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 > >