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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>