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

*To*: mathgroup at smc.vnet.net*Subject*: [mg54341] Re: [mg54300] Re: [mg54271] Re: Bug Report - Two numerical values for a same variable*From*: DrBob <drbob at bigfoot.com>*Date*: Sat, 19 Feb 2005 02:31:41 -0500 (EST)*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>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Your "structure" argument is too vague to be useful. ls={3+2*I,3+E*I,3.+E*I,Pi+2.*I,Pi+2*I,Pi+E*I}; AtomQ/@ls {True,False,True,True,False,False} Length/@ls {0,2,0,0,2,2} Map[g, ls, -1] {g[3 + 2*I], g[g[3] + g[g[I]*g[E]]], g[3. + 2.718281828459045*I], g[3.141592653589793 + 2.*I], g[g[2*I] + g[Pi]], g[g[Pi] + g[g[I]*g[E]]]} Map[NumericQ, ls, -1] {True, False, True, True, False, False} Map[NumericQ, ls, 1] {True, True, True, True, True, True} NumericQ[Pi + E*I] NumericQ[Complex[Pi, E]] True False The last result, at least, seems unambiguously wrong. Bobby On Thu, 17 Feb 2005 08:37:48 +0100, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > *This message was transferred with a trial version of CommuniGate(tm) Pro* > The reasons why Rational[2,3] or Complex[2,3] are atoms are nor really > mathematical but come from considering the structure of expressions in > the Mathematica language and way expressions are transformed by various > structured operations. To see what I mean consider the following list > > ls = {1, 2, 3/4, 5 + 6*I, Rational[a, b]}; > > > Note that 3/4 evaluates to the atom Rational[3,4] but Rational[a,b] is > not an atom and is actually meaningless. > I think most people would agree that we would like all the numbers > 1.2,3/4 and 5+6I to be treated "in the same way" by various structured > operations that accept level specifications, such as like Map, Apply > etc. This is indeed the case. Consider > > In[2]:= > Map[g, ls, -1] > > Out[2]= > {g[1], g[2], g[3/4], g[5 + 6*I], g[Rational[g[a], g[b]]]} > > You can see the difference between the treatment of the atomic > Rational[3,4] (or Complex[5,6]) and non-atomic Rational[a,b]. This and > similar reasons justify treating Rational[3,4] and Complex[5,6] as > atoms. This is a quite different issue from the one whether rationals > or complex numbers are in some mathematical sense "atoms" or not. A > case can be made both for the "yes" and the "no" answer, but it has > nothing to do with the reason why in Mathematica Rational[2,3] and > Complex[5,6] are atoms. > > Andrzej Kozlowski > > > On 16 Feb 2005, at 20:36, Murray Eisenberg wrote: > >> 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 >> >> > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**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>