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# Root system data for (untwisted) type E affine

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

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

  EXAMPLES:

      sage: ct = CartanType(['E',6,1])
      sage: ct
      ['E', 6, 1]
      sage: ct._repr_(compact = True)
      'E6~'

      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()
      ['E', 6]
      sage: ct.dual()
      ['E', 6, 1]

  TESTS:

      sage: TestSuite(ct).run()

  `ascii_art`(label=<function <lambda> at 0xe0b31294>)

    Returns a ascii art representation of the extended Dynkin diagram

    EXAMPLES:

        sage: print CartanType(['E',6,1]).ascii_art(label = lambda x: x+2)
                O 2
                |
                |
                O 4
                |
                |
        O---O---O---O---O
        3   5   6   7   8
        sage: print CartanType(['E',7,1]).ascii_art(label = lambda x: x+2)
                    O 4
                    |
                    |
        O---O---O---O---O---O---O
        2   3   5   6   7   8   9
        sage: print CartanType(['E',8,1]).ascii_art(label = lambda x: x+1)
                O 3
                |
                |
        O---O---O---O---O---O---O---O
        2   4   5   6   7   8   9   1

  `dynkin_diagram`()

    Returns the extended Dynkin diagram for affine type E.

    EXAMPLES:

        sage: e = CartanType(['E', 6, 1]).dynkin_diagram()
        sage: e
                O 0
                |
                |
                O 2
                |
                |
        O---O---O---O---O
        1   3   4   5   6
        E6~
        sage: sorted(e.edges())
        [(0, 2, 1),
         (1, 3, 1),
         (2, 0, 1),
         (2, 4, 1),
         (3, 1, 1),
         (3, 4, 1),
         (4, 2, 1),
         (4, 3, 1),
         (4, 5, 1),
         (5, 4, 1),
         (5, 6, 1),
         (6, 5, 1)]

        sage: e = CartanType(['E', 7, 1]).dynkin_diagram()
        sage: e
                    O 2
                    |
                    |
        O---O---O---O---O---O---O
        0   1   3   4   5   6   7
        E7~
        sage: sorted(e.edges())
        [(0, 1, 1), (1, 0, 1), (1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1),
         (4, 2, 1), (4, 3, 1), (4, 5, 1), (5, 4, 1), (5, 6, 1),
         (6, 5, 1), (6, 7, 1), (7, 6, 1)]
        sage: e = CartanType(['E', 8, 1]).dynkin_diagram()
        sage: e
                O 2
                |
                |
        O---O---O---O---O---O---O---O
        1   3   4   5   6   7   8   0
        E8~
        sage: sorted(e.edges())
        [(0, 8, 1), (1, 3, 1), (2, 4, 1), (3, 1, 1), (3, 4, 1),
         (4, 2, 1), (4, 3, 1), (4, 5, 1), (5, 4, 1), (5, 6, 1),
         (6, 5, 1), (6, 7, 1), (7, 6, 1), (7, 8, 1), (8, 0, 1), (8, 7, 1)]

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