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 ≤ x ≤ 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

**References**:**Why does Reduce work this way ...?***From:*jackgoldberg@comcast.net