using Polynomials

data_P = Float64[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]

data_p = Float64[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]

data_P = flipdim(data_P, 1)
P_Poly = Poly(data_P)
p_poly = poly(data_p)
zero_places = roots(P_Poly)
println(zero_places,"\n")
zero_places = flipdim(zero_places, 1)

for i = 1:length(zero_places)
    println("|P(z$(i))|:\t$(abs(polyval(P_Poly,zero_places[i])))")
    println("|p(z$(i))|:\t$(abs(polyval(p_poly,zero_places[i])))")
    println("|z$(i)-$(i)|: \t$(abs(zero_places[i] - i))\n")
end