Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine, sage.combinat.root_system.cartan_type.CartanType_simply_laced
EXAMPLES:
sage: ct = CartanType(['D',4,1])
sage: ct
['D', 4, 1]
sage: ct._repr_(compact = True)
'D4~'
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()
['D', 4]
sage: ct.dual()
['D', 4, 1]
TESTS:
sage: ct == loads(dumps(ct))
True
Returns a ascii art representation of the extended Dynkin diagram
TESTS:
sage: print CartanType(['D',6,1]).ascii_art(label = lambda x: x+2)
2 O O 8
| |
| |
O---O---O---O---O
3 4 5 6 7
sage: print CartanType(['D',4,1]).ascii_art(label = lambda x: x+2)
O 6
|
|
O---O---O
3 |4 5
|
O 2
sage: print CartanType(['D',3,1]).ascii_art(label = lambda x: x+2)
2
O-------+
| |
| |
O---O---O
5 3 4
Returns the extended Dynkin diagram for affine type D.
EXAMPLES:
sage: d = CartanType(['D', 6, 1]).dynkin_diagram()
sage: d
0 O O 6
| |
| |
O---O---O---O---O
1 2 3 4 5
D6~
sage: sorted(d.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 1),
(3, 2, 1), (3, 4, 1), (4, 3, 1), (4, 5, 1), (4, 6, 1), (5, 4, 1), (6, 4, 1)]
sage: d = CartanType(['D', 4, 1]).dynkin_diagram()
sage: d
O 4
|
|
O---O---O
1 |2 3
|
O 0
D4~
sage: sorted(d.edges())
[(0, 2, 1),
(1, 2, 1),
(2, 0, 1),
(2, 1, 1),
(2, 3, 1),
(2, 4, 1),
(3, 2, 1),
(4, 2, 1)]
sage: d = CartanType(['D', 3, 1]).dynkin_diagram()
sage: d
0
O-------+
| |
| |
O---O---O
3 1 2
D3~
sage: sorted(d.edges())
[(0, 2, 1), (0, 3, 1), (1, 2, 1), (1, 3, 1), (2, 0, 1), (2, 1, 1), (3, 0, 1), (3, 1, 1)]