Root system data for type Q¶
- class sage.combinat.root_system.type_Q.CartanType(m)[source]¶
- Bases: - CartanType_standard_finite- Cartan Type \(Q_n\). - See also - CartanType()- dual()[source]¶
- Return dual of - self.- EXAMPLES: - sage: Q = CartanType(['Q',3]) sage: Q.dual() ['Q', 3] - >>> from sage.all import * >>> Q = CartanType(['Q',Integer(3)]) >>> Q.dual() ['Q', 3] 
 - index_set()[source]¶
- Return the index set for Cartan type Q. - The index set for type Q is of the form \(\{-n, \ldots, -1, 1, \ldots, n\}\). - EXAMPLES: - sage: CartanType(['Q', 3]).index_set() (1, 2, -2, -1) - >>> from sage.all import * >>> CartanType(['Q', Integer(3)]).index_set() (1, 2, -2, -1) 
 - is_irreducible()[source]¶
- Return whether this Cartan type is irreducible. - EXAMPLES: - sage: Q = CartanType(['Q',3]) sage: Q.is_irreducible() True - >>> from sage.all import * >>> Q = CartanType(['Q',Integer(3)]) >>> Q.is_irreducible() True