Lagrange Coefficients in Maple

Question

I'm trying to compute Lagrange coefficients in Maple. Having found the $n$ roots of a Lagrange polynomial, I want to calculate the $j$-th coefficient:

$$L_j(x) = \prod_{{i=0}\atop{j \neq i}}^{n}\frac{x-x_i}{x_j-x_i}$$

Is it possible to do elegantly with the Maple product() function?

Answer 1

The s indeed, but why not use the built in procedures:

withApplyFunction(CurveFitting):
PolynomialInterpolationApplyFunction([[0,0],[1,3],[2,1],[3,3]],z)

where the points are listed as ordered pairs in square brackets, add "form=Lagrange" if you want the products to not be multiplied out.

PolynomialInterpolationApplyFunction([0,2,4,7],[2,a,1,3],z,form=Lagrange)