Root system data for type I¶
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class
sage.combinat.root_system.type_I.
CartanType
(n)¶ Bases:
sage.combinat.root_system.cartan_type.CartanType_standard_finite
,sage.combinat.root_system.cartan_type.CartanType_simple
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
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coxeter_diagram
()¶ Returns the Coxeter matrix for this type.
EXAMPLES:
sage: ct = CartanType(['I', 4]) sage: ct.coxeter_diagram() Graph on 2 vertices sage: ct.coxeter_diagram().edges() [(1, 2, 4)] sage: ct.coxeter_matrix() [1 4] [4 1]
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coxeter_number
()¶ Return the Coxeter number associated with
self
.EXAMPLES:
sage: CartanType(['I',3]).coxeter_number() 3 sage: CartanType(['I',12]).coxeter_number() 12
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index_set
()¶ Type \(I_2(p)\) is indexed by \(\{1,2\}\).
EXAMPLES:
sage: CartanType(['I', 5]).index_set() (1, 2)
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rank
()¶ Type \(I_2(p)\) is of rank 2.
EXAMPLES:
sage: CartanType(['I', 5]).rank() 2
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