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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Hasse diagrams of posets

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Finite semilattices and lattices

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