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

• To: mathgroup at smc.vnet.net
• Subject: [mg56918] Re: [mg56878] ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Tue, 10 May 2005 03:42:20 -0400 (EDT)
• References: <200505090545.BAA13789@smc.vnet.net>
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

I don't know about other version, but the following makes me worried:
In[1]:=
Limit[ArcTan[1/x],x->0]==Limit[ArcTan[1/x],x->0,Direction->-1]
Out[1]=
True
In[2]:=
Limit[ArcTan[1/x],x->0]==Limit[ArcTan[1/x],x->0,Direction->1]
Out[2]=
False
In[3]:=
$Version
Out[3]=
5.0 for Microsoft Windows (November 18, 2003)

Isn't there a requirement that the right and left limits match before
a limit exists?

On 5/9/05, 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?
> 
> What function do I need to wrap 1/0 with to
> cause it to become Infinity[1] instead of
> Infinity[] ?  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?
> 
> 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?
> 
> thanks,
> Steve
> 
> 


-- 
Chris Chiasson
http://chrischiasson.com/
1 (810) 265-3161

• References:
  • ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
    • From: "steve" <nma124@hotmail.com>