Let $\Lambda$ be an $n$ dimensional sublattice of the integer lattice $\mathbb{Z}^n$. The quotient $\mathbb{Z}^n/\Lambda$ has order $\sqrt{\det{\Lambda}}$. 


What is the best/standard way to compute a set of coset representatives for this quotient?


Edit: I initially forgot to take the square root of $\det{\Lambda}$, which is likely the reason for KCronrad's initial comment.



Computing a set of coset representatives for $\mathbb{Z}^n / \Lambda$
As KConrad suggested (why only in the comments?), Smith's normal formal is your best bet. Its running time is insensitive to $m=|{\mathbb Z}^n/\Lambda |$ (unless you need to use arbitrary long entries in your matrix) and behaves as $n^3$.


You may also try coset enumeration, whose running time is usually unbounded but may be bounded in this case by something like $(mn)^2$.


