def test_sympyissue_8438():
p = Poly([1, y, -2, -3], x).as_expr()
roots = roots_cubic(Poly(p, x), x)
z = -Rational(3, 2) - 7*I/2 # this will fail in code given in commit msg
post = [r.subs({y: z}) for r in roots]
assert set(post) == set(roots_cubic(Poly(p.subs({y: z}), x)))
# /!\ if p is not made an expression, this is *very* slow
assert all(p.subs({y: z, x: i}).evalf(2, chop=True) == 0 for i in post)
def test_sympyissue_8438():
p = Poly([1, y, -2, -3], x).as_expr()
roots = roots_cubic(Poly(p, x), x)
z = -Rational(3,
2) - 7 * I / 2 # this will fail in code given in commit msg
post = [r.subs({y: z}) for r in roots]
assert set(post) == set(roots_cubic(Poly(p.subs({y: z}), x)))
# /!\ if p is not made an expression, this is *very* slow
assert all(p.subs({y: z, x: i}).evalf(2, chop=True) == 0 for i in post)
def test_roots_cubic():
assert roots_cubic(Poly(2 * x**3, x)) == [0, 0, 0]
assert roots_cubic(Poly(x**3 - 3 * x**2 + 3 * x - 1, x)) == [1, 1, 1]
assert roots_cubic(Poly(x**3 + 1, x)) == \
[-1, Rational(1, 2) - I*sqrt(3)/2, Rational(1, 2) + I*sqrt(3)/2]
assert roots_cubic(Poly(2*x**3 - 3*x**2 - 3*x - 1, x))[0] == \
Rational(1, 2) + cbrt(3)/2 + 3**Rational(2, 3)/2
eq = -x**3 + 2 * x**2 + 3 * x - 2
assert roots(eq, trig=True, multiple=True) == \
roots_cubic(Poly(eq, x), trig=True) == [
Rational(2, 3) + 2*sqrt(13)*cos(acos(8*sqrt(13)/169)/3)/3,
-2*sqrt(13)*sin(-acos(8*sqrt(13)/169)/3 + pi/6)/3 + Rational(2, 3),
-2*sqrt(13)*cos(-acos(8*sqrt(13)/169)/3 + pi/3)/3 + Rational(2, 3),
]
def test_roots_cubic():
assert roots_cubic(Poly(2 * x**3, x)) == [0, 0, 0]
assert roots_cubic(Poly(x**3 - 3 * x**2 + 3 * x - 1, x)) == [1, 1, 1]
assert roots_cubic(Poly(x**3 + 1, x)) == \
[-1, Rational(1, 2) - I*sqrt(3)/2, Rational(1, 2) + I*sqrt(3)/2]
assert roots_cubic(Poly(2*x**3 - 3*x**2 - 3*x - 1, x))[0] == \
Rational(1, 2) + cbrt(3)/2 + 3**Rational(2, 3)/2
eq = -x**3 + 2 * x**2 + 3 * x - 2
assert roots(eq, trig=True, multiple=True) == \
roots_cubic(Poly(eq, x), trig=True) == [
Rational(2, 3) + 2*sqrt(13)*cos(acos(8*sqrt(13)/169)/3)/3,
-2*sqrt(13)*sin(-acos(8*sqrt(13)/169)/3 + pi/6)/3 + Rational(2, 3),
-2*sqrt(13)*cos(-acos(8*sqrt(13)/169)/3 + pi/3)/3 + Rational(2, 3),
]
res = roots_cubic(Poly(x**3 + 2 * a / 27, x))
assert res == [
-root(a + sqrt(a**2), 3) / 3,
Mul(Rational(-1, 3),
Rational(-1, 2) + sqrt(3) * I / 2,
root(a + sqrt(a**2), 3),
evaluate=False),
Mul(Rational(-1, 3),
Rational(-1, 2) - sqrt(3) * I / 2,
root(a + sqrt(a**2), 3),
