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# Root system data for type I

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

  Bases: `sage.combinat.root_system.cartan_type.CartanType_standard_finite`, `sage.combinat.root_system.cartan_type.CartanType_simple`

  EXAMPLES:

      sage: ct = CartanType(['I',5])
      sage: ct
      ['I', 5]
      sage: ct._repr_(compact = True)
      'I5'
      sage: ct.rank()
      2
      sage: ct.index_set()
      [1, 2]

      sage: ct.is_irreducible()
      True
      sage: ct.is_finite()
      True
      sage: ct.is_affine()
      False
      sage: ct.is_crystallographic()
      False
      sage: ct.is_simply_laced()
      False

  TESTS:

      sage: TestSuite(ct).run()

  `coxeter_diagram`()

    Returns the Coxeter matrix for this type.

    EXAMPLES:

        sage: ct = CartanType(['I', 4])
        sage: ct.coxeter_diagram()
        Graph on 2 vertices
        sage: ct.coxeter_diagram().edges()
        [(1, 2, 4)]
        sage: ct.coxeter_matrix()
        [1 4]
        [4 1]

  `coxeter_number`()

    Return the Coxeter number associated with `self`.

    EXAMPLES:

        sage: CartanType(['I',3]).coxeter_number()
        3
        sage: CartanType(['I',12]).coxeter_number()
        12

  `index_set`()

    Type \(I_p\) is of rank 2

    EXAMPLES::
      sage: CartanType([‘I’, 5]).index_set() [1, 2]
  `rank`()

    Type \(I_p\) is of rank 2

    EXAMPLES::
      sage: CartanType([‘I’, 5]).rank() 2

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