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MathGroup Archive 2005

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Re: Re: Unexpected non-evaluation problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63157] Re: [mg63142] Re: Unexpected non-evaluation problem
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 16 Dec 2005 07:22:10 -0500 (EST)
  • References: <dnrch3$kie$1@smc.vnet.net> <200512151107.GAA24729@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 15 Dec 2005, at 20:07, Jean-Marc Gulliet wrote:

> Carl Cotner wrote:
>> I am totally baffled by the following Mathematica behavior:
>>
>>   In[1]:= InverseFourierTransform[FourierTransform[x^2, x, y], y, x]
>>   Out[1]= Sqrt[2 Pi] x^2 FourierTransform[DiracDelta[y], y, x]
>>
>>   In[2]:= Sqrt[2 Pi] x^2 FourierTransform[DiracDelta[y], y, x]
>>   Out[2]= x^2
>>
>> I've already asked my local guru without success, so I'm hoping  
>> someone
>> here can help me. Does anyone know why the first expression doesn't
>> evaluate to x^2 all by itself? How I can force it to do so?
>>
>> Carl
>>
> Hi Carl,
>
> Mapping *Evaluate* to all parts will do it. Why? I do not know...
>
> In[1]:=
> Evaluate //@ InverseFourierTransform[FourierTransform[x^2, x, y],  
> y, x]
>
> Out[1]=
> x^2
>
> Best regards,
> /J.M.
>


Another possible workaround is to wrap Unevaluated around the  
argument of InverseFourierTransform:


In[1]:=
InverseFourierTransform[Unevaluated[FourierTransform[x^2,
     x, y]], y, x]

Out[1]=
x^2

Essentially the same approach is:


InverseFourierTransform[FourierTransform[u, x, y], y,
    x] /. u -> x^2

x^2

There is no mystery why this works: both approaches are based on the  
obvious fact:


InverseFourierTransform[FourierTransform[u, x, y], y,
    x]

u

It seems hard to tell what causes the original problem, except that  
it is certainly a bug.

Andrzej Kozlowski


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