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Re: Integrate a Piecewise funition, stange behaviour


Try posting in InputForm, so that the code isn't so garbled.

http://www.eclecticdreams.net/DrBob/copy_as_inputform.htm

Bobby

On Fri, 28 Jan 2005 02:43:42 -0500 (EST), rik <rikypi_CREPA_SPAMMONE at libero.it> wrote:

> hi,
> i must evaluate this Integrate[]:
>
> int1 = Integrate[f,  {w[2], - \[Infinity], \[Infinity]}]
>
> where:
>
> f = Piecewise[
> 	{{2/355, Inequality[2, LessEqual, w[2], LessEqual, 8] &&
>             Inequality[4, LessEqual, w[2] + w[3], LessEqual, 12] &&
> 	Inequality[5, LessEqual, w[1] + w[2], LessEqual, 10] && w[1]
>            � 0 && w[3] � 0}}, 0]
>
> if i try to evaluate int, Mathematica (ver 5.1) takes 500-600 Mbyte of
> ram and, after hours and hours, not arrives to any result :-(
>
> But if i apply Reduce to domain like this:
>
> red1 = Reduce[Inequality[2, LessEqual, w[2], LessEqual, 8] &&
>             Inequality[4, LessEqual, w[2] + w[3], LessEqual, 12] &&
> 	Inequality[5, LessEqual, w[1] + w[2], LessEqual, 10] && w[1]
>            � 0 && w[3] � 0]
>
> and then i try to evaluate the follow command:
>
> Integrate[2/355 Boole[red1],  {w[2], - \[Infinity], \[Infinity]}]
>
>
> Mathematica do the calculation in few seconds!!!
>
> Why this behaviour?
>
> The two expression, f and "2/355 Boole[red1]", are not equal for the
> Kernel of Mathematica?
>
> Is there a way to predict the complexity of a integral of a Piecewise
> function?
>
> thanks and SORRY for my english
>
> Riccardo Piovosi
>
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net


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