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# Root system data for type BC affine

class `sage.combinat.root_system.type_BC_affine.``CartanType`(n)

  Bases: `sage.combinat.root_system.cartan_type.CartanType_standard_affine`

  EXAMPLES:

      sage: ct = CartanType(['BC',4,2])
      sage: ct
      ['BC', 4, 2]
      sage: ct._repr_(compact = True)
      'BC4~'
      sage: ct.dynkin_diagram()
      O=<=O---O---O=<=O
      0   1   2   3   4
      BC4~

      sage: ct.is_irreducible()
      True
      sage: ct.is_finite()
      False
      sage: ct.is_affine()
      True
      sage: ct.is_crystallographic()
      True
      sage: ct.is_simply_laced()
      False
      sage: ct.classical()
      ['C', 4]

      sage: dual = ct.dual()
      sage: dual.dynkin_diagram()
      O=>=O---O---O=>=O
      0   1   2   3   4
      BC4~*

      sage: dual.special_node()
      0
      sage: dual.classical().dynkin_diagram()
      O---O---O=>=O
      1   2   3   4
      B4

      sage: CartanType(['BC',1,2]).dynkin_diagram()
        4
      O=<=O
      0   1
      BC1~

  TESTS:

      sage: TestSuite(ct).run()

  `ascii_art`(label=<function <lambda> at 0xe9e39c34>)

    Returns a ascii art representation of the extended Dynkin diagram

    EXAMPLES:

        sage: print CartanType(['BC',2,2]).ascii_art()
        O=<=O=<=O
        0   1   2
        sage: print CartanType(['BC',3,2]).ascii_art()
        O=<=O---O=<=O
        0   1   2   3
        sage: print CartanType(['BC',5,2]).ascii_art(label = lambda x: x+2)
        O=<=O---O---O---O=<=O
        2   3   4   5   6   7

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

  `basic_untwisted`()

    Return the basic untwisted Cartan type associated with this affine Cartan type.

    Given an affine type \(X_n^{(r)}\), the basic untwisted type is \(X_n\). In other words, it is the classical Cartan type that is twisted to obtain `self`.

    EXAMPLES:

        sage: CartanType(['A', 2, 2]).basic_untwisted()
        ['A', 2]
        sage: CartanType(['A', 4, 2]).basic_untwisted()
        ['A', 4]
        sage: CartanType(['BC', 4, 2]).basic_untwisted()
        ['A', 8]

  `classical`()

    Returns the classical Cartan type associated with self

    > sage: CartanType([“BC”, 3, 2]).classical() [‘C’, 3]

  `dynkin_diagram`()

    Returns the extended Dynkin diagram for affine type BC.

    EXAMPLES:

        sage: c = CartanType(['BC',3,2]).dynkin_diagram()
        sage: c
        O=<=O---O=<=O
        0   1   2   3
        BC3~
        sage: sorted(c.edges())
        [(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]

        sage: c = CartanType(["A", 6, 2]).dynkin_diagram() # should be the same as above; did fail at some point!
        sage: c
        O=<=O---O=<=O
        0   1   2   3
        BC3~
        sage: sorted(c.edges())
        [(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]

        sage: c = CartanType(['BC',2,2]).dynkin_diagram()
        sage: c
        O=<=O=<=O
        0   1   2
        BC2~
        sage: sorted(c.edges())
        [(0, 1, 1), (1, 0, 2), (1, 2, 1), (2, 1, 2)]

        sage: c = CartanType(['BC',1,2]).dynkin_diagram()
        sage: c
          4
        O=<=O
        0   1
        BC1~
        sage: sorted(c.edges())
        [(0, 1, 1), (1, 0, 4)]

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