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Re: Re: solve and Abs

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  • Subject: [mg69456] Re: [mg69398] Re: solve and Abs
  • From: Andrzej Kozlowski <akoz at>
  • Date: Wed, 13 Sep 2006 04:01:46 -0400 (EDT)

On 12 Sep 2006, at 20:40, Peter Pein wrote:

> Andrzej Kozlowski schrieb:
>> (tm) Pro*
>> 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
> all variables can have all possible values =:AVAPV
> solve rteurns {{}} =:SRE
> But if AVAPV=>SRE but not SRE=>AVAPV, what use has SRE? It would be  
> better to admit "no solutions found" (by returning {}).
> Or am I completely wrong?
> Confused greetings,
>  Peter

Oops, I think you are right. In fact, when Solve can find no generic  
solutions it returns {} and not {{}}.

Solve[{x + y == 1, x + y == a}, {x, y}]


So it does seem that {} has a different meaning from {{}}, which  
makes me now also confused ;-)


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