On 2012-06-16, Alastair Irving <[email protected]> wrote:
> Hi
>       
> I want to numerically evaluate the integral of a function f(x,y) over a 
> region defined by linear inequalities, for example
> 1/8<=y<=x<=1/3
> x+y<=1/3.
> I can do this with a repeated call to numerical_integral because I can 
> re-write the constraints as y<=min(x,1/3-x).  However, this solution 
> isn't very satisfying in general.  If I have more constraints and/or 
> more variables then working out the limits on the repeated integrals by 
> hand is going to be rather unpleasant.
>
> Is there any way I can get sage to compute the integral directly from 
> the inequalities.  For example, if I use a Polyhedron object to store 
> the region of interest is there any way of getting functions from it 
> which describe the limits of integration?  Ideally, if P is a Polyhedron 
> it would be nice to have something like P.integral(f) which computes the 
> integral of f over P.

there are plans to create a Sage interface to LattE Integrale, a package
that can in particular solve these kinds of tasks.
(see http://www.math.ucdavis.edu/~latte/)

For the time being you can roll your own, at least for compact P: 
compute a triangulation of P and for each simplex of triangulation use
an explicit formula.

HTH,
Dmitrii
>
> Many thanks
>
> Alastair Irving
>

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