Bases: sage.combinat.root_system.cartan_type.CartanType_standard_affine
EXAMPLES:
sage: ct = CartanType(['BC',4,2])
sage: ct
['BC', 4, 2]
sage: ct._repr_(compact = True)
'BC4~'
sage: ct.dynkin_diagram()
O=<=O---O---O=<=O
0 1 2 3 4
BC4~
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
False
sage: ct.classical()
['C', 4]
sage: dual = ct.dual()
sage: dual.dynkin_diagram()
O=>=O---O---O=>=O
0 1 2 3 4
BC4~*
sage: dual.special_node()
0
sage: dual.classical().dynkin_diagram()
O---O---O=>=O
1 2 3 4
B4
sage: CartanType(['BC',1,2]).dynkin_diagram()
4
O=<=O
0 1
BC1~
TESTS:
sage: TestSuite(ct).run()
Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES:
sage: print CartanType(['BC',2,2]).ascii_art()
O=<=O=<=O
0 1 2
sage: print CartanType(['BC',3,2]).ascii_art()
O=<=O---O=<=O
0 1 2 3
sage: print CartanType(['BC',5,2]).ascii_art(label = lambda x: x+2)
O=<=O---O---O---O=<=O
2 3 4 5 6 7
sage: print CartanType(['BC',1,2]).ascii_art(label = lambda x: x+2)
4
O=<=O
2 3
Return the basic untwisted Cartan type associated with this affine Cartan type.
Given an affine type , the basic untwisted type is
.
In other words, it is the classical Cartan type that is twisted to
obtain self.
EXAMPLES:
sage: CartanType(['A', 2, 2]).basic_untwisted()
['A', 2]
sage: CartanType(['A', 4, 2]).basic_untwisted()
['A', 4]
sage: CartanType(['BC', 4, 2]).basic_untwisted()
['A', 8]
Returns the classical Cartan type associated with self
sage: CartanType([“BC”, 3, 2]).classical() [‘C’, 3]
Returns the extended Dynkin diagram for affine type BC.
EXAMPLES:
sage: c = CartanType(['BC',3,2]).dynkin_diagram()
sage: c
O=<=O---O=<=O
0 1 2 3
BC3~
sage: sorted(c.edges())
[(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
sage: c = CartanType(["A", 6, 2]).dynkin_diagram() # should be the same as above; did fail at some point!
sage: c
O=<=O---O=<=O
0 1 2 3
BC3~
sage: sorted(c.edges())
[(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
sage: c = CartanType(['BC',2,2]).dynkin_diagram()
sage: c
O=<=O=<=O
0 1 2
BC2~
sage: sorted(c.edges())
[(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 2)]
sage: c = CartanType(['BC',1,2]).dynkin_diagram()
sage: c
4
O=<=O
0 1
BC1~
sage: sorted(c.edges())
[(0, 1, 1), (1, 0, 4)]