Inversion of integer matrices in residue number system

The presented algorithm makes use of the recently introduced incompletely specified residue number system. This system enables the operations necessary in the inversion process to be done quickly, completely in parallel for different moduli, even if divisors and some system moduli are not relatively prime. The algorithm guarantees the result correctness and the only condition for its applicability is that the determinant of the starting matrix is not a multiple of the product of all system moduli.