def retract(self, elt):
r"""
Return the canonical representative of the orbit of the
integer ``elt`` under the action of the permutation group
defining ``self``.
If the element ``elt`` is already maximal in its orbits for
the lexicographic order, ``elt`` is thus the good
representative for its orbit.
EXAMPLES::
sage: S = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), sum=2, max_part=1)
sage: S.retract([1,1,0,0])
[1, 1, 0, 0]
sage: S.retract([1,0,1,0])
[1, 0, 1, 0]
sage: S.retract([1,0,0,1])
[1, 1, 0, 0]
sage: S.retract([0,1,1,0])
[1, 1, 0, 0]
sage: S.retract([0,1,0,1])
[1, 0, 1, 0]
sage: S.retract([0,0,1,1])
[1, 1, 0, 0]
"""
# TODO: Once Sage integer vector will have a data structure
# based on ClonableIntArray, remove the conversion intarray
assert len(elt) == self.n, "%s is a quotient set of %s"%(self, self.ambient())
if self._sum is not None:
assert sum(elt) == self._sum, "%s is a quotient set of %s"%(self, self.ambient())
if self._max_part >= 0:
assert max(elt) <= self._max_part, "%s is a quotient set of %s"%(self, self.ambient())
intarray = self.element_class(self, elt, check=False)
return self.element_class(self, canonical_representative_of_orbit_of(self._sgs, intarray), check=False)
def retract(self, elt):
r"""
Return the canonical representative of the orbit of the
integer ``elt`` under the action of the permutation group
defining ``self``.
If the element ``elt`` is already maximal in its orbits for
the lexicographic order, ``elt`` is thus the good
representative for its orbit.
EXAMPLES::
sage: S = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), sum=2, max_part=1)
sage: S.retract([1,1,0,0])
[1, 1, 0, 0]
sage: S.retract([1,0,1,0])
[1, 0, 1, 0]
sage: S.retract([1,0,0,1])
[1, 1, 0, 0]
sage: S.retract([0,1,1,0])
[1, 1, 0, 0]
sage: S.retract([0,1,0,1])
[1, 0, 1, 0]
sage: S.retract([0,0,1,1])
[1, 1, 0, 0]
"""
# TODO: Once Sage integer vector will have a data structure
# based on ClonableIntArray, remove the conversion intarray
assert len(elt) == self.n, "%s is a quotient set of %s"%(self, self.ambient())
if self._sum is not None:
assert sum(elt) == self._sum, "%s is a quotient set of %s"%(self, self.ambient())
if self._max_part >= 0:
assert max(elt) <= self._max_part, "%s is a quotient set of %s"%(self, self.ambient())
intarray = self.element_class(self, elt, check=False)
return self.element_class(self, canonical_representative_of_orbit_of(self._sgs, intarray), check=False)
