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

• To: mathgroup at smc.vnet.net
• Subject: [mg54342] Re: [mg54300] Re: [mg54271] Re: Bug Report - Two numerical values for a same variable
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 19 Feb 2005 02:31:42 -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>
• Sender: owner-wri-mathgroup at wolfram.com

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

• 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>