Let R be a ring and I an ideal in R then the map \phi : R\rightarrow R/I is a homomorphism.


Then we interpolate points {(x_k,f_k)} by polynomial

(1)   \begin{equation*} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}\end{equation*}


Its coefficients {a_j} are found as a solution of system of linear equations:

(2)   \begin{equation*} \left{ P_{N-1}(x_k) = f_k\right},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2}\end{equation*}


Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).