Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['C',4,1])
sage: ct
['C', 4, 1]
sage: ct._repr_(compact = True)
'C4~'
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()
['C', 4]
sage: ct.dual()
['C', 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(['C',5,1]).ascii_art(label = lambda x: x+2)
O=>=O---O---O---O=<=O
2 3 4 5 6 7
sage: print CartanType(['C',3,1]).ascii_art()
O=>=O---O=<=O
0 1 2 3
sage: print CartanType(['C',2,1]).ascii_art()
O=>=O=<=O
0 1 2
sage: print CartanType(['C',1,1]).ascii_art()
O<=>O
0 1
Returns the extended Dynkin diagram for affine type C.
EXAMPLES:
sage: c = CartanType(['C',3,1]).dynkin_diagram()
sage: c
O=>=O---O=<=O
0 1 2 3
C3~
sage: sorted(c.edges())
[(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]