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# Elements of posets, lattices, semilattices, etc.

class `sage.combinat.posets.elements.``JoinSemilatticeElement`(poset, element, vertex)

  Bases: `sage.combinat.posets.elements.PosetElement`

  Establishes the parent-child relationship between `poset` and `element`, where `element` is associated to the vertex `vertex` of the Hasse diagram of the poset.

  INPUT:

  - `poset` - a poset object
  - `element` - any object
  - `vertex` - a vertex of the Hasse diagram of the poset

  TESTS:

      sage: from sage.combinat.posets.elements import PosetElement
      sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False)
      sage: e = P(0)
      sage: e.parent() is P
      True
      sage: TestSuite(e).run()

class `sage.combinat.posets.elements.``LatticePosetElement`(poset, element, vertex)

  Bases: `sage.combinat.posets.elements.MeetSemilatticeElement`, `sage.combinat.posets.elements.JoinSemilatticeElement`

  Establishes the parent-child relationship between `poset` and `element`, where `element` is associated to the vertex `vertex` of the Hasse diagram of the poset.

  INPUT:

  - `poset` - a poset object
  - `element` - any object
  - `vertex` - a vertex of the Hasse diagram of the poset

  TESTS:

      sage: from sage.combinat.posets.elements import PosetElement
      sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False)
      sage: e = P(0)
      sage: e.parent() is P
      True
      sage: TestSuite(e).run()

class `sage.combinat.posets.elements.``MeetSemilatticeElement`(poset, element, vertex)

  Bases: `sage.combinat.posets.elements.PosetElement`

  Establishes the parent-child relationship between `poset` and `element`, where `element` is associated to the vertex `vertex` of the Hasse diagram of the poset.

  INPUT:

  - `poset` - a poset object
  - `element` - any object
  - `vertex` - a vertex of the Hasse diagram of the poset

  TESTS:

      sage: from sage.combinat.posets.elements import PosetElement
      sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False)
      sage: e = P(0)
      sage: e.parent() is P
      True
      sage: TestSuite(e).run()

class `sage.combinat.posets.elements.``PosetElement`(poset, element, vertex)

  Bases: `sage.structure.element.Element`

  Establishes the parent-child relationship between `poset` and `element`, where `element` is associated to the vertex `vertex` of the Hasse diagram of the poset.

  INPUT:

  - `poset` - a poset object
  - `element` - any object
  - `vertex` - a vertex of the Hasse diagram of the poset

  TESTS:

      sage: from sage.combinat.posets.elements import PosetElement
      sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False)
      sage: e = P(0)
      sage: e.parent() is P
      True
      sage: TestSuite(e).run()

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