Coxeter matrices¶
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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]
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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]