solveset(sin(pi*x), x, domain=S.Reals) doesn't give the solution

[asmeurer]

See https://stackoverflow.com/questions/37603511/sympy-solve-for-all-solutions-on-domain.

In [2]: solveset(sin(x), x, domain=S.Reals)
Out[2]: {2⋅n⋅π | n ∊ ℤ} ∪ {2⋅n⋅π + π | n ∊ ℤ}

In [3]: solveset(sin(pi*x), x, domain=S.Reals)
Out[3]:
⎧               ⎛ 2⋅ⅈ⋅π⋅x    ⎞  -ⅈ⋅π⋅x     ⎫
⎪            -ⅈ⋅⎝ℯ        - 1⎠⋅ℯ           ⎪
⎨x | x ∊ ℝ ∧ ────────────────────────── = 0⎬
⎪                        2                 ⎪
⎩                                          ⎭

[kshitij10496]

For solving trigonometric functions, we rewrite them in terms of exponential function.
As can be seen in this example, we cannot solve all the corresponding exponential equations.

However, some can be solved via solve_decomposition. #11141
I have been working on solving this particular example for some time.

[oscarbenjamin]

This works fine-ish now in master:

In [5]: solveset(sin(x), x, domain=Reals)                                                                                                                     
Out[5]: {2⋅n⋅π | n ∊ ℤ} ∪ {2⋅n⋅π + π | n ∊ ℤ}

That should simplify a bit but it is an explicit form of the solution.

[asmeurer]

The problem is with the sin(pi*x) version. I still get the nonuseful result for it in master.

[gschintgen]

With the draft PR #19507:

In [4]: solveset(sin(pi*x), x, domain=S.Reals)
Out[4]:
                ⎧2⋅n⋅π + π        ⎫
{2⋅n | n ∊ ℤ} ∪ ⎨───────── | n ∊ ℤ⎬
                ⎩    π            ⎭

In [5]: simplify(_)
Out[5]: {2⋅n | n ∊ ℤ} ∪ {2⋅n + 1 | n ∊ ℤ}