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Re: Multiple integration: bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg122381] Re: Multiple integration: bug?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 27 Oct 2011 06:29:07 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201110262141.RAA00170@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

$Version

"8.0 for Mac OS X x86 (64-bit) (October 5, 2011)"

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}]

1/720

Bobby

On Wed, 26 Oct 2011 16:41:20 -0500, Dr. Wolfgang Hintze <weh at snafu.de>  
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

• References:
  • Multiple integration: bug?
    • From: "Dr. Wolfgang Hintze" <weh@snafu.de>