Re: Bug in Reduce?

*To*: mathgroup at smc.vnet.net*Subject*: [mg60427] Re: [mg60406] Bug in Reduce?*From*: Andrzej Kozlowski <andrzej at yhc.att.ne.jp>*Date*: Fri, 16 Sep 2005 03:49:07 -0400 (EDT)*References*: <dfrhi4$g4l$1@smc.vnet.net> <dg8lfv$r8g$1@smc.vnet.net> <200509140926.FAA01590@smc.vnet.net> <200509150916.FAA15875@smc.vnet.net>*Reply-to*: Andrzej Kozlowski <andrzej at akikoz.net>*Sender*: owner-wri-mathgroup at wolfram.com

This does indeed like a bug. The documentation states: When expr involves only polynomial conditions, Reduce[expr, vars, Reals] gives a cylindrical algebraic decomposition of expr. However FullSimplify[CylindricalDecomposition[ {a*c - b*d == 0, a*d + b*c == 0}, {a, b, c, d}]] (a == 0 && b == 0) || (c == 0 && d == 0) so something is definitely fishy, particularly that if you call Reduce without explicit variables you get the same correct answer as above FullSimplify[Reduce[{a*c - b*d == 0, a*d + b*c == 0}, Reals]] (c == 0 && d == 0) || (a == 0 && b == 0) Andrzej Kozlowski On 15 Sep 2005, at 18:16, Kennedy wrote: > The source of this apparent bug could be my misunderstanding of the > middle, > "vars" parameter of Reduce, but it sure seems like the following > output > indicates that c must be 0 for my two equations to be > satisfied, when in > fact if a and b are both 0, c does not need to be 0. > > Regards, > Jack > > In[1]:= > Reduce[{a c - b d == 0, a d + b c == 0}, {a, b, c, d}, Reals] // > FullSimplify > > Out[1]= > c == 0 && (d == 0 || (a == 0 && b == 0)) > > (version 5.1 for Windows) > >

**References**:**Re: Simplify and Noncommutativity***From:*Robert Schoefbeck <schoefbeck@hep.itp.tuwien.ac.at>

**Bug in Reduce?***From:*"Kennedy" <jack@realmode.com>