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Well, if you want to change the representation of the objects, so when you type Integers(6)(5) it returns -1, I think that it is not implemented in sage.

However, if computing the symmetric representant of an element in Integers(n) can be done with the following code:

I use this function in some multimodular algorithms.

def lift_pm(p):  
Compute a representative of the element p mod n in [-n/2 , n/2]


- ``p`` an integer mod n


- An integer r such that  -n/2 < r <= n/2


    sage: p = Mod(2,4)
    sage: lift_pm(p)
    sage: p = Mod(3,4)
    sage: lift_pm(p)
r = p.lift()
if r*2 > p.modulus():
    r -= p.modulus()
return r