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Re: Simplify and Abs

  • To: mathgroup at
  • Subject: [mg54641] Re: [mg54602] Simplify and Abs
  • From: Andrzej Kozlowski <akoz at>
  • Date: Fri, 25 Feb 2005 01:18:40 -0500 (EST)
  • References: <>
  • Sender: owner-wri-mathgroup at

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?
>    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:



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 

Andrzej Kozlowski

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