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 >

**References**:**FindInstance returning incorrect results***From:*Jason Grout <jason-mathematica@creativetrax.com>