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(['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)