  Let $G$ be a finitely generated solvable-by-finite linear group. We present
an algorithm to compute the torsion-free rank of $G$ and a bound on the
Pr\"{u}fer rank of $G$. This yields in turn an algorithm to decide whether a
finitely generated subgroup of $G$ has finite index. The algorithms are
implemented in MAGMA for groups over algebraic number fields.
