On Tue, Aug 25, 2009 at 04:26:54PM -0700, Anne Schilling wrote:
> The labeling of the Dynkin nodes for type E_7 in sage does not
> seem consistent with the labeling of the affine nodes:
> Should we fix this? It would make much more sense to attach node 2
> in E_7 to node 4 instead of node 5.
Err ???
I could not reproduce that. On my machine, everything is fine:
sage: DynkinDiagram(["E",7,1])
O 2
|
|
O---O---O---O---O---O---O
0 1 3 4 5 6 7
E7~
sage: DynkinDiagram(["E",7])
O 2
|
|
O---O---O---O---O---O
1 3 4 5 6 7
E7
sage: DynkinDiagram(["E",7,1]).edges()
[(0, 1, 1), (1, 0, 1),
(1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1), (4, 2, 1), (4, 3, 1), (4, 5, 1),
(5, 4, 1), (5, 6, 1), (6, 5, 1), (6, 7, 1), (7, 6, 1)]
sage: DynkinDiagram(["E",7]).edges()
[(1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1), (4, 2, 1), (4, 3, 1), (4, 5, 1),
(5, 4, 1), (5, 6, 1), (6, 5, 1), (6, 7, 1), (7, 6, 1)]
Besides, there is an automatic test for this line 1168 of cartan_type.py::
We check that :meth:`classical`, :meth:`.dynkin_diagram`, and
:meth:`.special_node` are consistent::
sage: for ct in CartanType.samples(affine = True):
... g1 = ct.classical().dynkin_diagram()
... g2 = ct.dynkin_diagram()
... g2.delete_vertex(ct.special_node())
... assert sorted(g1.vertices()) == sorted(g2.vertices())
... assert sorted(g1.edges()) == sorted(g2.edges())
Cheers,
Nicolas
> sage: CartanType(['E',7]).dynkin_diagram()
>
> O 2
> |
> |
> O---O---O---O---O---O
> 1 3 4 5 6 7
> E7
>
>
> sage: CartanType(['E',7,1]).dynkin_diagram()
>
> O 2
> |
> |
> O---O---O---O---O---O---O
> 0 1 3 4 5 6 7
> E7~
>
>
> For type E_6 things are consistent:
>
>
> sage: CartanType(['E',6]).dynkin_diagram()
>
> O 2
> |
> |
> O---O---O---O---O
> 1 3 4 5 6
> E6
> sage: CartanType(['E',6,1]).dynkin_diagram()
>
> O 0
> |
> |
> O 2
> |
> |
> O---O---O---O---O
> 1 3 4 5 6
> E6~
>
>
> Anne
>
> Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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