How to solve x**2 + y**2 == 0 in real domain?

[Jisoo Song]

It seems that solveset only deals with univariate equation, while solve does not consider the domain.

How can I get x==0 & y==0 by solving x**2 + y**2 == 0 in real domain?

[Aaron Meurer]

I'm not sure if it's supported. Normally to get solve() to return only
real solutions you set real=True on the variables. But it doesn't seem
to handle this case. It only wants to give the solutions [(-I*y, y),
(I*y, y)].

Aaron Meurer

On Tue, Jan 21, 2020 at 7:00 AM Jisoo Song <jeeso...@gmail.com> wrote:
>
> It seems that solveset only deals with univariate equation, while solve does not consider the domain.
>
> How can I get x==0 & y==0 by solving x**2 + y**2 == 0 in real domain?
>

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[Aaron Meurer]

solve() could be doing something like this to filter out the
parametric solution for x given the real assumption on x

>>> x, y = symbols('x y', real=True)
>>> solve(x**2 + y**2, [x, y])
[(-I*y, y), (I*y, y)]
>>> solve(Eq(I*y, re(I*y)), y)
[0]
>>> (I*y).subs(y, 0)
0

I don't know if it would work in more general cases.

Aaron Meurer