# [Maxima] double integrals seem to give different answers

G. Jay Kerns gkerns at ysu.edu
Sun Nov 22 01:28:04 CST 2009

```On Sun, Nov 22, 2009 at 2:12 AM, Andrej Vodopivec
<andrej.vodopivec at gmail.com> wrote:
>> A possible correction might be to do the simplification of atan(tan(x))
>> --> x in the routine INTSUBS to avoid a call of ATAN-POLES.
>
> I don't think this is a correct solution. With this substitution
> integrate(atan(tan(x)), x, 0, 2*%pi) would be 2*%p^2. Maxima gets a
> wrong answer for both values of triginverses:
>
> (%i2) integrate(atan(tan(x)), x, 0, 2*%pi), triginverses=all;
> (%o2) 2*%pi^2
> (%i3) integrate(atan(tan(x)), x, 0, 2*%pi), triginverses=true;
> (%o3) %pi^2/2
>
> I think that atan-poles should figure out that the correct value in 0.
>
> Andrej
> _______________________________________________

I would just like to say "thanks" to Richard (both of them), Deiter,
and Andrej.   I definitely have a better idea of what is happening. I
should have remembered about the ambiguity of roots, and now I have
learned about the atan-poles problem.

Thanks again.

Best,
Jay
```