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

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# Root system data for (untwisted) type C affine

class sage.combinat.root_system.type_C_affine.CartanType(n)

  Bases: `CartanType_standard_untwisted_affine`

  EXAMPLES:

  Sage

      sage: ct = CartanType(['C',4,1])
      sage: ct
      ['C', 4, 1]
      sage: ct._repr_(compact = True)
      'C4~'

      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()
      ['C', 4]
      sage: ct.dual()
      ['C', 4, 1]^*
      sage: ct.dual().is_untwisted_affine()
      False

  Python

      >>> from sage.all import *
      >>> ct = CartanType(['C',Integer(4),Integer(1)])
      >>> ct
      ['C', 4, 1]
      >>> ct._repr_(compact = True)
      'C4~'

      >>> 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()
      ['C', 4]
      >>> ct.dual()
      ['C', 4, 1]^*
      >>> ct.dual().is_untwisted_affine()
      False

  PieriFactors

    alias of `PieriFactors_type_C_affine`

  ascii_art(label=None, node=None)

    Return a ascii art representation of the extended Dynkin diagram.

    EXAMPLES:

    Sage

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

        sage: print(CartanType(['C',3,1]).ascii_art())
        O=>=O---O=<=O
        0   1   2   3

        sage: print(CartanType(['C',2,1]).ascii_art())
        O=>=O=<=O
        0   1   2

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

    Python

        >>> from sage.all import *
        >>> print(CartanType(['C',Integer(5),Integer(1)]).ascii_art(label = lambda x: x+Integer(2)))
        O=>=O---O---O---O=<=O
        2   3   4   5   6   7

        >>> print(CartanType(['C',Integer(3),Integer(1)]).ascii_art())
        O=>=O---O=<=O
        0   1   2   3

        >>> print(CartanType(['C',Integer(2),Integer(1)]).ascii_art())
        O=>=O=<=O
        0   1   2

        >>> print(CartanType(['C',Integer(1),Integer(1)]).ascii_art())
        O<=>O
        0   1

  dynkin_diagram()

    Return the extended Dynkin diagram for affine type C.

    EXAMPLES:

    Sage

        sage: c = CartanType(['C',3,1]).dynkin_diagram(); c                         # needs sage.graphs
         O=>=O---O=<=O
         0   1   2   3
         C3~
        sage: c.edges(sort=True)                                                    # needs sage.graphs
        [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]

    Python

        >>> from sage.all import *
        >>> c = CartanType(['C',Integer(3),Integer(1)]).dynkin_diagram(); c                         # needs sage.graphs
         O=>=O---O=<=O
         0   1   2   3
         C3~
        >>> c.edges(sort=True)                                                    # needs sage.graphs
        [(0, 1, 2), (1, 0, 1), (1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]