Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine, sage.combinat.root_system.cartan_type.CartanType_simply_laced
EXAMPLES:
sage: ct = CartanType(['E',6,1])
sage: ct
['E', 6, 1]
sage: ct._repr_(compact = True)
'E6~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystalographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['E', 6]
sage: ct.dual()
['E', 6, 1]
TESTS:
sage: ct == loads(dumps(ct))
True
Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES:
sage: print CartanType(['E',6,1]).ascii_art(label = lambda x: x+2)
O 2
|
|
O 4
|
|
O---O---O---O---O
3 5 6 7 8
sage: print CartanType(['E',7,1]).ascii_art(label = lambda x: x+2)
O 4
|
|
O---O---O---O---O---O---O
2 3 5 6 7 8 9
sage: print CartanType(['E',8,1]).ascii_art(label = lambda x: x+1)
O 3
|
|
O---O---O---O---O---O---O---O
2 4 5 6 7 8 9 1
Returns the extended Dynkin diagram for affine type E.
EXAMPLES:
sage: e = CartanType(['E', 6, 1]).dynkin_diagram()
sage: e
O 0
|
|
O 2
|
|
O---O---O---O---O
1 3 4 5 6
E6~
sage: sorted(e.edges())
[(0, 2, 1),
(1, 3, 1),
(2, 0, 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)]
sage: e = CartanType(['E', 7, 1]).dynkin_diagram()
sage: e
O 2
|
|
O---O---O---O---O---O---O
0 1 3 4 5 6 7
E7~
sage: sorted(e.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: e = CartanType(['E', 8, 1]).dynkin_diagram()
sage: e
O 2
|
|
O---O---O---O---O---O---O---O
1 3 4 5 6 7 8 0
E8~
sage: sorted(e.edges())
[(0, 8, 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), (7, 8, 1), (8, 0, 1), (8, 7, 1)]