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Bug introduced in 10.0.0 and fixed in 10.0.1

The integral $\int \int \ \delta(x) \delta(y) \ dx dy=1$ evaluates to 0 in Mathematica

Integrate[
    DiracDelta[x]*DiracDelta[y],
    {x, -Infinity, Infinity}, 
    {y, -Infinity, Infinity}
]

returns 0 even though

Integrate[
    DiracDelta[x],
    {x, -Infinity, Infinity}
]

correctly returns 1. What's going on?

Edit: This concerns Version 10.0.0.0 installed on Ubuntu 14.04. The notebook contains no other commands. Clear[x,y] does not affect the outcome.

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  • 1
    $\begingroup$ Works fine in version 10.1: Integrate[ DiracDelta[x]*DiracDelta[y], {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] yields $1$. $\endgroup$
    – David G. Stork
    Commented Apr 14, 2015 at 23:09
  • $\begingroup$ Integrate[DiracDelta[x]*DiracDelta[y],{x, -Infinity, Infinity}, {y, -Infinity,Infinity}] yeilds 1 in 10.0.1 as well. $\endgroup$
    – Mahdi
    Commented Apr 14, 2015 at 23:19
  • $\begingroup$ Can confirm correct behavior in 8.0.0.0 Win7x64 Enterprise $\endgroup$
    – LLlAMnYP
    Commented Apr 14, 2015 at 23:22
  • 1
    $\begingroup$ Try Clear[x,y] just incase you left them defined from something else? An unlikely silly mistake but you never know. $\endgroup$
    – Tom
    Commented Apr 14, 2015 at 23:25
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    $\begingroup$ Also okay in 7.0.1 and 5.2. So it seems highly likely, if not user error, that this is a regression that affected only one very specific version. (Perhaps version 6?) Anyway, please note in the question which version you are using. $\endgroup$
    – Oleksandr R.
    Commented Apr 15, 2015 at 0:21

1 Answer 1

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Summarizing the comments, this was a bug in version 10.0.0. It has been fixed as of version 10.0.1.

In[1]:= Integrate[
          DiracDelta[x]*DiracDelta[y], 
         {x, -Infinity, Infinity}, 
         {y, -Infinity, Infinity}]

Out[1]= 1
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