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MathGroup Archive 2006

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Re: Question about DiracDelta

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68645] Re: Question about DiracDelta
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Mon, 14 Aug 2006 06:44:24 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On 8/13/06 at 5:52 AM, michev at gmail.com (vasil michev) wrote:

>Plot[NIntegrate[DiracDelta[3 - Cos[x] - Cos[y] - Cos[z] - e], {x,
>-Pi, Pi}, {y, -Pi, Pi}, {z, -Pi, Pi}, MaxPoints -> 1000000]/8/Pi^3,
>{e, 0, 6}, PlotPoints -> 30]

>the problem is that the function always returns 0, no matter what
>the value of 'e' is. I saw that other people have reported incorect
>evaluation/simplification related to DiracDelta, but I was wondering
>can anyone tell me if there's some workaround?

I don't think the issue is a problem with DiracDelta specifically. You are asking Mathematica to do a numerical integral of a function that will be zero everywhere except a few specific points. So, unless NIntegrate causes the function to be sampled at one of those specific points, it will evaluate to zero.

I don't think increasing MaxPoints the way you have done forces NIntegrate to sample the function at more points. Instead, I believe this merely allows NIntegrate to sample at more points.
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