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 is_chevie_available():
r"""
Tests whether the GAP3 Chevie package is available
EXAMPLES::
sage: from sage.combinat.root_system.coxeter_group import is_chevie_available
sage: is_chevie_available() # random
False
sage: is_chevie_available() in [True, False]
True
"""
try:
from sage.interfaces.gap3 import gap3
gap3._start()
gap3.load_package("chevie")
return True
except Exception:
return False
def is_chevie_available():
r"""
Test whether the GAP3 Chevie package is available.
EXAMPLES::
sage: from sage.combinat.root_system.reflection_group_real import is_chevie_available
sage: is_chevie_available() # random
False
sage: is_chevie_available() in [True, False]
True
"""
try:
from sage.interfaces.gap3 import gap3
gap3._start()
gap3.load_package("chevie")
return True
except Exception:
return False
