def orbit(self, v):
r"""
Returns the orbit of the vector ``v`` under the action of the
permutation group defining ``self``. The result is a set.
INPUT:
- ``v`` - an element of ``self`` or any list of length the
degree of the permutation group.
EXAMPLES:
We convert the result in a list in increasing lexicographic
order, to get a reproducible doctest::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]),4)
sage: I.orbit([1,1,1,1])
{[1, 1, 1, 1]}
sage: sorted(I.orbit([3,0,0,1]))
[[0, 0, 1, 3], [0, 1, 3, 0], [1, 3, 0, 0], [3, 0, 0, 1]]
"""
assert isinstance(
v,
(list, ClonableIntArray
)), '%s should be a Python list or an element of %s' % (v, self)
try:
if v.parent() is self:
return orbit(self._sgs, v)
except Exception:
return orbit(self._sgs, self.element_class(self, v, check=False))
def orbit(self, v):
r"""
Returns the orbit of the vector ``v`` under the action of the
permutation group defining ``self``. The result is a set.
INPUT:
- ``v`` - an element of ``self`` or any list of length the
degree of the permutation group.
EXAMPLES:
We convert the result in a list in increasing lexicographic
order, to get a reproducible doctest::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]),4)
sage: I.orbit([1,1,1,1])
{[1, 1, 1, 1]}
sage: sorted(I.orbit([3,0,0,1]))
[[0, 0, 1, 3], [0, 1, 3, 0], [1, 3, 0, 0], [3, 0, 0, 1]]
"""
assert isinstance(v, (list, ClonableIntArray)), '%s shoud be a Python list or an element of %s'%(v, self)
try:
if v.parent() is self:
return orbit(self._sgs, v)
except Exception:
return orbit(self._sgs, self.element_class(self, v, check=False))
def orbit(self, v):
r"""
Returns the orbit of the integer vector ``v`` under the action of the
permutation group defining ``self``. The result is a set.
EXAMPLES:
In order to get reproducible doctests, we convert the returned sets
into lists in increasing lexicographic order::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]))
sage: sorted(I.orbit([2,2,0,0]))
[[0, 0, 2, 2], [0, 2, 2, 0], [2, 0, 0, 2], [2, 2, 0, 0]]
sage: sorted(I.orbit([2,1,0,0]))
[[0, 0, 2, 1], [0, 2, 1, 0], [1, 0, 0, 2], [2, 1, 0, 0]]
sage: sorted(I.orbit([2,0,1,0]))
[[0, 1, 0, 2], [0, 2, 0, 1], [1, 0, 2, 0], [2, 0, 1, 0]]
sage: sorted(I.orbit([2,0,2,0]))
[[0, 2, 0, 2], [2, 0, 2, 0]]
sage: I.orbit([1,1,1,1])
{[1, 1, 1, 1]}
"""
assert isinstance(
v,
(list, ClonableIntArray
)), '%s should be a Python list or an element of %s' % (v, self)
try:
if v.parent() is self:
return orbit(self._sgs, v)
raise TypeError
except Exception:
return orbit(self._sgs, self.element_class(self, v, check=False))
def orbit(self, v):
r"""
Returns the orbit of the integer vector ``v`` under the action of the
permutation group defining ``self``. The result is a set.
EXAMPLES:
In order to get reproducible doctests, we convert the returned sets
into lists in increasing lexicographic order::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]))
sage: sorted(I.orbit([2,2,0,0]))
[[0, 0, 2, 2], [0, 2, 2, 0], [2, 0, 0, 2], [2, 2, 0, 0]]
sage: sorted(I.orbit([2,1,0,0]))
[[0, 0, 2, 1], [0, 2, 1, 0], [1, 0, 0, 2], [2, 1, 0, 0]]
sage: sorted(I.orbit([2,0,1,0]))
[[0, 1, 0, 2], [0, 2, 0, 1], [1, 0, 2, 0], [2, 0, 1, 0]]
sage: sorted(I.orbit([2,0,2,0]))
[[0, 2, 0, 2], [2, 0, 2, 0]]
sage: I.orbit([1,1,1,1])
{[1, 1, 1, 1]}
"""
assert isinstance(v, (list, ClonableIntArray)), '%s shoud be a Python list or an element of %s'%(v, self)
try:
if v.parent() is self:
return orbit(self._sgs, v)
raise TypeError
except Exception:
return orbit(self._sgs, self.element_class(self, v, check=False))