def __init__(self, cartan_type):
"""
TESTS::
sage: from sage.libs.coxeter3.coxeter_group import CoxeterGroup # optional - coxeter3
sage: CoxeterGroup(['A',2]) # optional - coxeter3
Coxeter group of type ['A', 2] implemented by Coxeter3
sage: TestSuite(CoxeterGroup(['A',2])).run() # optional - coxeter3
"""
category = CoxeterGroups()
if cartan_type.is_finite():
category = category.Finite()
Parent.__init__(self, category=category)
self._coxgroup = get_CoxGroup(cartan_type)
self._cartan_type = cartan_type
def __classcall_private__(cls, W, q1, q2=-1, base_ring=None, prefix="T"):
"""
TESTS::
sage: H = IwahoriHeckeAlgebraT("A2", 1)
sage: H.coxeter_group() == WeylGroup("A2")
True
sage: H.cartan_type() == CartanType("A2")
True
sage: H.base_ring() == ZZ
True
sage: H._q2 == -1
True
"""
if W not in CoxeterGroups():
W = WeylGroup(W)
if base_ring is None:
base_ring = q1.parent()
q2 = base_ring(q2)
return super(IwahoriHeckeAlgebraT,
cls).__classcall__(cls,
W,
q1=q1,
q2=q2,
base_ring=base_ring,
prefix=prefix)
def __init__(self, cartan_type):
"""
TESTS::
sage: from sage.libs.coxeter3.coxeter_group import CoxeterGroup # optional - coxeter3
sage: CoxeterGroup(['A',2]) # optional - coxeter3
Coxeter group of type ['A', 2] implemented by Coxeter3
As degrees and codegrees are not implemented, they are skipped in the
testsuite::
sage: to_skip = ['_test_degrees', '_test_codegrees']
sage: TestSuite(CoxeterGroup(['A',2])).run(skip=to_skip) # optional - coxeter3
"""
category = CoxeterGroups()
if cartan_type.is_finite():
category = category.Finite()
Parent.__init__(self, category=category)
self._coxgroup = get_CoxGroup(cartan_type)
self._cartan_type = cartan_type