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Re: FindInstance returning incorrect results
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71388] Re: [mg71344] FindInstance returning incorrect results
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Thu, 16 Nov 2006 00:53:49 -0500 (EST)
*References*: <200611151144.GAA01342@smc.vnet.net>
You are using FindInstance correctly and it seems you have found a
bug. Besides your another thing that suggest that something is wrong
is this:
In[59]:=
FindInstance[c*c == -1 && c*d == I && c != 0, {c, d}]
From In[59]:=
"TriangularSet in Reduce.m is incorrect"
Out[59]=
{{c -> -I, d -> -1}}
This is with
In[60]:=
$Version
Out[60]=
5.1 for Mac OS X (October 25, 2004)
Andrzej Kozlowski
On 15 Nov 2006, at 20:44, Jason Grout wrote:
> I ran into the following problem with FindInstance today. Is this a
> known problem? Am I using FindInstance correctly? A simple example
> where the problem comes up is in finding values c and d such that
> c^2=-1
> and c*d=I.
>
> First, let's make sure a solution exists:
>
> Clear[c,d]; Solve[{c*c== -1, c*d== I},{c,d}]
>
> gives
>
> {{c -> -I, d -> -1}, {c -> I, d -> 1}}, which is correct.
>
> FindInstance[c*c== -1 && c*d == I, {c,d}] gives the _incorrect_ answer
> {{c -> 0, d -> 0}}.
>
> FindInstance[c*c == -1 && c*d == I, {c,d}, Complexes]
> also gives {{ c -> 0, d -> 0}}, which again is an incorrect answer.
>
> However, if I ask for more than one solution, FindInstance gives
> correct
> answers. For example:
>
> FindInstance[c*c == -1 && c*d == I, {c,d}, 2] gives the answers that
> Solve gave above.
>
> Am I using FindInstance incorrectly? It seems odd that I get correct
> answers only when I ask for more than one answer. The documentation
> mentions that FindInstance uses a faster method for generating an
> example if only one example is needed--is that causing a problem here?
> Can I be sure that if I ask for more than one answer, I'll get correct
> answers? On a related note, if FindInstance returns {}, does that
> mean
> a solution does not exist, or merely that FindInstance couldn't find a
> solution?
>
> Thanks,
>
> Jason Grout
>
> --
> Jason Grout
> jason-mathematica at creativetrax.com
>
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