def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['E',6]) sage: ct ['E', 6] sage: ct._repr_(compact = True) 'E6' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystalographic() True sage: ct.is_simply_laced() True sage: ct.affine() ['E', 6, 1] sage: ct.dual() ['E', 6] TESTS: sage: ct == loads(dumps(ct)) True """ assert n >= 6 and n <= 8 CartanType_standard_finite.__init__(self, "E", n)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['A',4]) sage: ct ['A', 4] sage: ct._repr_(compact = True) 'A4' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystallographic() True sage: ct.is_simply_laced() True sage: ct.affine() ['A', 4, 1] sage: ct.dual() ['A', 4] TESTS:: sage: TestSuite(ct).run() """ assert n >= 0 CartanType_standard_finite.__init__(self, "A", n)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['H',3]) sage: ct ['H', 3] sage: ct._repr_(compact = True) 'H3' sage: ct.rank() 3 sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystallographic() False sage: ct.is_simply_laced() False TESTS:: sage: TestSuite(ct).run() """ assert n in [3, 4] CartanType_standard_finite.__init__(self, "H", n)
def __init__(self): """ EXAMPLES:: sage: ct = CartanType(['G',2]) sage: ct ['G', 2] sage: ct._repr_(compact = True) 'G2' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_crystalographic() True sage: ct.is_simply_laced() False sage: ct.dual() ['G', 2]^* sage: ct.affine() ['G', 2, 1] TESTS: sage: ct == loads(dumps(ct)) True """ CartanType_standard_finite.__init__(self, "G", 2)
def __init__(self): """ EXAMPLES:: sage: ct = CartanType(['G',2]) sage: ct ['G', 2] sage: ct._repr_(compact = True) 'G2' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_crystallographic() True sage: ct.is_simply_laced() False sage: ct.dual() ['G', 2] relabelled by {1: 2, 2: 1} sage: ct.affine() ['G', 2, 1] TESTS:: sage: TestSuite(ct).run() """ CartanType_standard_finite.__init__(self, "G", 2)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['I',5]) sage: ct ['I', 5] sage: ct._repr_(compact = True) 'I5' sage: ct.rank() 2 sage: ct.index_set() [1, 2] sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystallographic() False sage: ct.is_simply_laced() False TESTS:: sage: TestSuite(ct).run() """ assert n >= 1 CartanType_standard_finite.__init__(self, "I", n)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['H',3]) sage: ct ['H', 3] sage: ct._repr_(compact = True) 'H3' sage: ct.rank() 3 sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystalographic() False sage: ct.is_simply_laced() False TESTS: sage: ct == loads(dumps(ct)) True """ assert n in [3, 4] CartanType_standard_finite.__init__(self, "H", n)
def __init__(self): """ EXAMPLES:: sage: ct = CartanType(['F',4]) sage: ct ['F', 4] sage: ct._repr_(compact = True) 'F4' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_crystalographic() True sage: ct.is_simply_laced() False sage: ct.dual() ['F', 4]^* sage: ct.affine() ['F', 4, 1] TESTS:: sage: ct == loads(dumps(ct)) True """ CartanType_standard_finite.__init__(self, "F", 4)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['I',5]) sage: ct ['I', 5] sage: ct._repr_(compact = True) 'I5' sage: ct.rank() 2 sage: ct.index_set() [1, 2] sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystalographic() False sage: ct.is_simply_laced() False TESTS:: sage: ct == loads(dumps(ct)) True """ assert n >= 1 CartanType_standard_finite.__init__(self, "I", n)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['E',6]) sage: ct ['E', 6] sage: ct._repr_(compact = True) 'E6' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystallographic() True sage: ct.is_simply_laced() True sage: ct.affine() ['E', 6, 1] sage: ct.dual() ['E', 6] TESTS:: sage: TestSuite(ct).run() """ if n < 6 or n > 8: raise ValueError("Invalid Cartan Type for Type E") CartanType_standard_finite.__init__(self, "E", n)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['D',4]) sage: ct ['D', 4] sage: ct._repr_(compact = True) 'D4' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_crystallographic() True sage: ct.is_simply_laced() True sage: ct.dual() ['D', 4] sage: ct.affine() ['D', 4, 1] sage: ct = CartanType(['D',2]) sage: ct.is_irreducible() False sage: ct.dual() ['D', 2] sage: ct.affine() Traceback (most recent call last): ... ValueError: ['D', 2, 1] is not a valid Cartan type TESTS:: sage: TestSuite(ct).run() """ assert n >= 2 CartanType_standard_finite.__init__(self, "D", n) if n >= 3: self._add_abstract_superclass(CartanType_simple)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['D',4]) sage: ct ['D', 4] sage: ct._repr_(compact = True) 'D4' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_crystalographic() True sage: ct.is_simply_laced() True sage: ct.dual() ['D', 4] sage: ct.affine() ['D', 4, 1] sage: ct = CartanType(['D',2]) sage: ct.is_irreducible() False sage: ct.dual() ['D', 2] sage: ct.affine() Traceback (most recent call last): ... ValueError: ['D', 2, 1] is not a valid cartan type TESTS: sage: ct == loads(dumps(ct)) True """ assert n >= 2 CartanType_standard_finite.__init__(self, "D", n) if n >= 3: self._add_abstract_superclass(CartanType_simple)
def __init__(self, n): """ EXAMPLES:: sage: ct = CartanType(['B',4]) sage: ct ['B', 4] sage: ct._repr_(compact = True) 'B4' sage: ct.is_irreducible() True sage: ct.is_finite() True sage: ct.is_affine() False sage: ct.is_crystalographic() True sage: ct.is_simply_laced() False sage: ct.affine() ['B', 4, 1] sage: ct.dual() ['C', 4] sage: ct = CartanType(['B',1]) sage: ct.is_simply_laced() True sage: ct.affine() ['B', 1, 1] TESTS:: sage: ct == loads(dumps(ct)) True """ assert n >= 1 CartanType_standard_finite.__init__(self, "B", n) if n == 1: self._add_abstract_superclass(CartanType_simply_laced)