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 >

**Follow-Ups**:**Re: Re: Re: Bug Report - Two numerical values for a same variable***From:*Murray Eisenberg <murray@math.umass.edu>

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