//Pogorzelski Paweł Informatyka IO  Kolokwium nr2 B
clear;
clc;
n=10;
a_b=(-1:0.1:1);
g=wspolczynnik_g(n, wezly1)
ro=wspolczynnik_ro(n, wezly1)
a=rownanie(g,ro)
disp(n,"n=");
disp(a_b,"(a,b)=");
function out=wezly(n)
    for i=0:n
        out(i+1)=cos(((2*i+1)/2*(n+1))*%pi)
    end
function out = f(x, n)
    for i = 0 : n - 1
        out(n+1) = exp(x(i)) - (x(i) + 1)^2;
    end
    exp(e) = (x-1)^2;
endfunction
function g=licz(n, vx)
    n=length(vx)-1
    for j=0:2
        for i=0:n
            tmp(i+1)=vx(i+1)^j
        end
        g(j+1)=sum(tmp)
    end
endfunction

function ro=licz(n, vx)
    n=length(vx)-1
    for j=0:2
        for i=0:n
            tmp(i+1)=f(vx(i+1))*(vx(i+1)^j)
        end
        rho(j+1)=sum(tmp)
    end
endfunction
function a=rownania(g, ro)
    a(1)=(-g(3)*ro(1)+g(2)*ro(2))/(g(2)*g(2)-g(1)*g(3));
    a(2)=(-g(2)*ro(1)-g(1)*ro(2))/(g(2)*g(2)-g(1)*g(3));
endfunction
function y=F(x, va)
    y=va(1) + va(2)*x