# Integration over a polyhedron

We face the problem of computing the integral of a function f over a polyhedron P (defined by a mixed integer linear program) and we were thinking of using Latte (link) for this task. We would like to ask for your opinion regarding the following aspects:

The rational variables in our MILP correspond to some continuous independent random variables and we think that by computing the integral of the joint density function over the polyhedron P will give us the desired answer. Probably the joint density function will have to be approximated by polynomials, but we are not very sure of this. Does the computation of the integral is affected in any way by the linear relations between the rational variables, in the sense that, assuming that the MILP program is feasible only for some values of the rational variables?

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