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MathGroup Archive 2005

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Re: DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55818] Re: [mg55802] DirectedInfinity[1 + I], why does it get replaced by (1 + I)/(sqrt(2) ?
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 7 Apr 2005 05:09:56 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200504060711.DAA13652@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

Evidently, the resulting complex number inside the DirectedInfinity 
expression has complex modulus 1, so that number is suitable to 
represent a "pure direction", without a magnitude.  If you think of a 
complex number as a vector in the real plane, then you're getting a unit 
vector with the same direction as the original vector.

Of course it would have been nice to have this properly documented!

Matt wrote:
> Hello,
>   This isn't particularly important probably, however, I am trying to
> learn as much about Mathematica as possible, and I thought this might
> shed some light on a 'Why Mathematica does this or that' principle.
> 
>   I'm working my way through 'The Mathematica Guidebook for
> Programming' and on page 177, he gives an example as follows:
> 
> In[39]:= DirectedInfinity[1 + I] DirectedInfinity[I]
> Out[39]:= DirectedInfinity[-(1 - I)/sqrt(2)]
> 
> That puzzled me a bit, so I decided to see what Mathematica would do
> with just the first part:
> 
> In[40]:= DirectedInfinity[1 + I]
> Out[40]:= DirectedInfinity[(1 + I)/sqrt(2)]
> 
> I realize that (1 + I)/sqrt(2) is in the same direction as (1 + I), but
> why did Mathematica change it to the more 'strange' form?
> 
> Thanks,
> 
> Matt
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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