In maxima, if you evaluate
atan2(y,x)+atan2(-y,x)
you get zero as you should. If you try something more complicated,
like:
atan2(2^(1/2)*omega^(1/2)+2*k,omega+2^(1/2)*k*omega^(1/2)+k^2-1)
+atan2(-2^(1/2)*omega^(1/2)-2*k,omega+2^(1/2)*k*omega^(1/2)+k^2-1)
where all variables are declared real and assumed to be positive,
you don't get zero. On the other hand, if I substitute z^2 for omega in
the last expression, I get zero again. It seems that maxima is having
trouble with a possible sqrt branch issue and ignoring the assume(omega
> 0 ).
Thanks in advance.
David