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MathGroup Archive 2005

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Re: Re: Re: Simplify and Abs

On 27 Feb 2005, at 07:29, Murray Eisenberg wrote:

> Strangely, though, the docs for version 5.1 say:
>    FunctionExpand is automatically called by FullSimplify

Yes, but it is a question of ComplexityFunstion in FullSimplify. 
FunctionExpand is one of the transformations used by FullSimplify, and 
FullSimplify does reach the  form -p+1 but but with the default 
ComplexityFucntion Abs[p-1] is preferred to -p+1.

One way to avoid such problems is to use the ComplexityFunction I 
suggested a while ago, which is based on what is visually the simplest 

VisibleSimplify[expr_, opts___] := Simplify[
     expr, opts, ComplexityFunction ->
(StringLength[ToString[TraditionalForm[#]]] &)]




VisibleSimplify should always return the "simplest form" from the point 
of view of traditional mathematical notation that Simplify is able to 
find (of course that also depends on TransforationFunctions) but 
VisibleSimplify is much slower than the default ComplexityFunction!

Andrzej Kozlowski

> Bob Hanlon wrote:
>> FunctionExpand[Abs[p-1],p<1&&p>1/2]
>> 1-p
>>> From: Simon Anders <simon.anders at>
To: mathgroup at
>>> Date: 2005/02/24 Thu AM 03:21:06 EST
>>> Subject: [mg54712] [mg54687] [mg54640] [mg54602] Simplify and Abs
>>> can it really be that this is already beyond Mathematica?
>>>    In :=  FullSimplify[Abs[p - 1], p < 1 && p > 1/2]
>>>    Out := Abs[-1 + p]
> -- 
> Murray Eisenberg                     murray at
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305

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