def is_canonical(self, v, check=True):
r"""
Returns ``True`` if the integer list ``v`` is maximal in its
orbit under the action of the permutation group given to
define ``self``. Such integer vectors are said to be
canonical. A vector `v` is canonical if and only if
.. MATH::
v = \max_{\text{lex order}} \{g \cdot v | g \in G \}
EXAMPLES::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), max_part=3)
sage: I.is_canonical([3,0,0,0])
True
sage: I.is_canonical([1,0,2,0])
False
sage: I.is_canonical([2,0,1,0])
True
"""
if check:
assert isinstance(
v, (ClonableIntArray,
list)), '%s should be a list or a integer vector' % v
assert (
self.n == len(v)), '%s should be of length %s' % (v, self.n)
for p in v:
assert (p == NN(p)), 'Elements of %s should be integers' % v
return is_canonical(self._sgs,
self.element_class(self, list(v), check=False))
def is_canonical(self, v, check=True):
r"""
Returns ``True`` if the integer list ``v`` is maximal in its
orbit under the action of the permutation group given to
define ``self``. Such integer vectors are said to be
canonical. A vector `v` is canonical if and only if
.. math::
v = \max_{\text{lex order}} \{g \cdot v | g \in G \}
EXAMPLES::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3,4)]]), max_part=3)
sage: I.is_canonical([3,0,0,0])
True
sage: I.is_canonical([1,0,2,0])
False
sage: I.is_canonical([2,0,1,0])
True
"""
if check:
assert isinstance(v, (ClonableIntArray, list)), '%s should be a list or a integer vector'%v
assert (self.n == len(v)), '%s should be of length %s'%(v, self.n)
for p in v:
assert (p == NN(p)), 'Elements of %s should be integers'%s
return is_canonical(self._sgs, self.element_class(self, list(v), check=False))
