Bonus_01_Lagrange

Lagrange

Given a set of points, polynomial interpolation is the task of finding a polynomial with lowest degree that passes through all the points. Assume the set $(x_0, y_0), \dots, (x_n, y_n)$ of points. Then a suitable polynomial is given by

$$L(x):=\sum_{j=0}^n y_j l_j (x)$$

where the Lagrange polynomials $l_j (x)$ are defined as follows:

$$l_j (x):=\prod_{0\leq k\leq n \land k \ne j} \frac{x-x_k}{x_j-x_k}$$

1. lagrange
   Implement the function lagrange : (float * float) list -> (float -> float) that returns the interpolated polynomial $L$.