Re: Simplify and Abs

*To*: mathgroup at smc.vnet.net*Subject*: [mg54654] Re: Simplify and Abs*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Fri, 25 Feb 2005 01:18:59 -0500 (EST)*References*: <cvk3fu$d6j$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Simon Anders <simon.anders at uibk.ac.at> 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] Strange. > How do I make Matheamtica notice, that the assumptions constrain the > argument of Abs[] to positive values? Huh? The assumptions constrain the argument of Abs[] to _negative_ values, and thus the expression should simplify to 1 - p. > 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? How about using Refine instead? For example, In[14]:= Refine[Abs[p - 1], 1/2 < p < 1] Out[14]= 1 - p But I don't understand why Simplify (or FullSimplify) doesn't give that also. After all, the documentation states that "Refine is one of the transformations tried by Simplify." David Cantrell