We present a general and numerically efficient method for calculation of collision integrals for interacting quantum gases on a discrete momentum lattice. Here we employ the original analytical approach based on Fourier transform covering a wide spectrum of solid-state problems with various particle statistics and arbitrary interaction models, including the case of momentum-dependent interaction. The comprehensive set of the transformation principles is given in detail and realized as a computer Fortran 90 library FLBE (Fast Library for Boltzmann Equation).