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

• To: mathgroup at smc.vnet.net
• Subject: [mg56878] ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
• From: "steve" <nma124 at hotmail.com>
• Date: Mon, 9 May 2005 01:45:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: ArcTan[1/0] no result, but ArcTan[Infinity] ok. How to resolve?
    • From: Chris Chiasson <chris.chiasson@gmail.com>