#3892 limit(atan2(y,zeroa),y,1) --> errror

[Barton Willis]

Maybe zerob & zeroa shouldn't be used this way, but giving an error for the following isn't ideal

(%i16)  limit(atan2(y,zeroa),y,1);
expt: undefined: 0 to a negative exponent.

Possibly limit(atan2(y,x),x,0,plus) should be atan2(y,zeroa). That could be useful in the iterated limit limit(limit(atan2(y,x),x,0,plus),y,1).

[Stavros Macrakis]

Certainly the bug should be fixed.

I understand the temptation to use atan2(...,zeroa), but this is problematic:

• It is not mathematically correct. Once you've taken the limit, the result doesn't "know" where it came from: mathematically, signum(limit(x,x,0,plus)) is 0, not 1, as opposed to limit(signum(x),x,0,plus).

• If we start using zeroa here, it suggests to the user that we support infinitesimals as part of symbolic expressions, which we do not.

On the other hand, Maxima currently has no way of expressing multivariate limits, e.g., limit(atan2(x,y),[y,x],[1,zeroa]). That might be worth thinking about.

[Barton Willis]

So maybe a nounform for limit(atan2(y,zeroa),y,1) would be best.