Root system data for type I

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

Bases: sage.combinat.root_system.cartan_type.CartanType_standard_finite, sage.combinat.root_system.cartan_type.CartanType_simple

EXAMPLES:

sage: ct = CartanType(['I',5])
sage: ct
['I', 5]
sage: ct._repr_(compact = True)
'I5'
sage: ct.rank()
2
sage: ct.index_set()
(1, 2)

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

coxeter_diagram()

Returns the Coxeter matrix for this type.

EXAMPLES:

sage: ct = CartanType(['I', 4])
sage: ct.coxeter_diagram()
Graph on 2 vertices
sage: ct.coxeter_diagram().edges(sort=True)
[(1, 2, 4)]
sage: ct.coxeter_matrix()
[1 4]
[4 1]

coxeter_number()

Return the Coxeter number associated with self.

EXAMPLES:

sage: CartanType(['I',3]).coxeter_number()
3
sage: CartanType(['I',12]).coxeter_number()
12

index_set()

Type \(I_2(p)\) is indexed by \(\{1,2\}\).

EXAMPLES:

sage: CartanType(['I', 5]).index_set()
(1, 2)

rank()

Type \(I_2(p)\) is of rank 2.

EXAMPLES:

sage: CartanType(['I', 5]).rank()
2