Root system data for (untwisted) type B affine

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

Bases: sage.combinat.root_system.cartan_type.CartanType_standard_untwisted_affine

EXAMPLES:

sage: ct = CartanType(['B',4,1])
sage: ct
['B', 4, 1]
sage: ct._repr_(compact = True)
'B4~'

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()
['B', 4]
sage: ct.dual()
['B', 4, 1]^*
sage: ct.dual().is_untwisted_affine()
False

TESTS:

sage: TestSuite(ct).run()
ascii_art(label=<function <lambda> at 0x7f51a4ee9488>)

Returns a ascii art representation of the extended Dynkin diagram

EXAMPLES:

sage: print CartanType(['B',3,1]).ascii_art()
    O 0
    |
    |
O---O=>=O
1   2   3

sage: print CartanType(['B',5,1]).ascii_art(label = lambda x: x+2)
    O 2
    |
    |
O---O---O---O=>=O
3   4   5   6   7

sage: print CartanType(['B',2,1]).ascii_art(label = lambda x: x+2)
O=>=O=<=O
2   4   3
sage: print CartanType(['B',1,1]).ascii_art(label = lambda x: x+2)
O<=>O
2   3
dynkin_diagram()

Returns the extended Dynkin diagram for affine type B.

EXAMPLES:

sage: b = CartanType(['B',3,1]).dynkin_diagram()
sage: b
    O 0
    |
    |
O---O=>=O
1   2   3
B3~
sage: sorted(b.edges())
[(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 2), (3, 2, 1)]

sage: b = CartanType(['B',2,1]).dynkin_diagram(); b
O=>=O=<=O
0   2   1
B2~
sage: sorted(b.edges())
[(0, 2, 2), (1, 2, 2), (2, 0, 1), (2, 1, 1)]

sage: b = CartanType(['B',1,1]).dynkin_diagram(); b
O<=>O
0   1
B1~
sage: sorted(b.edges())
[(0, 1, 2), (1, 0, 2)]

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