Elements of posets, lattices, semilattices, etc.¶
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class
sage.combinat.posets.elements.
JoinSemilatticeElement
(poset, element, vertex)¶ Bases:
sage.combinat.posets.elements.PosetElement
Establishes the parent-child relationship between
poset
andelement
, whereelement
is associated to the vertexvertex
of the Hasse diagram of the poset.INPUT:
poset
- a poset objectelement
- any objectvertex
- 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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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
andelement
, whereelement
is associated to the vertexvertex
of the Hasse diagram of the poset.INPUT:
poset
- a poset objectelement
- any objectvertex
- 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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class
sage.combinat.posets.elements.
MeetSemilatticeElement
(poset, element, vertex)¶ Bases:
sage.combinat.posets.elements.PosetElement
Establishes the parent-child relationship between
poset
andelement
, whereelement
is associated to the vertexvertex
of the Hasse diagram of the poset.INPUT:
poset
- a poset objectelement
- any objectvertex
- 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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class
sage.combinat.posets.elements.
PosetElement
(poset, element, vertex)¶ Bases:
sage.structure.element.Element
Establishes the parent-child relationship between
poset
andelement
, whereelement
is associated to the vertexvertex
of the Hasse diagram of the poset.INPUT:
poset
- a poset objectelement
- any objectvertex
- 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()