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FindInstance returning incorrect results
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71344] FindInstance returning incorrect results
*From*: Jason Grout <jason-mathematica at creativetrax.com>
*Date*: Wed, 15 Nov 2006 06:44:16 -0500 (EST)
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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