def cartan_type(self):
r"""
Return the Cartan type of ``self``.
EXAMPLES::
sage: W = ReflectionGroup(['A',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
['A', 3]
sage: W = ReflectionGroup(['A',3], ['B',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
A3xB3 relabelled by {1: 3, 2: 2, 3: 1}
TESTS:
Check that dihedral types are handled properly::
sage: W = ReflectionGroup(['I',3]); W # optional - gap3
Irreducible real reflection group of rank 2 and type A2
sage: W = ReflectionGroup(['I',4]); W # optional - gap3
Irreducible real reflection group of rank 2 and type C2
sage: W = ReflectionGroup(['I',5]); W # optional - gap3
Irreducible real reflection group of rank 2 and type I2(5)
"""
if len(self._type) == 1:
ct = self._type[0]
if ct['series'] == "I":
C = CartanType([ct['series'], ct['bond']])
else:
C = CartanType([ct['series'], ct['rank']])
CG = C.coxeter_diagram()
G = self.coxeter_diagram()
return C.relabel(
CG.is_isomorphic(G, edge_labels=True, certificate=True)[1])
else:
return CartanType(
[W.cartan_type() for W in self.irreducible_components()])
def cartan_type(self):
r"""
Return the Cartan type of ``self``.
EXAMPLES::
sage: W = ReflectionGroup(['A',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
['A', 3]
sage: W = ReflectionGroup(['A',3], ['B',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
A3xB3 relabelled by {1: 3, 2: 2, 3: 1}
"""
if len(self._type) == 1:
ct = self._type[0]
C = CartanType([ct['series'], ct['rank']])
CG = C.coxeter_diagram()
G = self.coxeter_diagram()
return C.relabel(CG.is_isomorphic(G, edge_labels=True, certificate=True)[1])
else:
return CartanType([W.cartan_type() for W in self.irreducible_components()])
def cartan_type(self):
r"""
Return the Cartan type of ``self``.
EXAMPLES::
sage: W = ReflectionGroup(['A',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
['A', 3]
sage: W = ReflectionGroup(['A',3], ['B',3]) # optional - gap3
sage: W.cartan_type() # optional - gap3
A3xB3 relabelled by {1: 3, 2: 2, 3: 1}
"""
if len(self._type) == 1:
ct = self._type[0]
C = CartanType([ct['series'], ct['rank']])
CG = C.coxeter_diagram()
G = self.coxeter_diagram()
return C.relabel(CG.is_isomorphic(G, edge_labels=True, certificate=True)[1])
else:
return CartanType([W.cartan_type() for W in self.irreducible_components()])
