Lagrange polynomial and its subpolynomials

Construction of the Lagrange interpolation polynomial from its definition.

Given a set of n discrete points xp, the function computes coefficients of n Lagrange subpolynomials L_1(x), L_2(x), ...., L_n(x) satisfying the property L_i(xp_j)=0 if i~=j, L_i(xp_j)=1 if i=j, for i,j=1,...,n. A linear combination (with coefficients yp) of these subpolynomials defines a Lagrange polynomial passing through points (xp,yp).