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

• To: mathgroup at smc.vnet.net
• Subject: [mg54322] Re: Re: Bug Report - Two numerical values for a same variable
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Thu, 17 Feb 2005 10:30:42 -0500 (EST)
• References: <00ed01c512b0\$2f242850\$6400a8c0@Main> <curpbn\$r28\$1@smc.vnet.net> <200502150438.XAA29728@smc.vnet.net> <cv0953\$jbg\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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
>

```

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