Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['A',4,1])
sage: ct
['A', 4, 1]
sage: ct._repr_(compact = True)
'A4~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['A', 4]
sage: ct.dual()
['A', 4, 1]
sage: ct = CartanType(['A', 1, 1])
sage: ct.is_simply_laced()
False
sage: ct.dual()
['A', 1, 1]
TESTS:
sage: TestSuite(ct).run()
Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES:
sage: print CartanType(['A',3,1]).ascii_art()
0
O-------+
| |
| |
O---O---O
1 2 3
sage: print CartanType(['A',5,1]).ascii_art(label = lambda x: x+2)
2
O---------------+
| |
| |
O---O---O---O---O
3 4 5 6 7
sage: print CartanType(['A',1,1]).ascii_art()
O<=>O
0 1
sage: print CartanType(['A',1,1]).ascii_art(label = lambda x: x+2)
O<=>O
2 3
Type is self dual despite not being simply laced.
EXAMPLES:
sage: CartanType(['A',1,1]).dual()
['A', 1, 1]
Returns the extended Dynkin diagram for affine type A.
EXAMPLES:
sage: a = CartanType(['A',3,1]).dynkin_diagram()
sage: a
0
O-------+
| |
| |
O---O---O
1 2 3
A3~
sage: sorted(a.edges())
[(0, 1, 1),
(0, 3, 1),
(1, 0, 1),
(1, 2, 1),
(2, 1, 1),
(2, 3, 1),
(3, 0, 1),
(3, 2, 1)]
sage: a = DynkinDiagram(['A',1,1])
sage: a
O<=>O
0 1
A1~
sage: sorted(a.edges())
[(0, 1, 2), (1, 0, 2)]