Re: How to force Mathematica to treat a number as positive and real?

*To*: mathgroup at smc.vnet.net*Subject*: [mg51881] Re: [mg51831] How to force Mathematica to treat a number as positive and real?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 4 Nov 2004 01:49:41 -0500 (EST)*References*: <200411030624.BAA08310@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 3 Nov 2004, at 15:24, Rainer wrote: > I'd like to do some symbolic computation with parameters. These > parameters (named, e.g. "a") are always *real-valued* and positive. I > managed to tell Mathematica that a is a real number by using: > > a/:Im[a]=0; > > This works since the response to "Re[a]" is now "a" (and not "Re[a]" > which is the general result when one does not use the above definition > of a). > > Now, I would like to do a similar thing, forcing Mathematica to assume > that a is a positive number. I want that the result of Abs[a] is equal > to a. I tried: > > a/:Positive[a]=True; > > but it does not work. Does anybody know how I can do this? > Thanks > Rainer > > Assuming you have Mathematica 5.0 you should use Refine and the Assumptions mechanism. You can even do it in a "global" way, as folows: This tells Mathematica to Refine every statement using the current assumptions: $Pre = Refine[#] &; Next, define the assumptions: $Assumptions = {a ³ 0}; Now Abs[a] a Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/~andrzej/ http://www.mimuw.edu.pl/~akoz/

**References**:**How to force Mathematica to treat a number as positive and real?***From:*wilhelm.rainer@gmx.net (Rainer)