The atan2 simplification function sometimes asks questions:
(%i1) atan2(x,x);
Is x positive or negative? pos;
(%o1) %pi/4
Regardless of your opinion about asksign in general, it seems
wrong for a simplification function to use asksign. We could
change atan2 to use atan2(x,x) = (%pi/4) * (2 * signum(x) - 1).
This is wrong for x = 0, x = %i, ... Suggestions?
Also
(%i1) atan2(sqrt(x-1),x);
(%o1) atan(sqrt(x-1)/x) <-- atan not atan2
(%i2) atan2(sqrt(x),x);
(%o2) atan2(sqrt(x),x) <-- this time atan2
Barton