Re: volume calculation

• To: mathgroup at smc.vnet.net
• Subject: [mg100243] Re: [mg100240] volume calculation
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Fri, 29 May 2009 20:56:54 -0400 (EDT)
• References: <200905282335.TAA15300@smc.vnet.net>

```Hi,

I would just use NIntegrate[Boole[D(x1,x2,x3,...,xn) < L],{whatever your
limits in xi}]. possibly with a Monte-Carlo method. If integration limits in
coordinates depend on other coordinates in a way that is hard to
disentangle, I would  find the minimal multidimensional "box" with fixed
dimensions that contains your domain, and integrate over that box.

Regards,
Leonid

On Thu, May 28, 2009 at 4:35 PM, Filippo Miatto <miatto at gmail.com> wrote:

> Dear all,
> I need a way to find the volume of a multidimensional shape in the
> coordinates (x1,x2,x3,...,xn), that comes from an inequality like
> D(x1,x2,x3,...,xn) < L (with 3 variables i get a nice weird shape in
> R^3, with more i don't plot it)
> In other words I let Mathematica calculate where in the space of the
> solutions the inequality is solved and i'd like to have the numerical
> "volume of the solutions".
> What strategy should i use? The function D is not invertible...
> Thank you,
> Filippo
>
>
>
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```

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