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

• To: mathgroup at smc.vnet.net
• Subject: [mg67238] Re: [mg67225] Why does Reduce work this way ...?
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Wed, 14 Jun 2006 06:28:44 -0400 (EDT)
• References: <200606130507.BAA23801@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[1]  FullForm[-3<=x<=1]
> Out[1]  LessEqual[-3,x,1]
>
> In[2] Reduce[-3<=x<=1]
> Out[2]  -3<=x<=1
>
> In[3]  FullForm[%2]
> Out[3]  Inequality[-3, LessEqual, y, LessEqual, 1]
>
> In[4] Reduce[ LessEqual[-3,x,1]
> Out[4] -3 &#8804; x &#8804; 1
>
> In[5] FullForm[%4]
> Out[5]  Inequality[-3, LessEqual, y, LessEqual, 1]
>
> This defies my understanding.  What is qoing on with Reduce?
>
> Jack

Jack,

I think that Reduce converts inequalities to a canonical form for
further processing. The form of the inequality with head Inequality is
more general than the one with the head LessEqual. For example,

-3<x<=1

cannot be expressed using LessEqual (or Less).

Carl Woll
Wolfram Research

```

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