About the partial quotients of one of the continued fractions

This paper is devoted to the computation of partial quotiens of decomposition of $\frac{a_m}{N_m}$ into a continued fraction, where ${a_m}$ and ${N_m}$ are parameters of a parallelepipedal grid, which is an approximation of a quadratic algebraic grid by a rational grid.
The results of this work allow us to implement fast algorithms for calculating the quality function of these rational approximations.