Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['B',4,1])
sage: ct
['B', 4, 1]
sage: ct._repr_(compact = True)
'B4~'
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()
False
sage: ct.classical()
['B', 4]
sage: ct.dual()
['B', 4, 1]^*
sage: ct.dual().is_untwisted_affine()
False
TESTS:
sage: TestSuite(ct).run()
Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES:
sage: print CartanType(['B',3,1]).ascii_art()
O 0
|
|
O---O=>=O
1 2 3
sage: print CartanType(['B',5,1]).ascii_art(label = lambda x: x+2)
O 2
|
|
O---O---O---O=>=O
3 4 5 6 7
sage: print CartanType(['B',2,1]).ascii_art(label = lambda x: x+2)
O=>=O=<=O
2 4 3
sage: print CartanType(['B',1,1]).ascii_art(label = lambda x: x+2)
O<=>O
2 3
Returns the extended Dynkin diagram for affine type B.
EXAMPLES:
sage: b = CartanType(['B',3,1]).dynkin_diagram()
sage: b
O 0
|
|
O---O=>=O
1 2 3
B3~
sage: sorted(b.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]
sage: b = CartanType(['B',2,1]).dynkin_diagram(); b
O=>=O=<=O
0 2 1
B2~
sage: sorted(b.edges())
[(0, 2, 2), (1, 2, 2), (2, 0, 1), (2, 1, 1)]
sage: b = CartanType(['B',1,1]).dynkin_diagram(); b
O<=>O
0 1
B1~
sage: sorted(b.edges())
[(0, 1, 2), (1, 0, 2)]