Root system data for (untwisted) type F affine

class sage.combinat.root_system.type_F_affine.CartanType

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_crystallographic()
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

ascii_art(label=<function CartanType.<lambda> at 0x7f134bdf5ab0>, node=None)

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

dynkin_diagram()

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: f.edges(sort=True)
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]