n=20
x=[0:6/n:6]
xc=[0]
for i=1:n+1
    xc(i)=3+3*cos(((2*i-1)*%pi)/(2*(n+1)))
end
my_y=[0]
for i=1:n+1
    my_y(i)=exp(sin(x(i)))
    //disp(my_y(i))
end
my_yc=[0]
for i=1:n+1
    my_yc(i)=exp(sin(xc(i)))
    //disp(my_y(i))
end
function Lagrange = Lag(x, my_y, n)
    Lagrange=poly([0],"x","c")
    for i=1:n+1
        Li=poly([1],"x","c")
        for j=1:n+1
            if i~=j then
                li=poly([(-1)*x(j)/(x(i)-x(j)),1/(x(i)-x(j))],"x","c")
                Li=Li*li
            end
        end
        disp(horner(Li,6))
        Lagrange=Lagrange+my_y(i)*Li
    end
endfunction
Lagrange = Lag(x, my_y, n)
LagrangeCh = Lag(xc, my_yc, n)
_nodes=[0:1/1000:6]
value_calc = horner(Lagrange,_nodes)
value_calcCh = horner(LagrangeCh,_nodes)
plot(_nodes,value_calc, "red")
plot(_nodes,value_calcCh, "green")
plot(_nodes,exp(sin(_nodes)), "blue")
disp(horner(Lagrange,6))
disp(horner(LagrangeCh,6))

///////
function Newtoon = Newt(x, n)
    Newtoon=poly([0],"x","c")

endfunction