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Re: Re: (x-y) DiracDelta[x-y] does not simplify to 0
*To*: mathgroup at smc.vnet.net
*Subject*: [mg56361] Re: [mg56297] Re: (x-y) DiracDelta[x-y] does not simplify to 0
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Fri, 22 Apr 2005 06:24:56 -0400 (EDT)
*References*: <d42kg5$39t$1@smc.vnet.net> <d45agf$ieu$1@smc.vnet.net> <200504210936.FAA05048@smc.vnet.net> <0e5459acc0a6eae9a16bda863b79434c@mimuw.edu.pl> <16999.49105.639076.187149@localhost.localdomain> <913e334e36e5b09dce4f89131131357d@mimuw.edu.pl> <17000.4781.157008.559505@localhost.localdomain>
*Sender*: owner-wri-mathgroup at wolfram.com
On 22 Apr 2005, at 05:53, Alain Cochard wrote:
> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> Andrzej Kozlowski writes:
>
>> Since [use inside Integrate] is the only context in which [x
>> DiracDelta[x] == 0] is useful and makes sense, I can't see any
>> justification for your application of Simplify.
>
> OK, I think I now understand what you say and I disagree with your
> conclusion. I indeed do find practical justifications for the use of
> that identity and had so far to perform the simplifications manually.
>
>
Of course I did not mean to doubt that this identity or this particular
way of treating the DiracDelta can't be useful for you or others. There
is no end to unexpected and ingenious uses that people make of various
built in functions in Mathematica. However, unless you actually
integrate your expressions containing the DiracDelta I do not think you
are really making use of the mathematical notion of a distribution. For
example, I could define a function MyDiscreteDelta by
MyDiscreteDelta[x_] := DiracDelta[x]/DiracDelta[0]
and then I would have
FullSimplify[x*MyDiscreteDelta[x]]
0
(Note that, as i pointed out earlier, the
FullSimplify[x*DiscreteDelta[x]] does not return 0). So one could argue
that I "used" the DiracDelta to get a "superior" version of the the
DiscreteDelta, and this may be further useful for something else. Even
if this were the case it would still be true that the mathematical
notion of a distribution is not being used here at all because that
notion is only meaningful when used in th context of integration.
Andrzej
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