Trouble with a simple trig equation and solveset

[Kevin Moore]

Hello - I'm trying to use Sympy Live to debug an issue with a program I'm writing. When I try to use solveset for sin(x)=1/2, I get no solutions. Apparently it thinks there's a tiny complex portion to the solution.

Why am I running into this? Ironically I'm not running into this problem in my own script - maybe it's a version issue?

Kevin

solveset(Eq(sin(x),1/2),x,S.Reals)

∅

solveset(Eq(sin(x),1/2),x,S.Complexes)

{−i(i(2nπ+0.523598775598299)−1.11022302462516⋅10−16)∣∣n∈Z}∪{−i(i(2nπ−0.523598775598299+π)−1.11022302462516⋅10−16)∣∣n∈Z}

[Oscar Benjamin]

This is a bug. Can you open an issue with sympy on GitHub?

The correct answer is given if you use exact rational numbers (S(1)/2
or Rational(1, 2)) rather than the float 1/2:

In [6]: solveset(Eq(sin(x), S(1)/2), x, Reals)
Out[6]:
⎧ 5⋅π │ ⎫ ⎧ π │ ⎫
⎨2⋅n⋅π + ─── │ n ∊ ℤ⎬ ∪ ⎨2⋅n⋅π + ─ │ n ∊ ℤ⎬
⎩ 6 │ ⎭ ⎩ 6 │ ⎭

The problem is that solveset solves this in an overly complicated way
using complex numbers even if the domain is reals. Then a small
rounding error makes it look like the solutions are not real.

--
Oscar

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[Chris Smith]

https://github.com/sympy/sympy/issues/25768