def 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]
"""
t = CartanType(t)
m = t.coxeter_matrix()
index_set = t.index_set()
reverse = dict((index_set[i], i) for i in range(len(index_set)))
return lambda i,j: m[reverse[i], reverse[j]]
def 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]
"""
t = CartanType(t)
m = t.coxeter_matrix()
index_set = t.index_set()
reverse = dict((index_set[i], i) for i in range(len(index_set)))
return lambda i,j: m[reverse[i], reverse[j]]
