def __classcall_private__(cls, arg0, cartan_type=None, kac_moody=True):
"""
Parse input to ensure a unique representation.
INPUT:
- ``arg0`` -- a simple Lie algebra or a base ring
- ``cartan_type`` -- a Cartan type
EXAMPLES::
sage: L1 = lie_algebras.Affine(QQ, ['A',4,1])
sage: cl = lie_algebras.sl(QQ, 5)
sage: L2 = lie_algebras.Affine(cl)
sage: L1 is L2
True
sage: cl.affine() is L1
True
"""
if isinstance(arg0, LieAlgebra):
ct = arg0.cartan_type()
if not ct.is_finite():
raise ValueError("the base Lie algebra is not simple")
cartan_type = ct.affine()
g = arg0
else:
# arg0 is the base ring
cartan_type = CartanType(cartan_type)
if not cartan_type.is_affine():
raise ValueError("the Cartan type must be affine")
g = LieAlgebra(arg0, cartan_type=cartan_type.classical())
if not cartan_type.is_untwisted_affine():
raise NotImplementedError("only currently implemented for untwisted affine types")
return super(AffineLieAlgebra, cls).__classcall__(cls, g, kac_moody)
def __classcall_private__(cls, arg0, cartan_type=None, kac_moody=True):
"""
Parse input to ensure a unique representation.
INPUT:
- ``arg0`` -- a simple Lie algebra or a base ring
- ``cartan_type`` -- a Cartan type
EXAMPLES::
sage: L1 = lie_algebras.Affine(QQ, ['A',4,1])
sage: cl = lie_algebras.sl(QQ, 5)
sage: L2 = lie_algebras.Affine(cl)
sage: L1 is L2
True
sage: cl.affine() is L1
True
"""
if isinstance(arg0, LieAlgebra):
ct = arg0.cartan_type()
if not ct.is_finite():
raise ValueError("the base Lie algebra is not simple")
cartan_type = ct.affine()
g = arg0
else:
# arg0 is the base ring
cartan_type = CartanType(cartan_type)
if not cartan_type.is_affine():
raise ValueError("the Cartan type must be affine")
g = LieAlgebra(arg0, cartan_type=cartan_type.classical())
if not cartan_type.is_untwisted_affine():
raise NotImplementedError("only currently implemented for untwisted affine types")
return super(AffineLieAlgebra, cls).__classcall__(cls, g, kac_moody)
