Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine
EXAMPLES:
sage: ct = CartanType(['F',4,1])
sage: ct
['F', 4, 1]
sage: ct._repr_(compact = True)
'F4~'
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()
['F', 4]
sage: ct.dual()
['F', 4, 1]^*
sage: ct.dual().is_untwisted_affine()
False
TESTS:
sage: ct == loads(dumps(ct))
True
Returns a ascii art representation of the extended Dynkin diagram
EXAMPLES:
sage: print CartanType(['F',4,1]).ascii_art(label = lambda x: x+2)
O---O---O=>=O---O
2 3 4 5 6
Returns the extended Dynkin diagram for affine type F.
EXAMPLES:
sage: f = CartanType(['F', 4, 1]).dynkin_diagram()
sage: f
O---O---O=>=O---O
0 1 2 3 4
F4~
sage: sorted(f.edges())
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]