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

TESTS:

sage: TestSuite(ct).run()
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()
[(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 \(I_p\) is of rank 2

EXAMPLES::
sage: CartanType([‘I’, 5]).index_set() [1, 2]
rank()

Type \(I_p\) is of rank 2

EXAMPLES::
sage: CartanType([‘I’, 5]).rank() 2

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