### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »
- Root Systems »
- Root System Types »

# Root system data for (untwisted) type D affine

class `sage.combinat.root_system.type_D_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(['D',4,1])
      sage: ct
      ['D', 4, 1]
      sage: ct._repr_(compact = True)
      'D4~'

      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()
      ['D', 4]
      sage: ct.dual()
      ['D', 4, 1]

  TESTS:

      sage: TestSuite(ct).run()

  `ascii_art`(label=<function <lambda> at 0xe0489294>)

    Returns a ascii art representation of the extended Dynkin diagram

    TESTS:

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

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

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

  `dynkin_diagram`()

    Returns the extended Dynkin diagram for affine type D.

    EXAMPLES:

        sage: d = CartanType(['D', 6, 1]).dynkin_diagram()
        sage: d
           0 O       O 6
             |       |
             |       |
         O---O---O---O---O
         1   2   3   4   5
         D6~
        sage: sorted(d.edges())
        [(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 1), (2, 3, 1),
         (3, 2, 1), (3, 4, 1), (4, 3, 1), (4, 5, 1), (4, 6, 1), (5, 4, 1), (6, 4, 1)]

        sage: d = CartanType(['D', 4, 1]).dynkin_diagram()
        sage: d
            O 4
            |
            |
        O---O---O
        1   |2  3
            |
            O 0
        D4~
        sage: sorted(d.edges())
        [(0, 2, 1),
         (1, 2, 1),
         (2, 0, 1),
         (2, 1, 1),
         (2, 3, 1),
         (2, 4, 1),
         (3, 2, 1),
         (4, 2, 1)]

        sage: d = CartanType(['D', 3, 1]).dynkin_diagram()
        sage: d
        0
        O-------+
        |       |
        |       |
        O---O---O
        3   1   2
        D3~
        sage: sorted(d.edges())
        [(0, 2, 1), (0, 3, 1), (1, 2, 1), (1, 3, 1), (2, 0, 1), (2, 1, 1), (3, 0, 1), (3, 1, 1)]

### Navigation

- index
- modules |
- next |
- previous |
- Combinatorics »
- Root Systems »
- Root System Types »