Re: Re: solve and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg69403] Re: [mg69397] Re: solve and Abs
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Mon, 11 Sep 2006 05:38:39 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <edtrmv\$le6\$1@smc.vnet.net> <200609101120.HAA11282@smc.vnet.net>

```And probably the most one should expect is:

Reduce[x - Abs[x] == 0, x] // InputForm
Re[x] >= 0 && Im[x] == 0

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.
>>
>
> Hello,
>
>   the result {{}} means that Solve did not find values for x, which
> fulfill the equation without "special conditions". The help browser
> tells us:
> "Solve gives generic solutions only. It discards solutions that are
> valid only when the parameters satisfy special conditions. Reduce gives
> the complete set of solutions. "
>
> The special condition in this case is obviously x>=0.
>
> Greetings,
>   Peter
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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