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)
>
>

```

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