n=20
x=[0:6/(n-1):6]
y=0
for i=1:n
    y(i)=5
    //print("F:\y(i).txt",y(i))
end
w=poly([1], "x", "c")
function my = My(i)
    my=exp(sin(x(i)))
endfunction

function myfunc = Funct(i)
    myfunc=poly([1],"x", "c")
    for j=1:n
        if j~=i then
            myfunc1=poly([-x(j)/(x(i)-x(j));1/(x(i)-x(j))], "x", "c")
            myfunc = myfunc*myfunc1
        end
    end
endfunction

function Lagrange = Lag()
    Lagrange=poly([0],"x", "c")
    for i=1:n
        yLi=Funct(i)
        my=My(i)
        Lagrange=Lagrange+yLi*my
    end
endfunction

function razdrazn = RazdRazn (k)
    razdrazn=0
    if k == 1 then
        razdrazn=My(1)
    end
    if  k>1 then
        for j=1:k
            for l=1:n
                if l~=j
                    l1=(x(j)-x(l))
                end
            razdrazn=razdrazn+My(j)/l1
            end
        end
    end
endfunction

function w = W(i)
    if i==1 then
    end
    if i>1 then
        w1=poly([x(i)], "x", "r")
        w=w*w1
    end
endfunction

function Newton = MyNew()
    Newton=poly([0], "x", "c")
    for i=1:n
        Newton=Newton+RazdRazn(i)*W(i)
    end
endfunction

Newton=MyNew
Lagrange=Lag()
roots(Lagrange)
_nodes = [0:1/10000:6]
value_calc = horner(Lagrange,_nodes)
value_calcNewt = horner(Newton,_nodes)
plot(_nodes, value_calc, "red")
plot(_nodes, value_calcNewt, "green")
plot(_nodes, exp(sin(_nodes)), "blue")