Solve: If exist an imaginary value in the solutions and we send a ineq we get False

[latot]

Hi, well when we have a mix of eq + ineq, but the eq (or maybe too the ineq), have imaginary values (not alls) we always will get False:

>>> solve([Eq(-x**3+x-1,0), x<0])
False
the solution should be:
{x: -(3*sqrt(69)/2 + 27/2)**(1/3)/3 - 1/(3*sqrt(69)/2 + 27/2)**(1/3)}
>>> solve([Eq(-x**3+x-1,0), x>0])
False
The solutions should be:
[{x: -1/((-1/2 - sqrt(3)*I/2)*(3*sqrt(69)/2 + 27/2)**(1/3)) - (-1/2 - sqrt(3)*I/2)*(3*sqrt(69)/2 + 27/2)**(1/3)/3}, {x: -(-1/2 + sqrt(3)*I/2)*(3*sqrt(69)/2 + 27/2)**(1/3)/3 - 1/((-1/2 + sqrt(3)*I/2)*(3*sqrt(69)/2 + 27/2)**(1/3))}]

Thx. Cya.

[Shekharrajak]

In [1]: solveset(Eq(-x**3+x-1,0), x, Interval(-oo, 0))
Out[1]: ∅

In [2]: solveset(Eq(-x**3+x-1,0), x, Interval(-oo, oo))
Out[2]: 
⎧      ____________                   ⎫
⎪     ╱ 3⋅√69   27                    ⎪
⎪  3 ╱  ───── + ──                    ⎪
⎪  ╲╱     2     2            1        ⎪
⎨- ──────────────── - ────────────────⎬
⎪         3               ____________⎪
⎪                        ╱ 3⋅√69   27 ⎪
⎪                     3 ╱  ───── + ── ⎪
⎩                     ╲╱     2     2  ⎭

1st case should return ans.

[latot]

mm, seems solveset have other issue here:

>>> solveset(Eq(-x**3+x-1,0), x, Interval(-oo, 0))
EmptySet()
>>> solveset(Eq(-x**3+x-1,0), x, Interval(0, oo))
EmptySet()
>>> solveset(Eq(-x**3+x-1,0), x, Interval(0, 0))
EmptySet()

And remember this is an example, the idea its can send more than 1 eq.
Should i open a new issue for solveset?

Thx.