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MathGroup Archive 2006

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Re: Re: solve and Abs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69400] Re: [mg69398] Re: solve and Abs
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 11 Sep 2006 05:38:31 -0400 (EDT)

On 10 Sep 2006, at 20:20, Peter Pein wrote:

> Richard J. Fateman schrieb:
>> Is there a reason (in 5.1) for Solve[x-Abs[x]==0,x] to return {{}}?
>> This supposedly means all variables can have all possible values.
>>
>> Reduce does better.
>>
> Oops, I should have read further...
> Help says
> "Solve gives {{}} if all variables can have all possible values."
> I would consider this a bug, not a feature.
>
> Sorry for overhasty posting,
> Peter
>

However, the documentation does not say "Solve gives {{}} if and only  
if all variables can have all possible values." There are other cases  
when Solve returns {{}}. For example, Solve also gives {{}} when, for  
example, there is no "generic" solution. (This is stated in the Help  
also). In addition, although this does not seem to be stated, Solve  
never returns solutions that would have to be given in conditional  
form (like the solution returned in this example by Reduce). This  
does not appear to be stated in the help but has been pointed out  
several times on this list.

Andrzej Kozlowski
Tokyo, Japan


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