def PentagonPoset(facade = None):
"""
Returns the Pentagon poset.
INPUT:
- ``facade`` (boolean) -- whether to make the returned poset a
facade poset (see :mod:`sage.categories.facade_sets`). The
default behaviour is the same as the default behaviour of
the :func:`~sage.combinat.posets.posets.Poset` constructor).
EXAMPLES::
sage: P = Posets.PentagonPoset(); P
Finite lattice containing 5 elements
sage: P.cover_relations()
[[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]]
This is smallest lattice that is not modular::
sage: P.is_modular()
False
This poset and the :meth:`DiamondPoset` are the two smallest
lattices which are not distributive::
sage: P.is_distributive()
False
sage: Posets.DiamondPoset(5).is_distributive()
False
"""
p = LatticePoset([[1,2],[4],[3],[4],[]], facade = facade)
p.hasse_diagram()._pos = {0:[2,0],1:[0,2],2:[3,1],3:[3,3],4:[2,4]}
return p
def PentagonPoset(facade=False):
"""
Returns the "pentagon poset".
EXAMPLES::
sage: P = Posets.PentagonPoset(); P
Finite lattice containing 5 elements
sage: P.cover_relations()
[[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]]
This lattice and the diamond poset on 5 elements are the two
smallest lattices which are not distributive::
sage: P.is_distributive()
False
sage: Posets.DiamondPoset(5).is_distributive()
False
"""
p = LatticePoset([[1, 2], [4], [3], [4], []], facade=facade)
p.hasse_diagram()._pos = {
0: [2, 0],
1: [0, 2],
2: [3, 1],
3: [3, 3],
4: [2, 4]
}
return p
def PentagonPoset(facade = None):
"""
Returns the Pentagon poset.
INPUT:
- ``facade`` (boolean) -- whether to make the returned poset a
facade poset (see :mod:`sage.categories.facade_sets`). The
default behaviour is the same as the default behaviour of
the :func:`~sage.combinat.posets.posets.Poset` constructor).
EXAMPLES::
sage: P = Posets.PentagonPoset(); P
Finite lattice containing 5 elements
sage: P.cover_relations()
[[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]]
This is smallest lattice that is not modular::
sage: P.is_modular()
False
This poset and the :meth:`DiamondPoset` are the two smallest
lattices which are not distributive::
sage: P.is_distributive()
False
sage: Posets.DiamondPoset(5).is_distributive()
False
"""
p = LatticePoset([[1,2],[4],[3],[4],[]], facade = facade)
p.hasse_diagram()._pos = {0:[2,0],1:[0,2],2:[3,1],3:[3,3],4:[2,4]}
return p
def PentagonPoset(facade = False):
"""
Returns the "pentagon poset".
EXAMPLES::
sage: P = Posets.PentagonPoset(); P
Finite lattice containing 5 elements
sage: P.cover_relations()
[[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]]
This lattice and the diamond poset on 5 elements are the two
smallest lattices which are not distributive::
sage: P.is_distributive()
False
sage: Posets.DiamondPoset(5).is_distributive()
False
"""
p = LatticePoset([[1,2],[4],[3],[4],[]], facade = facade)
p.hasse_diagram()._pos = {0:[2,0],1:[0,2],2:[3,1],3:[3,3],4:[2,4]}
return p
