Re: ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?

• To: mathgroup at smc.vnet.net
• Subject: [mg56935] Re: ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Tue, 10 May 2005 03:42:51 -0400 (EDT)
• References: <d5mukl\$dru\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"steve" <nma124 at hotmail.com> wrote:
> hi;
> Mathematica 5.1, on windows.
>
> ArcTan[1/0] gives an error but
> ArcTan[Infinity] gives the correct answer.
>
> One way to make ArcTan[1/0] give Pi/2 is to
> write it as ArcTan[0,1].
>
> I do know that 1/0 is DirectedInfinity[] with
> unknown direction while Infinity is
> DirectedInfinity[1], and that is probably the
> reason that ArcTan[1/0] gives an error
> but ArcTan[Infinity] does not.
>
> I am asking is how to make 1/0 result in DirectedInfinity[1]
> to avoid the error? is this possible?

That could be done, by changing the definition of division, but doing so
would be highly inadvisable in general. (However, in some particular
contexts -- for example, if one were dealing only with nonnegative extended
reals -- then it would be perfectly correct to have 1/0 give
DirectedInfinity[1]. But how would we restrict Mathematica to such a
context?)

> What function do I need to wrap 1/0 with to cause it to become
> Infinity[1] instead of Infinity[] ?

The simplest would surely be Abs[]. That's a reasonable option iff the
result you want from ArcTan[t] is always supposed to be in the
interval [0, Pi/2]; otherwise, do as you suggested below, changing your
code to use ArcTan[x, y] instead.

> or may be I need to figure how
> to detect if a division results in Infinity[]
> and convert that to Infinity[1]? do I need
> to redfine 1/0 somehow? may be make a new
> rule to say if Mathematica see 1/0 expression then
> make it Infinity[1]? but may be this will screw
> other things?

The latter, IMO.

> Or may I should not mess with this stuff and
> just change the code to ArcTan[x,y] instead of
> ArcTan[y/x] and be happy?

Why not?

David

```

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