solveset_real(exp(I*x), x) for real `x`

[Gaurav Dhingra]

Hi all

Though `solveset_real` claimes to be complete in terms of real solution returned

But for this

>>> x = Symbol('x', real=True)

>>> solveset_real(exp(I*x), x)

FiniteSet(0)

But probably the solution is what is returned for the `solveset_complex`

>>> y = Symbol('y')

>>> solveset_complex(exp(I*y), y)

ImageSet(Lambda(_n, 2*_n*pi), Integers())    # correct solution returned

                                     # same should be returned for `solveset_real` ?

Is there any reason why we just get `FiniteSet(0)`  ?

Cheers

Gaurav

[Harsh Gupta]

> Though `solveset_real` claims to be complete in terms of real solution returned

Well, solveset_real assumes that you are working in a real system,
that means both the equation and the solutions are in a real domain.
So solveset_real expect users to input equations like `exp(I*x) = 0`
and it should probably raise an error or maybe the doc string needs to
be updated. As you have figured out for yourself if someone wants to
work in the complex domain they can always use solveset_complex.

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Harsh

[Gaurav Dhingra]

Thanks for answering

Though i forgot put `-1` 

Sorry

Now equation is `solveset_real(exp(I*x) - 1, x)` now this should return  `ImageSet(Lambda(_n, 2*_n*pi), Integers())`

but currently returns `FiniteSet(0)` what about this ?

[Harsh Gupta]

The "effective input" to exp in exp(I*x) is not real for any non-zero
real value of x, so 0 is the only real point in the domain hence the
solution is correct. I should clarify that the input function/equation
of solveset_real are functions of real variable [1] and are also
real-valued [2] functions. This means they should map a subset of real
numbers to a subset of real numbers.

[1]: https://en.wikipedia.org/wiki/Function_of_a_real_variable
[2]: https://en.wikipedia.org/wiki/Real-valued_function

> https://groups.google.com/d/msgid/sympy/dc3589c8-e9d7-40f6-b0ad-8810dedd5ae9%40googlegroups.com.