# How to permute strings from two lists (or vectors)

Suppose I have to vector of variables

NB=vector(var('x', n=3, latex_name='x'))
B=vector(var('y', n=4, latex_name='ϵ'))


I would like to construct a function say BNB(vec1, vec2, pr, pc) such that when applied to B and for legitiamte values --- i.e. : here, NB should be less than 3 and B should be less than 4 ---, permute the correspondant $x$ and $\epsilon from a vector to an other. That is : BNB(B, NB, 1,2) gives$B=[\epsilon_0,x_2,\epsilon_3,\epsilon_4]$and$NB=[x_0,x_1,\epsilon_1,x_3]\$

By advance thanks for the help.

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One solution is to define an exchange function as below.

The function starts by checking the validity of the indices.

If called with invalid indices, it will raise a value error.

def exchange(A, B, i, j):
r"""
Exchange entry i of A and entry j of B.
"""
if i not in range(len(A)):
a = len(A)
s = f"expected 0 <= i < len(A), got i = {i}, len(A) = {a}"
raise ValueError(s)
if j not in range(len(B)):
b = len(B)
s = f"expected 0 <= j < len(B), got j = {j}, len(B) = {b}"
raise ValueError(s)
A[i], B[j] = B[j], A[i]


To illustrate usage, define two vectors:

sage: A = vector(var('x', n=3, latex_name='x'))
sage: B = vector(var('y', n=4, latex_name='ϵ'))


and exchange some entries:

sage: exchange(A, B, 1, 2)
sage: A
(x0, y2, x2)
sage: B
(y0, y1, x1, y3)


Calling with invalid indices raises an error:

sage: exchange(A, B, 3, 3)
Traceback (most recent call last)
...
ValueError: expected 0 <= i < len(A), got i = 3, len(A) = 3

more

Thanks a lot the core action is so simple that it is nearly unbelievable

That's one of the benefits of having based Sage on the Python programming language!