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>