Re: Re: solve and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg69456] Re: [mg69398] Re: solve and Abs
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• 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 ;-)

Andrzej

```

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