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

• To: mathgroup at smc.vnet.net
• Subject: [mg56922] Re: ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
• From: dh <dh at metrohm.ch>
• Date: Tue, 10 May 2005 03:42:28 -0400 (EDT)
• References: <d5mukl\$dru\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Steve,
If you are know what you are doing, you could redefine the value of 0^-1
by the following:

Unprotect[Power];
Power[0, -1] = DirectedInfinity[1];

with this you will then get:
ArcTan[1/0]   -->   Pi/2

Sincerely, Daniel

steve 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
>

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