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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51880] Re: [mg51831] How to force Mathematica to treat a number as positive and real?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 4 Nov 2004 01:49:38 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

Clear[a];
a /: Abs[a]=a;

Abs[a]

a

However, trying to specify all desired results with upvalues (TagSet) can easily 
lead to recursion problems.  It is easier to just use an assumption with 
Simplify or FullSimplify.

Clear[a];

Simplify[
  {Re[a], Im[a], Abs[a], a>0, a<0, Sqrt[a^2]}, 
  a>0]

{a,0,a,True,False,a}


Bob Hanlon

> 
> From: wilhelm.rainer at gmx.net (Rainer)
To: mathgroup at smc.vnet.net
> Date: 2004/11/03 Wed AM 01:24:18 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg51880] [mg51831] How to force Mathematica to treat a number as positive 
and real?
> 
> 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
> 
> 


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