#/***********************************************************
#    cardano.c -- 3次方程式
#***********************************************************/

PI = 3.14159265358979323846264  # 円周率
$check = true

def cuberoot( x )  # $\sqrtxend$ 
    if (x == 0); return 0; end
    if (x > 0); pos = 1;  else; pos = 0; x = -x; end
    if (x > 1); s = x; else; s = x; end
    begin 
        prev = s;  s = (x / (s * s) + 2 * s) / 3
    end while (s < prev)
    if (pos); return prev; else; return -prev; end
end

def cardano( a,  b,  c,  d )
            # $ax^3 + bx^2 + cx + d = 0$, $a \ne 0$ 

    b /= (3 * a);  c /= a;  d /= a
    p = b * b - c / 3
    q = (b * (c - 2 * b * b) - d) / 2
    a = q * q - p * p * p
    if (a == 0) 
        q = cuberoot(q);  x1 = 2 * q - b;  x2 = -q - b
        printf("x = %g, %g (重解)\n", x1, x2)

        if ($check)
            printf("f(x1) = %g\n", x1 * (x1 * (x1 + 3 * b) + c) + d)
            printf("f(x2) = %g\n", x2 * (x2 * (x2 + 3 * b) + c) + d)
        end

    elsif (a > 0) 
        if (q > 0); a3 = cuberoot(q + Math::sqrt(a))
        else;       a3 = cuberoot(q - Math::sqrt(a))
        end
        b3 = p / a3
        x1 = a3 + b3 - b;  x2 = -0.5 * (a3 + b3) - b
        x3 = (a3 - b3).abs * Math::sqrt(3.0) / 2
        printf("x = %g; %g +- %g i\n", x1, x2, x3)

        if ($check)
            printf("f(x1) = %g\n", x1 * (x1 * (x1 + 3 * b) + c) + d)
            printf("f(x2+-x3i) = %g +- %g i\n",
            ((x2+3*b)*x2-x3*x3+c)*x2-(2*x2+3*b)*x3*x3+d,
            ((3*x2+6*b)*x2-x3*x3+c)*x3)
        end

    else 
        a = Math::sqrt(p);  t = Math::acos(q / (p * a));  a *= 2
        x1 = a * Math::cos( t           / 3) - b
        x2 = a * Math::cos((t + 2 * PI) / 3) - b
        x3 = a * Math::cos((t + 4 * PI) / 3) - b
        printf("x = %g, %g, %g\n", x1, x2, x3)

        if ($check)
            printf("f(x2) = %g\n", x2 * (x2 * (x2 + 3 * b) + c) + d)
            printf("f(x3) = %g\n", x3 * (x3 * (x3 + 3 * b) + c) + d)
        end

    end
end

printf("a b c d = ")
a, b, c, d = gets.split.collect {|data| data.to_f}
if (a == 0) 
    printf("3次方程式ではありません.\n")
    exit 1
end
cardano(a, b, c, d)

exit 0