it is the list [v0,v1] of the initial
vertex
- v0=(w,v) followed by the terminal vertex.
+ v0=(w,v) followed by the terminal vertex.
Whereas for lists:
- squares: ``[v0,v1,v2,v3,a,b]`` where v0,v1,v2 and v3 are
integers standing for vertices and a,b are positive letters
- labeling edges of G0 and G1:
+ labeling edges of G0 and G1::
a
- v3 ------> v2
- ^ ^
- | |
- |b |b
- | |
- | a |
- v0 ------>v1
+ v3 ------> v2
+ ^ ^
+ | |
+ |b |b
+ | |
+ | a |
+ v0 ------>v1
- edges: ``[v0,v1,(a,side)]`` where ``v0`` and ``v1`` are
integers standing for vertices a is a label of the tree on
@@ -799,30 +801,30 @@ class ConvexCore():
INPUT:
- -``cell``square, an edge or a vertex. Squares are bounded
- by four vertices, edges by two vertices.
+ - ``cell`` square, an edge or a vertex. Squares are bounded
+ by four vertices, edges by two vertices.
OUTPUT:
The boundary of a cell is the list of vertices bounding it.
EXAMPLES::
- sage: phi = FreeGroupAutomorphism("a->ab,b->ac,c->a")**2
- sage: C = ConvexCore(phi)
- sage: C.boundary((Word('C'), 0, 'c', 'a')) # boundary of a square
- [(word: C, 0, ('c', 0)),
- (word: , 0, ('a', 1)),
- (word: Bc, 0, ('C', 0)),
- (word: B, 0, ('A', 1))]
+ sage: phi = FreeGroupAutomorphism("a->ab,b->ac,c->a")**2
+ sage: C = ConvexCore(phi)
+ sage: C.boundary((Word('C'), 0, 'c', 'a')) # boundary of a
square
+ [(word: C, 0, ('c', 0)),
+ (word: , 0, ('a', 1)),
+ (word: Bc, 0, ('C', 0)),
+ (word: B, 0, ('A', 1))]
- sage: C.boundary([3, 0, 2, 1, 'c', 'a']) # boundary of a square
- [[3, 0, ('c', 0)], [0, 2, ('a', 1)], [2, 1, ('C', 0)], [1, 3,
('A', 1)]]
+ sage: C.boundary([3, 0, 2, 1, 'c', 'a']) # boundary of a
square
+ [[3, 0, ('c', 0)], [0, 2, ('a', 1)], [2, 1, ('C', 0)], [1, 3,
('A', 1)]]
- sage: C.boundary((Word('Bc'),0,('C',0))) # boundary of an edge
- [(word: Bc, 0), (word: B, 0)]
+ sage: C.boundary((Word('Bc'),0,('C',0))) # boundary of an
edge
+ [(word: Bc, 0), (word: B, 0)]
- sage: C.boundary([2,1,'C']) # boundary of an edge
- [2, 1]
+ sage: C.boundary([2,1,'C']) # boundary of an edge
+ [2, 1]
"""
if isinstance(cell, tuple):
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/20154#comment:19>
Sage <http://www.sagemath.org>
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