Root system data for type H

class sage.combinat.root_system.type_H.CartanType(n)

Bases: CartanType_standard_finite, CartanType_simple

EXAMPLES:

Sage

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

Python

>>> 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()

Returns a Coxeter diagram for type H.

EXAMPLES:

Sage

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]

Python

>>> 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()

Return the Coxeter number associated with self.

EXAMPLES:

Sage

sage: CartanType(['H',3]).coxeter_number()
10
sage: CartanType(['H',4]).coxeter_number()
30

Python

>>> from sage.all import *
>>> CartanType(['H',Integer(3)]).coxeter_number()
10
>>> CartanType(['H',Integer(4)]).coxeter_number()
30