Root system data for (untwisted) type G affine - Combinatorics

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# Root system data for (untwisted) type G affine

class sage.combinat.root_system.type_G_affine.CartanType

  Bases: `CartanType_standard_untwisted_affine`

  EXAMPLES:

  Sage

      sage: ct = CartanType(['G',2,1])
      sage: ct
      ['G', 2, 1]
      sage: ct._repr_(compact = True)
      'G2~'

      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()
      ['G', 2]
      sage: ct.dual()
      ['G', 2, 1]^*
      sage: ct.dual().is_untwisted_affine()
      False

  Python

      >>> from sage.all import *
      >>> ct = CartanType(['G',Integer(2),Integer(1)])
      >>> ct
      ['G', 2, 1]
      >>> ct._repr_(compact = True)
      'G2~'

      >>> ct.is_irreducible()
      True
      >>> ct.is_finite()
      False
      >>> ct.is_affine()
      True
      >>> ct.is_untwisted_affine()
      True
      >>> ct.is_crystallographic()
      True
      >>> ct.is_simply_laced()
      False
      >>> ct.classical()
      ['G', 2]
      >>> ct.dual()
      ['G', 2, 1]^*
      >>> ct.dual().is_untwisted_affine()
      False

  ascii_art(label=None, node=None)

    Return an ascii art representation of the Dynkin diagram.

    EXAMPLES:

    Sage

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

    Python

        >>> from sage.all import *
        >>> print(CartanType(['G',Integer(2),Integer(1)]).ascii_art(label = lambda x: x+Integer(2)))
          3
        O=<=O---O
        3   4   2

  dynkin_diagram()

    Return the extended Dynkin diagram for type G.

    EXAMPLES:

    Sage

        sage: g = CartanType(['G',2,1]).dynkin_diagram(); g                         # needs sage.graphs
          3
        O=<=O---O
        1   2   0
        G2~
        sage: g.edges(sort=True)                                                    # needs sage.graphs
        [(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 3)]

    Python

        >>> from sage.all import *
        >>> g = CartanType(['G',Integer(2),Integer(1)]).dynkin_diagram(); g                         # needs sage.graphs
          3
        O=<=O---O
        1   2   0
        G2~
        >>> g.edges(sort=True)                                                    # needs sage.graphs
        [(0, 2, 1), (1, 2, 1), (2, 0, 1), (2, 1, 3)]