Re: Simplify and Abs

*To*: mathgroup at smc.vnet.net*Subject*: [mg54665] Re: [mg54602] Simplify and Abs*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 25 Feb 2005 01:19:27 -0500 (EST)*References*: <200502240821.DAA13175@smc.vnet.net> <b18de451a8a7765509c8ec460cea5330@mimuw.edu.pl>*Sender*: owner-wri-mathgroup at wolfram.com

I have fallen yet again into the same old trap :-( Use: Refine[Abs[p - 1], p < 1 && p > 1/2] 1-p The problem is that LeafCount[Abs[p-1]] 4 while LeafCount[1-p] 5 So Abs[p-1] is, according to the Default ComplexityFunction actually simpler than 1-p Andrzej Kozlowski Chiba, Japan http://www.akikoz.net/andrzej/index.html http://www.mimuw.edu.pl/~akoz/ On 24 Feb 2005, at 12:24, Andrzej Kozlowski wrote: > 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>

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**Re: Simplify and Abs**

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