evaluate=False)
]
def test_roots1():
assert roots(1) == {}
assert roots(1, multiple=True) == []
q = Symbol('q', real=True)
assert roots(x**3 - q, x) == {cbrt(q): 1,
-cbrt(q)/2 - sqrt(3)*I*cbrt(q)/2: 1,
-cbrt(q)/2 + sqrt(3)*I*cbrt(q)/2: 1}
assert roots_cubic(Poly(x**3 - 1)) == [1, Rational(-1, 2) + sqrt(3)*I/2,
Rational(-1, 2) - sqrt(3)*I/2]
assert roots([1, x, y]) == {-x/2 - sqrt(x**2 - 4*y)/2: 1,
-x/2 + sqrt(x**2 - 4*y)/2: 1}
pytest.raises(ValueError, lambda: roots([1, x, y], z))
def test_roots_cubic():
assert roots_cubic((2 * x**3).as_poly()) == [0, 0, 0]
assert roots_cubic((x**3 - 3 * x**2 + 3 * x - 1).as_poly()) == [1, 1, 1]
assert roots_cubic((x**3 + 1).as_poly()) == \
[-1, Rational(1, 2) - I*sqrt(3)/2, Rational(1, 2) + I*sqrt(3)/2]
assert roots_cubic((2*x**3 - 3*x**2 - 3*x - 1).as_poly())[0] == \
Rational(1, 2) + cbrt(3)/2 + 3**Rational(2, 3)/2
eq = -x**3 + 2 * x**2 + 3 * x - 2
assert roots(eq, trig=True, multiple=True) == \
roots_cubic(eq.as_poly(), trig=True) == [
Rational(2, 3) + 2*sqrt(13)*cos(acos(8*sqrt(13)/169)/3)/3,
-2*sqrt(13)*sin(-acos(8*sqrt(13)/169)/3 + pi/6)/3 + Rational(2, 3),
-2*sqrt(13)*cos(-acos(8*sqrt(13)/169)/3 + pi/3)/3 + Rational(2, 3),
]
res = roots_cubic((x**3 + 2 * a / 27).as_poly(x))
assert res == [
-root(2, 3) * root(a, 3) / 3,
-root(2, 3) * root(a, 3) * (-Rational(1, 2) + sqrt(3) * I / 2) / 3,
-root(2, 3) * root(a, 3) * (-Rational(1, 2) - sqrt(3) * I / 2) / 3
]
res = roots_cubic((x**3 - 2 * a / 27).as_poly(x))
assert res == [
root(2, 3) * root(a, 3) / 3,
root(2, 3) * root(a, 3) * (-Rational(1, 2) + sqrt(3) * I / 2) / 3,
root(2, 3) * root(a, 3) * (-Rational(1, 2) - sqrt(3) * I / 2) / 3
]
# issue sympy/sympy#8438
p = -3 * x**3 - 2 * x**2 + x * y + 1
croots = roots_cubic(p.as_poly(x), x)
z = -Rational(3,
2) - 7 * I / 2 # this will fail in code given in commit msg
post = [r.subs({y: z}) for r in croots]
assert set(post) == set(roots_cubic(p.subs({y: z}).as_poly(x)))
# /!\ if p is not made an expression, this is *very* slow
assert all(p.subs({y: z, x: i}).evalf(2, chop=True) == 0 for i in post)
def test_roots1():
assert roots(1) == {}
assert roots(1, multiple=True) == []
q = Symbol('q', real=True)
assert roots(x**3 - q, x) == {
cbrt(q): 1,
-cbrt(q) / 2 - sqrt(3) * I * cbrt(q) / 2: 1,
-cbrt(q) / 2 + sqrt(3) * I * cbrt(q) / 2: 1
}
assert roots_cubic(Poly(x**3 - 1)) == [
1,
Rational(-1, 2) + sqrt(3) * I / 2,
Rational(-1, 2) - sqrt(3) * I / 2
]
assert roots([1, x, y]) == {
