def test_section_modulus_and_polar_second_moment_of_area():
d = Symbol('d', positive=True)
c = Circle((3, 7), 8)
assert c.polar_second_moment_of_area() == 2048 * pi
assert c.section_modulus() == (128 * pi, 128 * pi)
c = Circle((2, 9), d / 2)
assert c.polar_second_moment_of_area(
) == pi * d**3 * Abs(d) / 64 + pi * d * Abs(d)**3 / 64
assert c.section_modulus() == (pi * d**3 / S(32), pi * d**3 / S(32))
a, b = symbols('a, b', positive=True)
e = Ellipse((4, 6), a, b)
assert e.section_modulus() == (pi * a * b**2 / S(4), pi * a**2 * b / S(4))
assert e.polar_second_moment_of_area(
) == pi * a**3 * b / S(4) + pi * a * b**3 / S(4)
e = e.rotate(pi / 2) # no change in polar and section modulus
assert e.section_modulus() == (pi * a**2 * b / S(4), pi * a * b**2 / S(4))
assert e.polar_second_moment_of_area(
) == pi * a**3 * b / S(4) + pi * a * b**3 / S(4)
e = Ellipse((a, b), 2, 6)
assert e.section_modulus() == (18 * pi, 6 * pi)
assert e.polar_second_moment_of_area() == 120 * pi
e = Ellipse(Point(0, 0), 2, 2)
assert e.section_modulus() == (2 * pi, 2 * pi)
assert e.section_modulus(Point(2, 2)) == (2 * pi, 2 * pi)
assert e.section_modulus((2, 2)) == (2 * pi, 2 * pi)
