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

*To*: mathgroup at smc.vnet.net*Subject*: [mg54345] 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 02:31:45 -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> <opsmcn3rqciz9bcq@monster> <07c9f53bde86ce72650298f7c2a6ccbc@mimuw.edu.pl>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

All that was very puzzling. You're saying Pi+E I is numeric but Complex[Pi,E] isn't because... Umm... I've got no idea what your reasoning is. >> Complex[a,b] when a and b are numeric quantities, such >> as Pi or E or others is not numeric Because... because why? >> Complex[a,b] where a and b are non real is meaningless But Pi and E _are_ real. Are you saying Mathematica doesn't know that? >> Complex[Pi,E] (unlike Pi+ I E to which it is not equal [to] Why aren't they equal? We're really back to "things fall down" to explain gravity. Bobby On Thu, 17 Feb 2005 17:50:28 +0100, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > *This message was transferred with a trial version of CommuniGate(tm) Pro* > On 17 Feb 2005, at 17:29, DrBob wrote: > >> Your "structure" argument is too vague to be useful. > > Whether useful or not it is true. > > >> NumericQ[Pi + E*I] >> NumericQ[Complex[Pi, E]] >> True >> False >> >> The last result, at least, seems unambiguously wrong. > > > It is not only right but it is the only sensible possibility. > In Mathematica Complex[a,b] when a and b are numeric quantities, such > as Pi or E or others is not numeric but meaningless. It has to be > meaningless because Complex[a,b] where a and b are non real is > meaningless. However, if a and b are numeric but not numbers > Mathematica would have to use FullSimplify or high precision arithmetic > to determine if they are real or have non zero imaginary parts (and it > may not be able to do so anyway). > So until it was determined that a and b have zero imaginary parts > Complex[a,b] would have to be like the Schroedinger cat that is neither > dead nor alive: neither meaningful nor meaningless. That's is > definitely not the way to make a computer algebra program work. So > Complex[Pi,E] (unlike Pi+ I E to which it is not equal > > In[24]:= > Complex[Pi, E] == Pi + I*E > > Out[24]= > Complex[Pi, E] == I*E + Pi ) > > is meaningless. Hence it is not numeric and it is you and not > Mathematica that is "unambiguously wrong". > > Andrzej Kozlowski > > > > -- 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>