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 __classcall__(cls, G, sum=None, max_part=None, sgs=None):
r"""
TESTS::
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3)]]))
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3)]]), None)
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3)]]), 2)
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3)]]), -2)
Traceback (most recent call last):
...
ValueError: Value -2 in not in Non negative integer semiring.
sage: I = IntegerVectorsModPermutationGroup(PermutationGroup([[(1,2,3)]]), 8, max_part=5)
"""
if sum is None and max_part is None:
return IntegerVectorsModPermutationGroup_All(G, sgs=sgs)
else:
if sum is not None:
assert (sum == NN(sum))
if max_part is not None:
assert (max_part == NN(max_part))
return IntegerVectorsModPermutationGroup_with_constraints(G, sum, max_part, sgs=sgs)
