The strong approximation theorem and computing with linear groups

We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group H ≤ SL(n, Z) for n ≥ 2. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of SL(n, Q) for n > 2