Editing Polynomial ring (section)

====Lagrange interpolation====
{{main|Lagrange polynomial}}

Given a finite set of ordered pairs <math>(x_j, y_j)</math> with entries in a field and distinct values <math>x_j</math>, among the polynomials <math>f(x)</math> that interpolate these points (so that <math>f(x_j) = y_j</math> for all <math>j</math>), there is a unique polynomial of smallest degree.  This is the ''Lagrange interpolation polynomial'' <math>L(x)</math>. If there are <math>k</math> ordered pairs, the degree of <math>L(x)</math> is at most <math>k - 1</math>.  The polynomial <math>L(x)</math> can be computed explicitly in terms of the input data <math>(x_j, y_j)</math>.