  Model of laminated wave turbulence allows to study statistical and discrete
layers of turbulence in the frame of the same model. Statistical layer is
described by Zakharov-Kolmogorov energy spectra in the case of irrational
enough dispersion function. Discrete layer is covered by some system(s) of
Diophantine equations while their form is determined by wave dispersion
function. This presents a very special computational challenge - to solve
Diophantine equations in many variables, usually 6 to 8, in high degrees, say
16, in integers of order $10^{16}$ and more. Generic algorithms for solving
this problem in the case of
  {\it irrational} dispersion function have been presented in our previous
papers. In this paper we present a new generic algorithm for the case of {\it
rational} dispersion functions. Special importance of this case is due to the
fact that in wave systems with rational dispersion the statistical layer does
not exist and the general energy transport is governed by the discrete layer
alone.
