Root system data for (untwisted) type C affine

class sage.combinat.root_system.type_C_affine.CartanType(n)

Bases: CartanType_standard_untwisted_affine

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> ct = CartanType(['C',Integer(4),Integer(1)])
>>> ct
['C', 4, 1]
>>> ct._repr_(compact = True)
'C4~'

>>> 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()
['C', 4]
>>> ct.dual()
['C', 4, 1]^*
>>> ct.dual().is_untwisted_affine()
False

PieriFactors

alias of PieriFactors_type_C_affine

ascii_art(label=None, node=None)

Return a ascii art representation of the extended Dynkin diagram.

EXAMPLES:

Sage

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

Python

>>> from sage.all import *
>>> print(CartanType(['C',Integer(5),Integer(1)]).ascii_art(label = lambda x: x+Integer(2)))
O=>=O---O---O---O=<=O
2   3   4   5   6   7

>>> print(CartanType(['C',Integer(3),Integer(1)]).ascii_art())
O=>=O---O=<=O
0   1   2   3

>>> print(CartanType(['C',Integer(2),Integer(1)]).ascii_art())
O=>=O=<=O
0   1   2

>>> print(CartanType(['C',Integer(1),Integer(1)]).ascii_art())
O<=>O
0   1

dynkin_diagram()

Return the extended Dynkin diagram for affine type C.

EXAMPLES:

Sage

sage: c = CartanType(['C',3,1]).dynkin_diagram(); c                         # needs sage.graphs
 O=>=O---O=<=O
 0   1   2   3
 C3~
sage: c.edges(sort=True)                                                    # needs sage.graphs
[(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]

Python

>>> from sage.all import *
>>> c = CartanType(['C',Integer(3),Integer(1)]).dynkin_diagram(); c                         # needs sage.graphs
 O=>=O---O=<=O
 0   1   2   3
 C3~
>>> c.edges(sort=True)                                                    # needs sage.graphs
[(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]