# Coxeter matrices¶

sage.combinat.root_system.coxeter_matrix.coxeter_matrix(t)

Returns the Coxeter matrix of type t.

EXAMPLES:

sage: coxeter_matrix(['A', 4])
[1 3 2 2]
[3 1 3 2]
[2 3 1 3]
[2 2 3 1]
sage: coxeter_matrix(['B', 4])
[1 3 2 2]
[3 1 3 2]
[2 3 1 4]
[2 2 4 1]
sage: coxeter_matrix(['C', 4])
[1 3 2 2]
[3 1 3 2]
[2 3 1 4]
[2 2 4 1]
sage: coxeter_matrix(['D', 4])
[1 3 2 2]
[3 1 3 3]
[2 3 1 2]
[2 3 2 1]

sage: coxeter_matrix(['E', 6])
[1 2 3 2 2 2]
[2 1 2 3 2 2]
[3 2 1 3 2 2]
[2 3 3 1 3 2]
[2 2 2 3 1 3]
[2 2 2 2 3 1]

sage: coxeter_matrix(['F', 4])
[1 3 2 2]
[3 1 4 2]
[2 4 1 3]
[2 2 3 1]

sage: coxeter_matrix(['G', 2])
[1 6]
[6 1]

sage.combinat.root_system.coxeter_matrix.coxeter_matrix_as_function(t)

Returns the Coxeter matrix, as a function

INPUT:

• t – a Cartan type

EXAMPLES:

sage: from sage.combinat.root_system.coxeter_matrix import coxeter_matrix_as_function
sage: f = coxeter_matrix_as_function(['A',4])
sage: matrix([[f(i,j) for j in range(1,5)] for i in range(1,5)])
[1 3 2 2]
[3 1 3 2]
[2 3 1 3]
[2 2 3 1]


Coxeter Groups

Dynkin diagrams