def to_poset(self, root_to_leaf=False):
r"""
Return the poset obtained by interpreting the tree as a hasse
diagram. The default orientation is from leaves to root but you can
pass ``root_to_leaf=True`` to obtain the inverse orientation.
INPUT:
- ``root_to_leaf`` -- boolean, true if the poset orientation should
be from root to leaves. It is false by default.
EXAMPLES::
sage: t = OrderedTree([])
sage: t.to_poset()
Finite poset containing 1 elements
sage: p = OrderedTree([[[]],[],[]]).to_poset()
sage: p.cover_relations()
[[0, 4], [1, 4], [2, 3], [3, 4]]
sage: p = OrderedTree([[[]],[],[]]).to_poset(root_to_leaf=True)
sage: p.cover_relations()
[[0, 2], [0, 3], [0, 4], [4, 1]]
If the tree is labelled, we use its labelling to label the poset.
Otherwise, we use the poset canonical labelling::
sage: t = OrderedTree([[[]],[],[]]).canonical_labelling()
sage: t
1[2[3[]], 4[], 5[]]
sage: t.to_poset().cover_relations()
[[5, 1], [4, 1], [3, 2], [2, 1]]
"""
if self in LabelledOrderedTrees():
relabel = False
else:
self = self.canonical_labelling()
relabel = True
relations = []
elements = [self.label()]
roots = [self]
while len(roots) != 0:
node = roots.pop()
for child in node:
elements.append(child.label())
relations.append((node.label(),
child.label()) if root_to_leaf else (
child.label(), node.label()))
roots.append(child)
from sage.combinat.posets.posets import Poset
p = Poset([elements, relations])
if relabel:
p = p.canonical_label()
return p
def to_poset(self, root_to_leaf = False):
r"""
Return the poset obtained by interpreting the tree as a hasse
diagram. The default orientation is from leaves to root but you can
pass ``root_to_leaf=True`` to obtain the inverse orientation.
INPUT:
- ``root_to_leaf`` -- boolean, true if the poset orientation should
be from root to leaves. It is false by default.
EXAMPLES::
sage: t = OrderedTree([])
sage: t.to_poset()
Finite poset containing 1 elements
sage: p = OrderedTree([[[]],[],[]]).to_poset()
sage: p.cover_relations()
[[3, 4], [2, 4], [0, 1], [1, 4]]
sage: p = OrderedTree([[[]],[],[]]).to_poset(root_to_leaf=True)
sage: p.cover_relations()
[[0, 1], [0, 2], [0, 3], [3, 4]]
If the tree is labelled, we use its labelling to label the poset.
Otherwise, we use the poset canonical labelling::
sage: t = OrderedTree([[[]],[],[]]).canonical_labelling()
sage: t
1[2[3[]], 4[], 5[]]
sage: t.to_poset().cover_relations()
[[5, 1], [4, 1], [3, 2], [2, 1]]
"""
if self in LabelledOrderedTrees():
relabel = False
else:
self = self.canonical_labelling()
relabel = True
relations = []
elements = [self.label()]
roots = [self]
while len(roots)!=0:
node = roots.pop()
for child in node:
elements.append(child.label())
relations.append((node.label(),child.label()) if root_to_leaf else (child.label(),node.label()))
roots.append(child)
from sage.combinat.posets.posets import Poset
p = Poset([elements, relations])
if relabel:
p = p.canonical_label()
return p
