limit(x**n, x, -oo) is sometimes wrong

[pelegm]

For example,

>>> n = Symbol('n', integer=True, positive=True)  # could be 3
>>> limit(x**n, x, -oo)
oo

while

>>> limit(x**3, x, -oo)
-oo

It looks like it assumes n is even, because stating odd=True for n seems to solve this issue.

[Amitjha1412]

Hi ,
I am new to Sympy community. I wanted to get started with this bug. Can you please explain more about this bug ?

Thanks.
Amit

[pelegm]

Can you ask a more specific question?

[Amitjha1412]

Where should i start looking into?

[pelegm]

Where should i start looking into?

I have no idea. I just reported the bug, I don't have a clue about where to start looking for a solution.

[sandeepveethu]

It looks like it assumes n is even, because stating odd=True for n seems to solve this issue.

>>>n=symbols('n',integer=True,positive=True,odd=True)
>>>x=symbols('x')
>>>limit(x**n,x,-oo)
oo

@pelegm odd=True doesn't solve this issue
@jksuom can you help me in fixing this , i think limitinf function is causing this issue but i am not able to figure out where?

[jksuom]

I'm afraid this is not going to be easy to fix. It seems that limit invokes gruntz even if that would not be necessary in this case. That will routinely replace the variable x with an expression of type -exp(y) (as x is expected to be negative). Then x**n will take the form exp(y*n + I*pi*n), which is correct. But afterwards, in passing to the limit y -> oo, the I*pi*n term is lost and the result will be exp(oo) = oo.

It seems to me that the limit should be computed without passing over to gruntz, but that would imply a major rearrangement of limit.

[sandeepveethu]

@jksuom thanks a lot for the insight.

[anutosh491]

Currently this functions opposite to what the issue was reported for

>>> n = Symbol('n', integer=True, positive=True)
>>> limit(x**n, x, -oo)
-oo