In [1]:
from sympy import *
In [2]:
x, y, z = symbols('x y z')
In [3]:
init_printing()
In [17]:
i = -4; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[17]:
$$\left [ \left ( - \frac{9}{25} + \frac{4 \sqrt{11}}{25}, \quad \frac{2 \sqrt{11}}{25} + \frac{18}{25}, \quad -2\right ), \quad \left ( - \frac{4 \sqrt{11}}{25} - \frac{9}{25}, \quad - \frac{2 \sqrt{11}}{25} + \frac{18}{25}, \quad -2\right )\right ]$$
In [18]:
i = -3; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[18]:
$$\left [ \left ( - \frac{8}{25} + \frac{\sqrt{1119}}{25}, \quad \frac{16}{25} + \frac{\sqrt{1119}}{50}, \quad - \frac{3}{2}\right ), \quad \left ( - \frac{\sqrt{1119}}{25} - \frac{8}{25}, \quad - \frac{\sqrt{1119}}{50} + \frac{16}{25}, \quad - \frac{3}{2}\right )\right ]$$
In [19]:
i = -2; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[19]:
$$\left [ \left ( - \frac{7}{25} + \frac{2 \sqrt{451}}{25}, \quad \frac{14}{25} + \frac{\sqrt{451}}{25}, \quad -1\right ), \quad \left ( - \frac{2 \sqrt{451}}{25} - \frac{7}{25}, \quad - \frac{\sqrt{451}}{25} + \frac{14}{25}, \quad -1\right )\right ]$$
In [20]:
i = -1; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[20]:
$$\left [ \left ( - \frac{6}{25} + \frac{\sqrt{2231}}{25}, \quad \frac{12}{25} + \frac{\sqrt{2231}}{50}, \quad - \frac{1}{2}\right ), \quad \left ( - \frac{\sqrt{2231}}{25} - \frac{6}{25}, \quad - \frac{\sqrt{2231}}{50} + \frac{12}{25}, \quad - \frac{1}{2}\right )\right ]$$
In [21]:
i = 0; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[21]:
$$\left [ \left ( - \frac{1}{5} + \frac{4 \sqrt{6}}{5}, \quad \frac{2}{5} + \frac{2 \sqrt{6}}{5}, \quad 0\right ), \quad \left ( - \frac{4 \sqrt{6}}{5} - \frac{1}{5}, \quad - \frac{2 \sqrt{6}}{5} + \frac{2}{5}, \quad 0\right )\right ]$$
In [22]:
i = 1; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[22]:
$$\left [ \left ( - \frac{4}{25} + \frac{\sqrt{2311}}{25}, \quad \frac{8}{25} + \frac{\sqrt{2311}}{50}, \quad \frac{1}{2}\right ), \quad \left ( - \frac{\sqrt{2311}}{25} - \frac{4}{25}, \quad - \frac{\sqrt{2311}}{50} + \frac{8}{25}, \quad \frac{1}{2}\right )\right ]$$
In [23]:
i = 2; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[23]:
$$\left [ \left ( - \frac{3}{25} + \frac{2 \sqrt{491}}{25}, \quad \frac{6}{25} + \frac{\sqrt{491}}{25}, \quad 1\right ), \quad \left ( - \frac{2 \sqrt{491}}{25} - \frac{3}{25}, \quad - \frac{\sqrt{491}}{25} + \frac{6}{25}, \quad 1\right )\right ]$$
In [24]:
i = 3; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[24]:
$$\left [ \left ( - \frac{2}{25} + \frac{3 \sqrt{151}}{25}, \quad \frac{4}{25} + \frac{3 \sqrt{151}}{50}, \quad \frac{3}{2}\right ), \quad \left ( - \frac{3 \sqrt{151}}{25} - \frac{2}{25}, \quad - \frac{3 \sqrt{151}}{50} + \frac{4}{25}, \quad \frac{3}{2}\right )\right ]$$
In [25]:
i = 4; solve([x**2 + y**2 + z**2 - 5, -5*x + 10*y + 2*z - 5, z - Rational(i/2)],[x, y, z])
Out[25]:
$$\left [ \left ( - \frac{1}{25} + \frac{4 \sqrt{31}}{25}, \quad \frac{2}{25} + \frac{2 \sqrt{31}}{25}, \quad 2\right ), \quad \left ( - \frac{4 \sqrt{31}}{25} - \frac{1}{25}, \quad - \frac{2 \sqrt{31}}{25} + \frac{2}{25}, \quad 2\right )\right ]$$
In [ ]:
inserted by FC2 system