def __init__(self, m, n):
"""
Initialize ``self``.
EXAMPLES::
sage: C = ColoredPermutations(4, 3)
sage: TestSuite(C).run()
sage: C = ColoredPermutations(2, 3)
sage: TestSuite(C).run()
sage: C = ColoredPermutations(1, 3)
sage: TestSuite(C).run()
"""
if m <= 0:
raise ValueError("m must be a positive integer")
self._m = ZZ(m)
self._n = ZZ(n)
self._C = IntegerModRing(self._m)
self._P = Permutations(self._n)
if self._m == 1 or self._m == 2:
from sage.categories.finite_coxeter_groups import FiniteCoxeterGroups
category = FiniteCoxeterGroups().Irreducible()
else:
from sage.categories.complex_reflection_groups import ComplexReflectionGroups
category = ComplexReflectionGroups().Finite().Irreducible(
).WellGenerated()
Parent.__init__(self, category=category)
def __init__(self, cartan_type):
"""
Construct this Coxeter group as a Sage permutation group, by
fetching the permutation representation of the generators from
Chevie's database.
TESTS::
sage: from sage.combinat.root_system.coxeter_group import CoxeterGroupAsPermutationGroup
sage: W = CoxeterGroupAsPermutationGroup(CartanType(["H",3])) # optional - chevie
sage: TestSuite(W).run() # optional - chevie
"""
assert cartan_type.is_finite()
assert cartan_type.is_irreducible()
self._semi_simple_rank = cartan_type.n
from sage.interfaces.gap3 import gap3
gap3._start()
gap3.load_package("chevie")
self._gap_group = gap3('CoxeterGroup("%s",%s)' %
(cartan_type.letter, cartan_type.n))
# Following #9032, x.N is an alias for x.numerical_approx in every Sage object ...
N = self._gap_group.__getattr__("N").sage()
generators = [str(x) for x in self._gap_group.generators]
self._is_positive_root = [None] + [True] * N + [False] * N
PermutationGroup_generic.__init__(self,
gens=generators,
category=Category.join([
FinitePermutationGroups(),
FiniteCoxeterGroups()
]))
def super_categories(self):
r"""
EXAMPLES::
sage: FiniteWeylGroups().super_categories()
[Category of weyl groups, Category of finite coxeter groups]
"""
return [WeylGroups(), FiniteCoxeterGroups()]
def __init__(self, n):
"""
Initialize ``self``.
EXAMPLES::
sage: S = SignedPermutations(4)
sage: TestSuite(S).run()
"""
ColoredPermutations.__init__(self, 2, n, FiniteCoxeterGroups())