# Lista 2, Zadanie 4
# Grzegorz Ćwikliński
# 229750


using Polynomials;

x = [1, -210.0, 20615.0,-1256850.0,
      53327946.0,-1672280820.0, 40171771630.0, -756111184500.0,
      11310276995381.0, -135585182899530.0,
      1307535010540395.0,     -10142299865511450.0,
      63030812099294896.0,     -311333643161390640.0,
      1206647803780373360.0,     -3599979517947607200.0,
      8037811822645051776.0,      -12870931245150988800.0,
      13803759753640704000.0,      -8752948036761600000.0,
      2432902008176640000.0]

P = Poly(reverse(x)); # wielomian w postaci kanonicznej
Z = reverse(roots(P));

p = poly([i for i in 1.0:20.0]); #wielomian w postaci iloczynowej
z = roots(p)

println("Zera wielomianu P(x):");
for i = 1:20
        println("Z[$i] = $(Z[i])")
end

println("P(Z(k)):");
for i = 1 : 20
        println("P(Z($i)) = $(abs(polyval(P,Z[i])))")
end

println("p(Z(k)):");
for i = 1 : 20
        println("p(Z($i)) = $(abs(polyval(p,Z[i])))")
end

println("Z(k) - k:");
for i = 1 : 20
        println("Z($i) - $i = $(abs(Z[i]-i))")
end

x[2] = x[2] - 2^(-23.0)
P = Poly(reverse(x)); # wielomian w postaci kanonicznej
Z = reverse(roots(P));

println("Zera wielomianu P(x):");
for i = 1:20
        println("Z[$i] = $(Z[i])")
end

println("P(Z(k)):");
for i = 1 : 20
        println("P(Z($i)) = $(abs(polyval(P,Z[i])))")
end