-x / 2 - sqrt(x**2 - 4 * y) / 2: 1,
-x / 2 + sqrt(x**2 - 4 * y) / 2: 1
}
pytest.raises(ValueError, lambda: roots([1, x, y], z))
def test_roots_cubic():
assert roots_cubic(Poly(2 * x**3, x)) == [0, 0, 0]
assert roots_cubic(Poly(x**3 - 3 * x**2 + 3 * x - 1, x)) == [1, 1, 1]
assert roots_cubic(Poly(x**3 + 1, x)) == \
[-1, Rational(1, 2) - I*sqrt(3)/2, Rational(1, 2) + I*sqrt(3)/2]
assert roots_cubic(Poly(2*x**3 - 3*x**2 - 3*x - 1, x))[0] == \
Rational(1, 2) + cbrt(3)/2 + 3**Rational(2, 3)/2
eq = -x**3 + 2 * x**2 + 3 * x - 2
assert roots(eq, trig=True, multiple=True) == \
roots_cubic(Poly(eq, x), trig=True) == [
Rational(2, 3) + 2*sqrt(13)*cos(acos(8*sqrt(13)/169)/3)/3,
-2*sqrt(13)*sin(-acos(8*sqrt(13)/169)/3 + pi/6)/3 + Rational(2, 3),
-2*sqrt(13)*cos(-acos(8*sqrt(13)/169)/3 + pi/3)/3 + Rational(2, 3),
]
res = roots_cubic(Poly(x**3 + 2 * a / 27, x))
assert res == [
-root(a + sqrt(a**2), 3) / 3,
Mul(Rational(-1, 3),
Rational(-1, 2) + sqrt(3) * I / 2,
root(a + sqrt(a**2), 3),
evaluate=False),
Mul(Rational(-1, 3),
Rational(-1, 2) - sqrt(3) * I / 2,
root(a + sqrt(a**2), 3),
evaluate=False)
]
# issue sympy/sympy#8438
p = Poly([1, y, -2, -3], x).as_expr()
croots = roots_cubic(Poly(p, x), x)
z = -Rational(3,
2) - 7 * I / 2 # this will fail in code given in commit msg
post = [r.subs({y: z}) for r in croots]
assert set(post) == set(roots_cubic(Poly(p.subs({y: z}), x)))
# /!\ if p is not made an expression, this is *very* slow
assert all(p.subs({y: z, x: i}).evalf(2, chop=True) == 0 for i in post)
def test_roots_cubic():
assert roots_cubic(Poly(2*x**3, x)) == [0, 0, 0]
assert roots_cubic(Poly(x**3 - 3*x**2 + 3*x - 1, x)) == [1, 1, 1]
assert roots_cubic(Poly(x**3 + 1, x)) == \
[-1, Rational(1, 2) - I*sqrt(3)/2, Rational(1, 2) + I*sqrt(3)/2]
assert roots_cubic(Poly(2*x**3 - 3*x**2 - 3*x - 1, x))[0] == \
Rational(1, 2) + cbrt(3)/2 + 3**Rational(2, 3)/2
eq = -x**3 + 2*x**2 + 3*x - 2
assert roots(eq, trig=True, multiple=True) == \
roots_cubic(Poly(eq, x), trig=True) == [
Rational(2, 3) + 2*sqrt(13)*cos(acos(8*sqrt(13)/169)/3)/3,
-2*sqrt(13)*sin(-acos(8*sqrt(13)/169)/3 + pi/6)/3 + Rational(2, 3),
-2*sqrt(13)*cos(-acos(8*sqrt(13)/169)/3 + pi/3)/3 + Rational(2, 3),
]
res = roots_cubic(Poly(x**3 + 2*a/27, x))
assert res == [-root(a + sqrt(a**2), 3)/3,
Mul(Rational(-1, 3), Rational(-1, 2) + sqrt(3)*I/2,
root(a + sqrt(a**2), 3), evaluate=False),
Mul(Rational(-1, 3), Rational(-1, 2) - sqrt(3)*I/2,
root(a + sqrt(a**2), 3), evaluate=False)]