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Re: Simplify and Abs

• To: mathgroup at smc.vnet.net
• Subject: [mg54641] Re: [mg54602] Simplify and Abs
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 25 Feb 2005 01:18:40 -0500 (EST)
• References: <200502240821.DAA13175@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 24 Feb 2005, at 09:21, Simon Anders wrote:

> Hi,
>
> can it really be that this is already beyond Mathematica?
>
>     In :=  FullSimplify[Abs[p - 1], p < 1 && p > 1/2]
>
>     Out := Abs[-1 + p]
>
> How do I make Matheamtica notice, that the assumptions constrain the
> argument of Abs[] to positive values?
>
> Any suggestions how to treat these kinds of problems? Specifically, I
> have a list of products of absolute values of simple polynomials in p
> and I know that p is in the interval [0,1].
>
> I would like to know whether the polynomials have constant sign over 
> the
> interval so that the Abs[] can be removed. Can this be done 
> automatically?
>
> TIA
>    Simon
>
>
>

It seems to me that FullSimplify is indeed missing some rules for 
Simplifying expressions involving Absolute. However, in the case when 
you are dealing with real quantities there is a simple workaround;


FullSimplify[ComplexExpand[Abs[p - 1]], p < 1 && p > 1/2]


1 - p

In fact what ComplexExpand does here is:


ComplexExpand[Abs[x]]

Sqrt[x^2]

so when dealing only with reals you could use Sqrt[x^2] (for example by 
defining your own function abs). Functions like FullSimplify are 
generally better able to deal with expressions like Sqrt[x^2] than with 
Abs.

Andrzej Kozlowski

• References:
  • Simplify and Abs
    • From: Simon Anders <simon.anders@uibk.ac.at>