Re: Multiple integration: bug?
- To: mathgroup at smc.vnet.net
- Subject: [mg122375] Re: Multiple integration: bug?
- From: Heike Gramberg <heike.gramberg at gmail.com>
- Date: Thu, 27 Oct 2011 06:28:02 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <201110262141.RAA00170@smc.vnet.net>
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 > >
- References:
- Multiple integration: bug?
- From: "Dr. Wolfgang Hintze" <weh@snafu.de>
- Multiple integration: bug?