When taking modulo reduction by some integer $p$, one can regard this operation as reducing some number into a interval $[0,p-1]\cap\mathbb{Z}$ or another interval $(-p/2,p/2]\cap\mathbb{Z}$. I know the former usecase but do not know the latter usecase.
What is the advantage of modulo operation over $(-p/2,p/2]\cap\mathbb{Z}$ rather than $[0,p-1]\cap\mathbb{Z}$?