Root system data for type H¶
- class sage.combinat.root_system.type_H.CartanType(n)[source]¶
- Bases: - CartanType_standard_finite,- 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 - >>> from sage.all import * >>> ct = CartanType(['H',Integer(3)]) >>> ct ['H', 3] >>> ct._repr_(compact = True) 'H3' >>> ct.rank() 3 >>> ct.is_irreducible() True >>> ct.is_finite() True >>> ct.is_affine() False >>> ct.is_crystallographic() False >>> ct.is_simply_laced() False - coxeter_diagram()[source]¶
- Return a Coxeter diagram for type H. - EXAMPLES: - sage: ct = CartanType(['H',3]) sage: ct.coxeter_diagram() # needs sage.graphs Graph on 3 vertices sage: ct.coxeter_diagram().edges(sort=True) # needs sage.graphs [(1, 2, 3), (2, 3, 5)] sage: ct.coxeter_matrix() # needs sage.graphs [1 3 2] [3 1 5] [2 5 1] sage: ct = CartanType(['H',4]) sage: ct.coxeter_diagram() # needs sage.graphs Graph on 4 vertices sage: ct.coxeter_diagram().edges(sort=True) # needs sage.graphs [(1, 2, 3), (2, 3, 3), (3, 4, 5)] sage: ct.coxeter_matrix() # needs sage.graphs [1 3 2 2] [3 1 3 2] [2 3 1 5] [2 2 5 1] - >>> from sage.all import * >>> ct = CartanType(['H',Integer(3)]) >>> ct.coxeter_diagram() # needs sage.graphs Graph on 3 vertices >>> ct.coxeter_diagram().edges(sort=True) # needs sage.graphs [(1, 2, 3), (2, 3, 5)] >>> ct.coxeter_matrix() # needs sage.graphs [1 3 2] [3 1 5] [2 5 1] >>> ct = CartanType(['H',Integer(4)]) >>> ct.coxeter_diagram() # needs sage.graphs Graph on 4 vertices >>> ct.coxeter_diagram().edges(sort=True) # needs sage.graphs [(1, 2, 3), (2, 3, 3), (3, 4, 5)] >>> ct.coxeter_matrix() # needs sage.graphs [1 3 2 2] [3 1 3 2] [2 3 1 5] [2 2 5 1] 
 - coxeter_number()[source]¶
- Return the Coxeter number associated with - self.- EXAMPLES: - sage: CartanType(['H',3]).coxeter_number() 10 sage: CartanType(['H',4]).coxeter_number() 30 - >>> from sage.all import * >>> CartanType(['H',Integer(3)]).coxeter_number() 10 >>> CartanType(['H',Integer(4)]).coxeter_number() 30