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