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Re: Re: Abs[x] function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87896] Re: [mg87845] Re: Abs[x] function
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 19 Apr 2008 03:37:47 -0400 (EDT)
  • References: <fu9fn7$c8d$1@smc.vnet.net> <200804181110.HAA18822@smc.vnet.net>

On 18 Apr 2008, at 20:10, Szabolcs wrote:
> On 18 Apr, 08:39, Vladislav <kazimi... at yahoo.co.uk> wrote:
>> Who can explain the behavior. THe derivative Abs[x] at x=.5 is well
>> defined and is equal to 1.
>>
>> In[1]:= D[Abs[x], x]
>>
>> Out[1]=
>> \!\(\*SuperscriptBox["Abs", "\[Prime]",
>> MultilineFunction->None]\)[x]
>>
>> In[2]:= % /. x -> .5
>>
>> Out[2]=
>> \!\(\*SuperscriptBox["Abs", "\[Prime]",
>> MultilineFunction->None]\)[0.5]
>
> Hi,
>
> Please use "copy as plain text" when pasting Mathematica expressions,
> so it will be easier to read them.
>
> Just use FunctionExpand on the result to get a concrete value.
>


I never noticed that Function expand deos that and I am not sure that  
I am very happy that it does. In fact:

FunctionExpand[Derivative[1][Abs][x],
    Element[x, Reals]]
  x/Abs[x]

but that assumes that the derivative is taken along the real line,  
which is not what Mathematica normally assumes. In my opinion this  
makes it less clear exactly what FunctionExpand is really meant to do  
and what to expect of it. I don't think it ought to make additional  
assumptions beyond what it is told.

I think it would be better to let Derivative have a direction option,  
just as Limit does.

Andrzej Kozlowski 


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