Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['G',2,1])
sage: ct
['G', 2, 1]
sage: ct._repr_(compact = True)
'G2~'
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()
False
sage: ct.classical()
['G', 2]
sage: ct.dual()
['G', 2, 1]^*
sage: ct.dual().is_untwisted_affine()
False
TESTS:
sage: ct == loads(dumps(ct))
True
Returns an ascii art representation of the Dynkin diagram
EXAMPLES:
sage: print CartanType(['G',2,1]).ascii_art(label = lambda x: x+2)
3
O=<=O---O
3 4 2
Returns the extended Dynkin diagram for type G.
EXAMPLES:
sage: g = CartanType(['G',2,1]).dynkin_diagram()
sage: g
3
O=<=O---O
1 2 0
G2~
sage: sorted(g.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 3)]