Re: volume calculation

*To*: mathgroup at smc.vnet.net*Subject*: [mg100262] Re: volume calculation*From*: Sebastian <meznaric at gmail.com>*Date*: Fri, 29 May 2009 21:00:20 -0400 (EDT)*References*: <gvn74b$ets$1@smc.vnet.net>

On May 29, 12:35 am, Filippo Miatto <mia... 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 > > ------------------------------------------------------------ > Mobile (IT): +39 340 6104269 > Mobile (NL): +31 064 3949827 > Home (IT): +39 0438 59360 > > P.O. Box 9504 > NL 2300 RA LEIDEN > > msn: dr.zio... at hotmail.com > skype: filippo.miatto > Quantum Optics > Group Mail: mia... at molphys.leidenuniv.nl Try Monte Carlo integration, that's probably the easiest way to do high dimensional integrals. Of course this will only work if you are happy with a numerical result.