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Re: Possible Bug in ArcTan ?

• To: mathgroup at smc.vnet.net
• Subject: [mg64894] Re: Possible Bug in ArcTan ?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Tue, 7 Mar 2006 06:11:44 -0500 (EST)
• Organization: The University of Western Australia
• References: <du6o44$5rg$1@smc.vnet.net> <du83m5$sv3$1@smc.vnet.net> <du8are$fp7$1@smc.vnet.net> <dubgv0$fm7$1@smc.vnet.net> <due86a$9vj$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <due86a$9vj$1 at smc.vnet.net>,
 "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de> wrote:

> why you want avoid the two-argument form. The two-argument form help
> a lot during programing, because one has not to type
> 
> If[x=!=0,ArcTan[y/x]]
> 
> and a division by zero is in the most programing languages
> a very hard and evil error.

There is no "division by zero" error using the form

  2 ArcTan[y/(x+Sqrt[x^2+y^2])]

except when x == y == 0 -- where the result is undefined anyway. 
However, as David Cantrell points out, this form (only) fails if y is 
zero and x is negative (returning 0 instead of Pi), and so must be 
considered separately.

Since Mathematica has the two-argument form, one should use it. However, 
my point was that, mathematically, 2 ArcTan[y/(x+Sqrt[x^2+y^2])] is 
preferable to ArcTan[y/x].

Cheers,
Paul

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Paul Abbott                                      Phone:  61 8 6488 2734
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