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
is_simply_laced()[source]

Return whether this Cartan type is simply-laced.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.is_simply_laced()
True

>>> from sage.all import *
>>> Q = CartanType(['Q',Integer(3)])
>>> Q.is_simply_laced()
True
root_system()[source]

Return the root system of self.

EXAMPLES:

sage: Q = CartanType(['Q',3])
sage: Q.root_system()
Root system of type ['A', 2]

>>> from sage.all import *
>>> Q = CartanType(['Q',Integer(3)])
>>> Q.root_system()
Root system of type ['A', 2]