def __init__(self):
"""
EXAMPLES::
sage: ct = CartanType(['G',2,1])
sage: ct
['G', 2, 1]
sage: ct._repr_(compact = True)
'G2~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystalographic()
True
sage: ct.is_simply_laced()
False
sage: ct.classical()
['G', 2]
sage: ct.dual()
['G', 2, 1]^*
sage: ct.dual().is_untwisted_affine()
False
TESTS::
sage: ct == loads(dumps(ct))
True
"""
CartanType_standard_untwisted_affine.__init__(self, "G",2)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['E',6,1])
sage: ct
['E', 6, 1]
sage: ct._repr_(compact = True)
'E6~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['E', 6]
sage: ct.dual()
['E', 6, 1]
TESTS::
sage: TestSuite(ct).run()
"""
if n < 6 or n > 8:
raise ValueError("Invalid Cartan Type for Type E")
CartanType_standard_untwisted_affine.__init__(self, "E", n)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['D',4,1])
sage: ct
['D', 4, 1]
sage: ct._repr_(compact = True)
'D4~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystalographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['D', 4]
sage: ct.dual()
['D', 4, 1]
TESTS::
sage: ct == loads(dumps(ct))
True
"""
assert n >= 3
CartanType_standard_untwisted_affine.__init__(self, "D", n)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['C',4,1])
sage: ct
['C', 4, 1]
sage: ct._repr_(compact = True)
'C4~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
False
sage: ct.classical()
['C', 4]
sage: ct.dual()
['C', 4, 1]^*
sage: ct.dual().is_untwisted_affine()
False
TESTS::
sage: TestSuite(ct).run()
"""
assert n >= 1
CartanType_standard_untwisted_affine.__init__(self, "C", n)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['D',4,1])
sage: ct
['D', 4, 1]
sage: ct._repr_(compact = True)
'D4~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystalographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['D', 4]
sage: ct.dual()
['D', 4, 1]
TESTS::
sage: ct == loads(dumps(ct))
True
"""
assert n >= 3
CartanType_standard_untwisted_affine.__init__(self, "D", n)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['E',6,1])
sage: ct
['E', 6, 1]
sage: ct._repr_(compact = True)
'E6~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystallographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['E', 6]
sage: ct.dual()
['E', 6, 1]
TESTS::
sage: TestSuite(ct).run()
"""
if n < 6 or n > 8:
raise ValueError("Invalid Cartan Type for Type E")
CartanType_standard_untwisted_affine.__init__(self, "E", n)
def __init__(self, n):
"""
EXAMPLES::
sage: ct = CartanType(['A',4,1])
sage: ct
['A', 4, 1]
sage: ct._repr_(compact = True)
'A4~'
sage: ct.is_irreducible()
True
sage: ct.is_finite()
False
sage: ct.is_affine()
True
sage: ct.is_untwisted_affine()
True
sage: ct.is_crystalographic()
True
sage: ct.is_simply_laced()
True
sage: ct.classical()
['A', 4]
sage: ct.dual()
['A', 4, 1]
sage: ct = CartanType(['A', 1, 1])
sage: ct.is_simply_laced()
False
sage: ct.dual()
['A', 1, 1]
TESTS::
sage: ct == loads(dumps(ct))
True
"""
assert n >= 1
CartanType_standard_untwisted_affine.__init__(self, "A", n)
if n >= 2:
self._add_abstract_superclass(CartanType_simply_laced)