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# Root system data for (untwisted) type A affine

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

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

  EXAMPLES:

      sage: ct = CartanType(['A',4,1])
      sage: ct
      ['A', 4, 1]
      sage: ct._repr_(compact = True)
      'A4~'

      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()
      True
      sage: ct.classical()
      ['A', 4]
      sage: ct.dual()
      ['A', 4, 1]

      sage: ct = CartanType(['A', 1, 1])
      sage: ct.is_simply_laced()
      False
      sage: ct.dual()
      ['A', 1, 1]

  TESTS:

      sage: TestSuite(ct).run()

  `ascii_art`(label=<function <lambda> at 0xe9db948c>)

    Returns a ascii art representation of the extended Dynkin diagram

    EXAMPLES:

        sage: print CartanType(['A',3,1]).ascii_art()
        0
        O-------+
        |       |
        |       |
        O---O---O
        1   2   3

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

        sage: print CartanType(['A',1,1]).ascii_art()
        O<=>O
        0   1

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

  `dual`()

    Type \(A_1^1\) is self dual despite not being simply laced.

    EXAMPLES:

        sage: CartanType(['A',1,1]).dual()
        ['A', 1, 1]

  `dynkin_diagram`()

    Returns the extended Dynkin diagram for affine type A.

    EXAMPLES:

        sage: a = CartanType(['A',3,1]).dynkin_diagram()
        sage: a
         0
         O-------+
         |       |
         |       |
         O---O---O
         1   2   3
         A3~
        sage: sorted(a.edges())
        [(0, 1, 1),
         (0, 3, 1),
         (1, 0, 1),
         (1, 2, 1),
         (2, 1, 1),
         (2, 3, 1),
         (3, 0, 1),
         (3, 2, 1)]

        sage: a = DynkinDiagram(['A',1,1])
        sage: a
        O<=>O
        0   1
        A1~
        sage: sorted(a.edges())
        [(0, 1, 2), (1, 0, 2)]

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