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>
- Re: Simplify and Noncommutativity