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Re: Multiple integration: bug?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg122418] Re: Multiple integration: bug?
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Fri, 28 Oct 2011 05:33:33 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201110262141.RAA00170@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

You can also "automate" the Integral as follows:

n = 8;
xvec = Flatten@{0, Array[x, n]};
limits = Thread[{Rest@xvec, Most@xvec, 1}];
Integrate[1, Sequence @@ limits]

1/40320

Bobby

On Thu, 27 Oct 2011 05:28:02 -0500, Heike Gramberg  
<heike.gramberg at gmail.com> wrote:

> What version are you using? On Mathematica 8.0.1 I get the right answer  
> (1/720) with your code.
>
> BTW, you could also do something like this to calculate the integral;
>
> Integrate[1, {x[1], 0, 1}, {x[2], x[1], 1}, {x[3], x[2], 1}, {x[4],  
> x[3], 1},  {x[5], x[4], 1}, {x[6], x[5], 1}]
>
> Heike.
>
>
>
> On 26 Oct 2011, at 23:41, Dr. Wolfgang Hintze wrote:
>
>> In calculating Integrals of the type Integrate[0<x1<x2<...<xn<1] which
>> should give 1/n! I observed a strange behaviour
>>
>> Using UnitStep[] it works fine for n=2 to n=5:
>>
>> In[48]:=
>> Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] -
>> x[3]]*UnitStep[x[5] - x[4]], {x[1], 0, 1}, {x[2], 0, 1}, {x[3], 0, 1},
>> {x[4], 0, 1}, {x[5], 0, 1}]
>> Out[48]=
>> 1/120
>>
>>
>> It gives nonsense for n=6 (and higher):
>>
>> In[47]:=
>> Integrate[UnitStep[x[2] - x[1]]*UnitStep[x[3] - x[2]]*UnitStep[x[4] -
>> x[3]]*UnitStep[x[5] - x[4]]*UnitStep[x[6] - x[5]], {x[1], 0, 1}, {x[2],
>> 0, 1}, {x[3], 0, 1}, {x[4], 0, 1}, {x[5], 0, 1},
>> {x[6], 0, 1}]
>> Out[47]=
>> -(1/4)
>>
>> Is this a bug or did I make a mistake somewhere (did not consider
>> bounds or depth level etc.)?
>>
>> Any comment is appreciated.
>>
>> BTW: using Boolean instead of UnitStep seems to have no restriction.
>>
>> --- Wolfgang
>>
>>
>
>


-- 
DrMajorBob at yahoo.com



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