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# 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 0xe5f32fb4>)

    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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