Root system data for (untwisted) type F affine

class sage.combinat.root_system.type_F_affine.CartanType

Bases: CartanType_standard_untwisted_affine

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> ct = CartanType(['F',Integer(4),Integer(1)])
>>> ct
['F', 4, 1]
>>> ct._repr_(compact = True)
'F4~'

>>> ct.is_irreducible()
True
>>> ct.is_finite()
False
>>> ct.is_affine()
True
>>> ct.is_untwisted_affine()
True
>>> ct.is_crystallographic()
True
>>> ct.is_simply_laced()
False
>>> ct.classical()
['F', 4]
>>> ct.dual()
['F', 4, 1]^*
>>> ct.dual().is_untwisted_affine()
False

ascii_art(label=None, node=None)

Returns a ascii art representation of the extended Dynkin diagram

EXAMPLES:

Sage

sage: print(CartanType(['F',4,1]).ascii_art(label = lambda x: x+2))
O---O---O=>=O---O
2   3   4   5   6

Python

>>> from sage.all import *
>>> print(CartanType(['F',Integer(4),Integer(1)]).ascii_art(label = lambda x: x+Integer(2)))
O---O---O=>=O---O
2   3   4   5   6

dynkin_diagram()

Returns the extended Dynkin diagram for affine type F.

EXAMPLES:

Sage

sage: f = CartanType(['F', 4, 1]).dynkin_diagram(); f                       # needs sage.graphs
O---O---O=>=O---O
0   1   2   3   4
F4~
sage: f.edges(sort=True)                                                    # needs sage.graphs
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1),
 (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]

Python

>>> from sage.all import *
>>> f = CartanType(['F', Integer(4), Integer(1)]).dynkin_diagram(); f                       # needs sage.graphs
O---O---O=>=O---O
0   1   2   3   4
F4~
>>> f.edges(sort=True)                                                    # needs sage.graphs
[(0, 1, 1), (1, 0, 1), (1, 2, 1), (2, 1, 1),
 (2, 3, 2), (3, 2, 1), (3, 4, 1), (4, 3, 1)]