def test_roots_quadratic():
assert roots_quadratic(Poly(2*x**2, x)) == [0, 0]
assert roots_quadratic(Poly(2*x**2 + 3*x, x)) == [-Rational(3, 2), 0]
assert roots_quadratic(Poly(2*x**2 + 3, x)) == [-I*sqrt(6)/2, I*sqrt(6)/2]
assert roots_quadratic(Poly(2*x**2 + 4*x + 3, x)) == [-1 - I*sqrt(2)/2, -1 + I*sqrt(2)/2]
f = x**2 + (2*a*e + 2*c*e)/(a - c)*x + (d - b + a*e**2 - c*e**2)/(a - c)
assert (roots_quadratic(Poly(f, x)) ==
[-e*(a + c)/(a - c) - sqrt((a*b + 4*a*c*e**2 -
a*d - b*c + c*d)/(a - c)**2),
-e*(a + c)/(a - c) + sqrt((a*b + 4*a*c*e**2 -
a*d - b*c + c*d)/(a - c)**2)])
# check for simplification
f = Poly(y*x**2 - 2*x - 2*y, x)
assert roots_quadratic(f) == [-sqrt((2*y**2 + 1)/y**2) + 1/y,
sqrt((2*y**2 + 1)/y**2) + 1/y]
f = Poly(x**2 + (-y**2 - 2)*x + y**2 + 1, x)
assert roots_quadratic(f) == [y**2/2 - sqrt(y**4)/2 + 1,
y**2/2 + sqrt(y**4)/2 + 1]
f = Poly(sqrt(2)*x**2 - 1, x)
r = roots_quadratic(f)
assert r == _nsort(r)
# issue sympy/sympy#8255
f = Poly(-24*x**2 - 180*x + 264)
assert [w.evalf(2) for w in f.all_roots(radicals=True)] == \
[w.evalf(2) for w in f.all_roots(radicals=False)]
for _a, _b, _c in itertools.product((-2, 2), (-2, 2), (0, -1)):
f = Poly(_a*x**2 + _b*x + _c)
roots = roots_quadratic(f)
assert roots == _nsort(roots)
def test_roots_quadratic():
assert roots_quadratic(Poly(2 * x**2, x)) == [0, 0]
assert roots_quadratic(Poly(2 * x**2 + 3 * x, x)) == [-Rational(3, 2), 0]
assert roots_quadratic(Poly(2 * x**2 + 3,
x)) == [-I * sqrt(6) / 2, I * sqrt(6) / 2]
assert roots_quadratic(
Poly(2 * x**2 + 4 * x + 3,
x)) == [-1 - I * sqrt(2) / 2, -1 + I * sqrt(2) / 2]
f = x**2 + (2 * a * e + 2 * c * e) / (a - c) * x + (d - b + a * e**2 -
c * e**2) / (a - c)
assert roots_quadratic(Poly(f, x)) == \
[-e*(a + c)/(a - c) - sqrt((a*b + c*d - a*d - b*c + 4*a*c*e**2))/(a - c),
-e*(a + c)/(a - c) + sqrt((a*b + c*d - a*d - b*c + 4*a*c*e**2))/(a - c)]
# check for simplification
f = Poly(y * x**2 - 2 * x - 2 * y, x)
assert roots_quadratic(f) == \
[-sqrt(2*y**2 + 1)/y + 1/y, sqrt(2*y**2 + 1)/y + 1/y]
f = Poly(x**2 + (-y**2 - 2) * x + y**2 + 1, x)
assert roots_quadratic(f) == [1, y**2 + 1]
f = Poly(sqrt(2) * x**2 - 1, x)
r = roots_quadratic(f)
assert r == _nsort(r)
# issue 8255
f = Poly(-24 * x**2 - 180 * x + 264)
assert [w.n(2) for w in f.all_roots(radicals=True)] == \
[w.n(2) for w in f.all_roots(radicals=False)]
for _a, _b, _c in itertools.product((-2, 2), (-2, 2), (0, -1)):
f = Poly(_a * x**2 + _b * x + _c)
roots = roots_quadratic(f)
assert roots == _nsort(roots)
def test_sympyissue_14291():
p = Poly(((x - 1)**2 + 1) * ((x - 1)**2 + 2) * (x - 1))
assert set(
p.all_roots()) == {1, 1 - I, 1 + I, 1 - I * sqrt(2), 1 + sqrt(2) * I}
def test_sympyissue_14291():
p = Poly(((x - 1)**2 + 1)*((x - 1)**2 + 2)*(x - 1))
assert set(p.all_roots()) == {1, 1 - I, 1 + I, 1 - I*sqrt(2), 1 + sqrt(2)*I}