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

• To: mathgroup at smc.vnet.net
• Subject: [mg54300] Re: [mg54271] Re: Bug Report - Two numerical values for a same variable
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 16 Feb 2005 14:36:27 -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>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

The manipulations below are precisely what's so confusing about Rational 
objects (and Complex objects) being atoms.  If

   1/2 /. Rational[x_, 2] -> Rational[x, 7]

works, then why not the following?

   Part[Rational[1, 2], 2]

I can "believe" that integers and reals (and maybe strings) are atoms; 
but believing that rationals and complex numbers are atoms is a hard 
thing to swallow!

This has always bothered me -- and hence given me trouble trying to, um, 
rationalize this to students when I've taught Mathematica.


Scott Hemphill wrote:
> DrBob <drbob at bigfoot.com> writes:
> 
> 
>>That explains it, but only in the sense that "things fall down" is a theory of gravity. Why should Rationals be atomic, for goodness sake? And how did I use Mathematica all this time without hearing about it?
>>
>>Sigh...
> 
> 
> 
> In[1]:= FullForm[1/2]
> 
> Out[1]//FullForm= Rational[1, 2]
> 
> In[2]:= 1/2 /. Rational[x_,2] -> Rational[x,7]
> 
>         1
> Out[2]= -
>         7
> 
> Scott

-- 
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: Bug Report - Two numerical values for a same variable
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Re: Re: Bug Report - Two numerical values for a same variable
    • From: Sseziwa Mukasa <mukasa@jeol.com>

• References:
  • Re: Bug Report - Two numerical values for a same variable
    • From: Scott Hemphill <hemphill@hemphills.net>