def children(self, x):
r"""
Returns the list of children of the element ``x``. This method
is required to build the tree structure of ``self`` which
inherits from the class :class:`~sage.combinat.backtrack.SearchForest`.
EXAMPLES::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]))
sage: I.children(I([2,1,0,0], check=False))
[[2, 2, 0, 0], [2, 1, 1, 0], [2, 1, 0, 1]]
"""
return canonical_children(self._sgs, x, -1)
def children(self, x):
r"""
Returns the list of children of the element ``x``. This method
is required to build the tree structure of ``self`` which
inherits from the class :class:`~sage.sets.recursively_enumerated_set.RecursivelyEnumeratedSet_forest`.
EXAMPLES::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]))
sage: I.children(I([2,1,0,0], check=False))
[[2, 2, 0, 0], [2, 1, 1, 0], [2, 1, 0, 1]]
"""
return canonical_children(self._sgs, x, -1)
def children(self, x):
r"""
Returns the list of children of the element ``x``. This method
is required to build the tree structure of ``self`` which
inherits from the class :class:`~sage.combinat.backtrack.SearchForest`.
EXAMPLES::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]))
sage: I.children(I([2,1,0,0], check=False))
[[2, 2, 0, 0], [2, 1, 1, 0], [2, 1, 0, 1]]
"""
return canonical_children(self._sgs, x, -1)
def __iter__(self):
r"""
TESTS::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]),4)
sage: for i in I: i
[4, 0, 0, 0]
[3, 1, 0, 0]
[3, 0, 1, 0]
[3, 0, 0, 1]
[2, 2, 0, 0]
[2, 1, 1, 0]
[2, 1, 0, 1]
[2, 0, 2, 0]
[2, 0, 1, 1]
[1, 1, 1, 1]
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), sum=7, max_part=3)
sage: for i in I: i
[3, 3, 1, 0]
[3, 3, 0, 1]
[3, 2, 2, 0]
[3, 2, 1, 1]
[3, 2, 0, 2]
[3, 1, 3, 0]
[3, 1, 2, 1]
[3, 1, 1, 2]
[3, 0, 2, 2]
[2, 2, 2, 1]
"""
if self._max_part < 0:
return self.elements_of_depth_iterator(self._sum)
else:
SF = SearchForest(
(self([0] * (self.n), check=False), ),
lambda x: [
self(y, check=False)
for y in canonical_children(self._sgs, x, self._max_part)
],
algorithm='breadth')
if self._sum is None:
return iter(SF)
else:
return SF.elements_of_depth_iterator(self._sum)
def __iter__(self):
r"""
TESTS::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]),4)
sage: for i in I: i
[4, 0, 0, 0]
[3, 1, 0, 0]
[3, 0, 1, 0]
[3, 0, 0, 1]
[2, 2, 0, 0]
[2, 1, 1, 0]
[2, 1, 0, 1]
[2, 0, 2, 0]
[2, 0, 1, 1]
[1, 1, 1, 1]
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), sum=7, max_part=3)
sage: for i in I: i
[3, 3, 1, 0]
[3, 3, 0, 1]
[3, 2, 2, 0]
[3, 2, 1, 1]
[3, 2, 0, 2]
[3, 1, 3, 0]
[3, 1, 2, 1]
[3, 1, 1, 2]
[3, 0, 2, 2]
[2, 2, 2, 1]
"""
if self._max_part < 0:
return self.elements_of_depth_iterator(self._sum)
else:
SF = SearchForest(
(self([0] * (self.n), check=False),),
lambda x: map(lambda y: self(y, check=False), canonical_children(self._sgs, x, self._max_part)),
algorithm="breadth",
)
if self._sum is None:
return iter(SF)
else:
return SF.elements_of_depth_iterator(self._sum)