# [Maxima] atan2(x,x)

Robert Dodier robert.dodier at gmail.com
Sat Nov 29 17:48:44 CST 2008

```On 11/18/08, Viktor T. Toth <vttoth at vttoth.com> wrote:

> > Probably every variation you have thought of has been considered

> That's why I asked. Given Maxima's 30-year history, I hesitate every time it
>  occurs to me to "improve" on something, because there's a good chance that
>  whatever I have in mind has already been tried, and there's probably a good
>  reason why it wasn't done that way in the end.

Please don't be discouraged.

>  No argument there, I've cursed assume almost as often as I've cursed
>  asksign.

Yes, assume is pretty weak & needs to be strengthened.

> Since I mentioned Maple, I should also mention that I find the
>  construct "eval(<expr>) assuming <cond>" quite useful.

Agreed.

>  > e.g.  instead of simplifying x/x  to 1,   we might need
>  > "if x=0 then undefined else 1"  or "1 unless x=0"
>
> I always thought of this as unnecessary pedantry with little or no practical
>  value. Now x/abs(x) is another matter, since the left and right limits don't
>  agree (Maple, quite incorrectly in my opinion, evaluates x/abs(x) it to +1
>  at x=0, which can lead to contradictory results depending on the order of
>  evaluation), but what purpose would it serve to leave x/x undefined at 0?

Disagreed about pedantry here. A computer should be able to
keep track of details that would be burdensome to a human.
Sometimes the details matter, sometimes they don't --- when
you're solving a new problem, there's really no way to tell which
one in advance.

Maybe this business with implicit assumptions is, in part, a
display problem. Maybe a result could be tied to a collection
of assumptions, which is present in the display but usually
closed, and optionally opened to display stuff like "assuming x # 0".

FWIW

Robert Dodier
```

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