Several algorithms have been discussed in the literature for the exact resolution of sparse and integer linear systems . Following the analysis by Eberly et al. , we decided to implement Dixon's algorithm which relies on a modulo-prime inversion of the matrix. In accordance with their conclusion, this algorithm largely outperforms a sparse LU decomposition algorithm (which we implemented as a reference and for benchmarking), both algorithms leveraging GMP instructions specific to the BigRational type for improved performance. Yet, Dixon's algorithm can fail if matrix A happens not to be invertible modulo the chosen prime: hence, we chose to successively invert it modulo three hard-coded large primes and stop at the first succeeding one, and finally resort to LU decomposition if all three fail. This implementation is up to orders of magnitude faster than that used in the original Systre program written in Java. This extra performance is crucial for the use of the topology detection algorithm as part of large-scale screening methodologies.