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MathGroup Archive 2006

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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>
  • Reply-to: murray at math.umass.edu

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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