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

• To: mathgroup at smc.vnet.net
• Subject: [mg54353] Re: [mg54322] Re: Re: Bug Report - Two numerical values for a same variable
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 19 Feb 2005 02:31:54 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <00ed01c512b0$2f242850$6400a8c0@Main> <curpbn$r28$1@smc.vnet.net> <200502150438.XAA29728@smc.vnet.net> <cv0953$jbg$1@smc.vnet.net> <200502171530.KAA02364@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

Right.  And one can use something like

   StringTake["HelloWorld", {6}]

to extract part of the "atom" that is the string there.  (This is in 
contrast, say, to taking Floor[3.14] which is clearly applying an 
"operation" to the atome 3.14.)

So that's why I originally said I wasn't too sure why strings were 
atoms, either.

Steve Luttrell wrote:
> I am also uneasy about Complex and Rational being atomic. The only reason I 
> can think of is that computational efficiency might prefer these to be 
> atomic objects.
> 
> You can do the following to extract the parts of a Rational:
> 
> Numerator[Rational[1, 2]]
> 
> Denominator[Rational[1, 2]]
> 
> Analogously, Re and Im can be used to extract the "parts" of a Complex.
> 
> Steve Luttrell
> 
> "Murray Eisenberg" <murray at math.umass.edu> wrote in message 
> news:cv0953$jbg$1 at smc.vnet.net...
> 
>>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
>>
> 
> 
> 
> 

-- 
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: Bug Report - Two numerical values for a same variable
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• 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: "Steve Luttrell" <steve_usenet@_removemefirst_luttrell.org.uk>