Subject: double integrals seem to give different answers
From: Andrej Vodopivec
Date: Sun, 22 Nov 2009 08:12:12 +0100
> 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