Root system data for type H¶
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class
sage.combinat.root_system.type_H.
CartanType
(n)¶ Bases:
sage.combinat.root_system.cartan_type.CartanType_standard_finite
,sage.combinat.root_system.cartan_type.CartanType_simple
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
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coxeter_diagram
()¶ Returns a Coxeter diagram for type H.
EXAMPLES:
sage: ct = CartanType(['H',3]) sage: ct.coxeter_diagram() Graph on 3 vertices sage: sorted(ct.coxeter_diagram().edges()) [(1, 2, 3), (2, 3, 5)] sage: ct.coxeter_matrix() [1 3 2] [3 1 5] [2 5 1] sage: ct = CartanType(['H',4]) sage: ct.coxeter_diagram() Graph on 4 vertices sage: sorted(ct.coxeter_diagram().edges()) [(1, 2, 3), (2, 3, 3), (3, 4, 5)] sage: ct.coxeter_matrix() [1 3 2 2] [3 1 3 2] [2 3 1 5] [2 2 5 1]
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coxeter_number
()¶ Return the Coxeter number associated with
self
.EXAMPLES:
sage: CartanType(['H',3]).coxeter_number() 10 sage: CartanType(['H',4]).coxeter_number() 30
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