Re: global real variables

• To: mathgroup at smc.vnet.net
• Subject: [mg22047] Re: [mg22019] global real variables
• From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
• Date: Fri, 11 Feb 2000 02:38:27 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

on 00.2.10 4:26 PM, Naum Phleger at naum at cava.physics.ucsb.edu wrote:

> I asked a dumb question a few weeks ago about making variables real and
> found that Mathematica 4 took care of this better.  I have been using it
> since.  I still have a couple of problems with it though.  First, I can have
> variables be treated as real by using the assumption Element[x,Reals] in a
> simplify command, but I want x to be real in all commands so I don't have to
> keep using Simplify each time I want x to be recognized as real.  Second,
> even this doesn't seem to work quite right.  Here is what I mean.
>
>
> Say I have tow var.s, x and p.  Both are real so I can do this.
>
> Simplify[ Conjugate[ x ] , Element[ x , Reals ] ]  ----> x
>
> amd I get the same thing for p, but it stops working if I have functions of
> x and p, for instance I get
>
>
> Simplify[ Conjugate[ x + x * p^-1 ] , Element[ {x,p} , Reals ] ]  ---->
>
> Conjugate[ x + x * p^-1 ]
>
>
> It works if I use FullSimplify   AND   put p^-1 into the list of variables
> that I want to have real.  How can I get around this without listing every
> negative power of every variable and wasting time with FullSimplify.  Thanks
> for any help.  Thanks.
>
>
> -NAUM
>
This particular case can be best dealt with by using ComplexExpand:

In[1]:=
ComplexExpand[Conjugate[ x + x * p^-1 ]]
Out[1]=
x
x + -
p

ComplexExpand assumes that all the variables are real. If, for example, you
had another variable, say a, which you do not want to assume to be real you
can use:

In[3]:=
ComplexExpand[Conjugate[ x + x * p^-1 + a], {a}]
Out[3]=
x
x + - - I Im[a] + Re[a]
p

In certain cases you may need to combine Simplify with ComplexExpand  (you
can find a number of such examples in the archives of this list).
--
Andrzej Kozlowski
Toyama International University
Toyama, Japan
http://sigma.tuins.ac.jp/

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