function y = LI(x,n)
%lagrange interpolation of exp on [0,l]

z=linspace(0,1,n+1);
%z(1), ... , z(n+1) corresponds to the interpolation points
%x_0, x_1, . . ., x_n from the book

y = zeros(1,length(x));
for i = 1:n+1 
%This loop adds the n terms of the lagrange polynomial
    L = ones(1,length(x));
    for j = 1:n+1
        %This loop multiplies th n terms of the L_i,n polynomial
        if (j ~= i)
            L = L.*(x-z(j))./(z(i) - z(j));
        end
    end
    y = y + exp(z(i))*L;
end