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

**Follow-Ups**:**Re: FindInstance returning incorrect results***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>