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Re: v7.0.0 bug with PrincipalValue -> True

On 6/1/10 at 7:40 AM, januswesenberg at (janus) wrote:


>as a physicist I'm allowed to use Cauchy principal values (tongue in
>cheek), but it seems that my currently installed version of
>Mathematica (7.0.0 for Mac)  is having some difficulties. Consider
>the following integral (same result with PrincipalValue-
>>False as expected):
>Integrate[UnitBox[x]/(x0-x)/. x0->1,{x,-
>Infinity,Infinity},PrincipalValue->True] Log[3]

>Now, do the same integral with an unknown position of the pole, and
>an I sneaks in:
>>True,Assumptions-> {x0>0}]/.x0->1//Simplify
>I \[Pi]+Log[3]

>Would somebody with a newer kernel mind checking whether this is a
>fixed bug, or is there perhaps a workaround?

>Take[SystemInformation["Kernel"],2] {Version->7.0 for Mac OS X x86
>(64-bit) (November 11, 2008),ReleaseID-
>>7.0.0 (1148398, 1148273)}

I get the same results using

In[1]:= Take[SystemInformation["Kernel"], 2]

Out[1]= {Version->7.0 for Mac OS X x86 (64-bit) (February 19,
2009),ReleaseID->7.0.1 (1214020, 1213835)}

But if I replace x0 with 1, things are different. That is:

In[18]:= Integrate[UnitBox[x]/(1 - x), {x, -Infinity, Infinity},
   PrincipalValue -> True] // Simplify

Out[18]= log(3)

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