  We discuss various methods and their effectiveness for solving linear
equations over finitely generated abelian groups. More precisely, if
$\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups
and $b\in H$, we discuss various algorithms for checking whether $b\in
\im\varphi$ holds and if so, for computing a pre-image of $b$ in $G$ together
with the kernel of $\varphi$.
