def LatticePoset(data, *args, **options):
r"""
Construct a lattice from various forms of input data.
INPUT:
- ``data``, ``*args``, ``**options`` -- data and options that will
be passed down to :func:`Poset` to construct a poset that is
also a lattice.
OUTPUT:
FiniteLatticePoset -- an instance of :class:`FiniteLatticePoset`
.. seealso:: :class:`Posets`, :class:`FiniteLatticePosets`, :func:`JoinSemiLattice`, :func:`MeetSemiLattice`
EXAMPLES:
Using data that defines a poset::
sage: LatticePoset([[1,2],[3],[3]])
Finite lattice containing 4 elements
sage: LatticePoset([[1,2],[3],[3]], cover_relations = True)
Finite lattice containing 4 elements
Using a previously constructed poset::
sage: P = Poset([[1,2],[3],[3]])
sage: L = LatticePoset(P); L
Finite lattice containing 4 elements
sage: type(L)
<class 'sage.combinat.posets.lattices.FiniteLatticePoset_with_category'>
If the data is not a lattice, then an error is raised::
sage: elms = [1,2,3,4,5,6,7]
sage: rels = [[1,2],[3,4],[4,5],[2,5]]
sage: LatticePoset((elms, rels))
Traceback (most recent call last):
...
ValueError: Not a lattice.
Creating a facade lattice::
sage: L = LatticePoset([[1,2],[3],[3]], facade = True)
sage: L.category()
Category of facade finite lattice posets
sage: parent(L[0])
Integer Ring
sage: TestSuite(L).run(skip = ['_test_an_element']) # is_parent_of is not yet implemented
"""
if isinstance(data,FiniteLatticePoset) and len(args) == 0 and len(options) == 0:
return data
P = Poset(data, *args, **options)
if not P.is_lattice():
raise ValueError, "Not a lattice."
return FiniteLatticePoset(P, category = FiniteLatticePosets(), facade = P._is_facade)
def LatticePoset(data, *args, **options):
r"""
Construct a lattice from various forms of input data.
INPUT:
- ``data``, ``*args``, ``**options`` -- data and options that will
be passed down to :func:`Poset` to construct a poset that is
also a lattice.
OUTPUT:
FiniteLatticePoset -- an instance of :class:`FiniteLatticePoset`
.. seealso:: :class:`Posets`, :class:`FiniteLatticePosets`, :func:`JoinSemiLattice`, :func:`MeetSemiLattice`
EXAMPLES:
Using data that defines a poset::
sage: LatticePoset([[1,2],[3],[3]])
Finite lattice containing 4 elements
sage: LatticePoset([[1,2],[3],[3]], cover_relations = True)
Finite lattice containing 4 elements
Using a previously constructed poset::
sage: P = Poset([[1,2],[3],[3]])
sage: L = LatticePoset(P); L
Finite lattice containing 4 elements
sage: type(L)
<class 'sage.combinat.posets.lattices.FiniteLatticePoset_with_category'>
If the data is not a lattice, then an error is raised::
sage: elms = [1,2,3,4,5,6,7]
sage: rels = [[1,2],[3,4],[4,5],[2,5]]
sage: LatticePoset((elms, rels))
Traceback (most recent call last):
...
ValueError: Not a lattice.
Creating a facade lattice::
sage: L = LatticePoset([[1,2],[3],[3]], facade = True)
sage: L.category()
Join of Category of finite lattice posets and Category of finite enumerated sets and Category of facade sets
sage: parent(L[0])
Integer Ring
sage: TestSuite(L).run(skip = ['_test_an_element']) # is_parent_of is not yet implemented
"""
if isinstance(data,FiniteLatticePoset) and len(args) == 0 and len(options) == 0:
return data
P = Poset(data, *args, **options)
if not P.is_lattice():
raise ValueError("Not a lattice.")
return FiniteLatticePoset(P, category = FiniteLatticePosets(), facade = P._is_facade)
