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Re: Re: Re: Re: Bug Report - Two numerical values for a same variable

• To: mathgroup at smc.vnet.net
• Subject: [mg54411] Re: [mg54350] Re: [mg54300] Re: [mg54271] Re: Bug Report - Two numerical values for a same variable
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 20 Feb 2005 00:08:28 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <00ed01c512b0$2f242850$6400a8c0@Main> <curpbn$r28$1@smc.vnet.net> <200502150438.XAA29728@smc.vnet.net> <200502161936.OAA19223@smc.vnet.net> <d3d3aacf7f18939828890ce85676bd26@mimuw.edu.pl> <opsmcn3rqciz9bcq@monster> <07c9f53bde86ce72650298f7c2a6ccbc@mimuw.edu.pl> <opsmcqckt8iz9bcq@monster> <200502190731.CAA06012@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

I understand everything you say.  Here's the crux, I think, of my not 
being able to "rationalize" Mathematica's definition of what is or is 
not an atom:

Why is FullForm[2 + 3 I] not Plus[2, Times[3, I]]?

Why is FullForm[2/3] not  Times[2, Power[3, -1]] ?

My suspicion is that this was simply a design decision made for reasons 
of efficiency, and that therefore not much more can be said about it. 
That's what makes it hard for me to swallow and explain to others.

P.S. Unlike some others, I have no difficulty with Mathematica counting 
such things as Complex[E, Pi] as meaningless (although syntactically 
correct).


Andrzej Kozlowski wrote:
> ...
> Complex[Pi,E] does not have any meaning in Mathemaitca at all. Neither 
> does Complex[Sqrt[2],Sqrt[3]] etc. Complex[a,b] only has a meaning when 
> a and b are real numbers (exact or approximate).
> 
> ...
> Of course all of these statements refer to the design of the language. 
> To me they seem perfectly logical and natural. To you presumably not. 
> Well, then there is nothing else to say.

-- 
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

• Follow-Ups:
  • Re: Re: Re: Re: Re: Bug Report - Two numerical values for a same variable
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Re: Re: Re: Re: Bug Report - Two numerical values for a same variable
    • From: DrBob <drbob@bigfoot.com>

• References:
  • Re: Bug Report - Two numerical values for a same variable
    • From: Scott Hemphill <hemphill@hemphills.net>
  • Re: Re: Bug Report - Two numerical values for a same variable
    • From: Murray Eisenberg <murray@math.umass.edu>
  • Re: Re: Re: Bug Report - Two numerical values for a same variable
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>