Root system data for type I#
- class sage.combinat.root_system.type_I.CartanType(n)#
Bases:
CartanType_standard_finite
,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