n=19

from=0
to=6
x=[from:(to-from)/n:to]
xch=[0]
for i=1:n+1
    xch(i)=((to+from)/2)+((to-from)/2)*cos(((2*i-1)*%pi)/(2*(n+1)))
end
f=exp(sin(x))
my_y=[0]
for i=1:length(x)
    my_y(i)=exp(sin(x(i)))
end

my_ych=[0]
for i=1:length(xch)
    my_ych(i)=exp(sin(xch(i)))
end
function P = PP(a, b)
    for i=1:length(a)
        for j=1:length(b)
            P(i+j-1)=0
        end
    end
    for i=1:length(a)
        for j=1:length(b)
            P(i+j-1)=P(i+j-1)+a(i)*b(j)
        end
    end
endfunction
function sump = Sum(a, b)
    m=abs(length(a)-length(b))
    for i=1:length(a)
        for j=1:length(b)
            if i==j then
                sump(i)=a(i)+b(j)
            end
        end
    end
    k=length(sump)
    if m~=0 then
        for s=(k+1):(k+m)
            if length(a)>length(b) then
                sump(s)=a(s)
            end
            if length(b)>length(a) then
                sump(s)=b(s)
            end
        end
    end
endfunction
function difp = Diff(a, b)
    m=abs(length(a)-length(b))
    for i=1:length(a)
        for j=1:length(b)
            if i==j then
                difp(i)=a(i)-b(j)
            end
        end
    end
    k=length(difp)
    if m~=0 then
        for s=(k+1):(k+m)
            if length(a)>length(b) then
                difp(s)=a(s)
            end
            if length(b)>length(a) then
                difp(s)=-b(s)
            end
        end
    end
endfunction

function Lagrange = Lag(x, y)
    Lagrange=1
    for i=1:length(x)
        Li=1
        for j=1:length(x)
            if i~=j then
                li=[-x(j)/(x(i)-x(j)),1/(x(i)-x(j))]
                Li=PP(li,Li)
            end
        end
        Lagrange=Sum(Lagrange,PP(y(i),Li))
    end
endfunction
function DD = DivDiff(x,y,n)
        for i =1:length(x)
            DD(1,i) = x(i)
            DD(2,i) = y(i)
        end
        for i=3:n+2
            for j=1:length(x)+2-i
                DD(i,j) = (DD(i-1,j) - DD(i-1,j+1))/(DD(j) - DD(j+i-2))
            end
        end
endfunction

function Newtoon = Newt(x, y)
    N=1
    m= DivDiff(x,y,length(x))
    Newtoon=(1)
    for i=1:length(x)-1
        Ni=[-x(i),1]
        N=PP(N,Ni)
        Newtoon=PP(Newtoon,PP(N,m(2+i,1)))
    end
endfunction
function Error = Err(func)
    Error=abs(func-exp(sin(_nodes)))
endfunction
function mydeg = Mydeg (point, n)
    mydeg=1
    for i=1:n
        mydeg=mydeg*point/(2^(256/n))
    end
    mydeg=mydeg*2^(256)
endfunction
function myhorn = mhorner(pol, _nodes)
    for k=1:length(_nodes)
        myhorn(k)=1
    end
    for j=1:length(_nodes)
        myhorn(j)=0
        for i=1:n
            myhorn(j)=myhorn(j)+pol(i+1)*Mydeg(_nodes(j), i)
            //disp(myhorn(j))
        end
    end
endfunction
Newtoon=Newt(x,my_y)
Newtoonch=Newt(xch,my_ych)
PolLag=Lag(x, my_y)
//disp(PolLag)
PolLagCh=Lag(xch, my_ych)
_nodes=[from:1/1000:to]
value_calc = mhorner(PolLag,_nodes)
value_calc_R=abs(Diff(value_calc,exp(sin(_nodes))))
//plot(_nodes,value_calc_R, "red")
value_calcCh = mhorner(PolLagCh,_nodes)
value_calcN = mhorner(Newtoon,_nodes)
value_calcNch = mhorner(Newtoonch,_nodes)
plot(_nodes,value_calc, "red")
//plot(_nodes,value_calcCh, "green")
plot(_nodes,exp(sin(_nodes)), "blue")
//plot(_nodes,value_calcN, "red")