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: <email@example.com>
- 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, 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 > 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. 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 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? 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? 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