       Re: Why does Reduce work this way ...?

• To: mathgroup at smc.vnet.net
• Subject: [mg67236] Re: Why does Reduce work this way ...?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 14 Jun 2006 06:28:40 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <e6lhul\$nh2\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```jackgoldberg at comcast.net wrote:
> Hi folks,
>
> This post is related to a previous series of posts about ReplaceAll in a set of inequalities.
> I have "reduced" the problem to this unexpected situation:
>
> In  FullForm[-3<=x<=1]
> Out  LessEqual[-3,x,1]
>
> In Reduce[-3<=x<=1]
> Out  -3<=x<=1
>
> In  FullForm[%2]
> Out  Inequality[-3, LessEqual, y, LessEqual, 1]
>
> In Reduce[ LessEqual[-3,x,1]
> Out -3 &#8804; x &#8804; 1
>
> In FullForm[%4]
> Out  Inequality[-3, LessEqual, y, LessEqual, 1]
>
> This defies my understanding.  What is qoing on with Reduce?
>
> Jack
>
Hi Jack,

Yes, your results seem rather puzzling! I don not know from where you
can possibly get the 'y' especially with a freshly started Mathematica
session...

On my system everything is fine, no 'y'

In:=
FullForm[-3 <= x <= 1]

Out//FullForm=
LessEqual[-3, x, 1]

In:=
Reduce[-3 <= x <= 1]

Out=
-3 <= x <= 1

In:=
FullForm[%2]

Out//FullForm=
Inequality[-3, LessEqual, x, LessEqual, 1]

In:=
Reduce[-3 <= x <= 1]

Out=
-3 <= x <= 1

In:=
FullForm[%4]

Out//FullForm=
Inequality[-3, LessEqual, x, LessEqual, 1]

In:=
\$Version

Out=
5.2 for Microsoft Windows (June 20, 2005)

Best regards,
/Jean-Marc

```

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