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

• To: mathgroup at smc.vnet.net
• Subject: [mg51831] How to force Mathematica to treat a number as positive and real?
• From: wilhelm.rainer at gmx.net (Rainer)
• Date: Wed, 3 Nov 2004 01:24:18 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: How to force Mathematica to treat a number as positive and real?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>