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Re: Assume and $Assumptions and Results

• To: mathgroup at smc.vnet.net
• Subject: [mg102247] Re: [mg102216] Assume and $Assumptions and Results
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 2 Aug 2009 06:02:12 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200908010802.EAA07200@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Unless x already has a specific numeric value, the correct result of

   Simplify[x > 1, x > 0]

is:

   x > 1

This result is the same as that of:

   Simplify[x > 1 && x > 0]

It would be redundant to include Element[x,Reals], since x > 0 already 
implies that.


ivo welch wrote:
> [Easy Beginner's Query]
> 
> 
> Dear Experts:
> 
> My goal is to input a set of assumptions for various variables, and then
> determine whether an expression of these variables (a long derivative that
> is a few lines) is true or false. That is, I want to input many conditions,
> such as "$Assumptions = (x>y) && (y>1)" and then ask Mathematica whether "1/(X+Y) >
> 1.5" is true, for example.
> 
> Alas, I am a little stuck on home plate:
>    Simplify[ x > 1, x>0 ]
> given that x is greater than 0, isn't it supposed to be True?  Instead Mathematica 
> returns "x>1".  It also does not help to make the condition "(x
> <esc>elem<esc> Reals) && (x>0)" .
> 
> 
> (Another brief questions:  do $Assumptions assignments add or replace
> earlier assumptions?)
> 
> 
> Help appreciated.  Am I expecting too much of Mathematica?
> 
> /iaw
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Assume and $Assumptions and Results
    • From: ivo welch <ivowel@gmail.com>