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

**Follow-Ups**:**Re: Re: Re: solve and Abs***From:*Daniel Lichtblau <danl@wolfram.com>