Beginners Question

[ab0c...@gmail.com]

Dear user and developers,

I'm new to sympy and tried a few things out, of course I stumbled across smth I coudln't understand.
So here is my question:

If I define an expression like

g=sqrt(a/pi)*exp(-a*x**2)

and integrate it like

integrate(g,(x,-oo,oo))

I get the expected result (1).

But if I integrate an expression like

g=sqrt(1/a/pi)*exp(-x**2/a)

and integrate it the same way I get

( a * sqrt(1/a) ) / sqrt(polar_lift(a))

I must admit I'm a little bit frightened by the polar_lift function because I've never heard of it, but it seems to give the argument of a complex number. Is this correct?
But then I don't understand why for

a=Symbol('a',real=True)

g=sqrt(1/a/pi)*exp(-x**2/a)

simplify(integrate(g,(x,-oo,oo)))

I still don't get 1 as a result.

Would be nice to know.
Thanks in advance.

[Ondřej Čertík]

Hi ab0c1d0ef,

Thanks for reporting this, I think you might have discovered a bug.
Btw, this is what I get with the latest master:

https://gist.github.com/certik/cd8cd4c0a7f0ba04c719

But it still shows the behavior you described.

Ondrej

>
> Would be nice to know.
> Thanks in advance.
>

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[Aaron Meurer]

a needs to be positive for polar_lift to reduce. The result is
correct, but it doesn't reduce to 1 unless a is positive.

I'm not sure what the abs(periodic_argument(1/polar_lift(a), oo)) <=
pi/2 reduces to.

Aaron Meurer

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