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# Root system data for type H

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

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

  EXAMPLES:

      sage: ct = CartanType(['H',3])
      sage: ct
      ['H', 3]
      sage: ct._repr_(compact = True)
      'H3'
      sage: ct.rank()
      3

      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 a Coxeter diagram for type H.

    EXAMPLES:

        sage: ct = CartanType(['H',3])
        sage: ct.coxeter_diagram()
        Graph on 3 vertices
        sage: sorted(ct.coxeter_diagram().edges())
        [(1, 2, 3), (2, 3, 5)]
        sage: ct.coxeter_matrix()
        [1 3 2]
        [3 1 5]
        [2 5 1]

        sage: ct = CartanType(['H',4])
        sage: ct.coxeter_diagram()
        Graph on 4 vertices
        sage: sorted(ct.coxeter_diagram().edges())
        [(1, 2, 3), (2, 3, 3), (3, 4, 5)]
        sage: ct.coxeter_matrix()
        [1 3 2 2]
        [3 1 3 2]
        [2 3 1 5]
        [2 2 5 1]

  `coxeter_number`()

    Return the Coxeter number associated with `self`.

    EXAMPLES:

        sage: CartanType(['H',3]).coxeter_number()
        10
        sage: CartanType(['H',4]).coxeter_number()
        30

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