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Volume computation is $\#P$ hard. Take the $[0,1]^n$ polytope. Slice it by an half space inequality with $poly(n)$ bit rational coefficients into two unequal halves. Volume of bigger section is $\...

Where is the complexity of the problem 'Given two bounded compact convex integral polyhedra in $\mathbb R^n$ presented by $O(poly(n))$ integer valued halfspaces given by linear inequalities with ...

Consider the following problem: Given an $\mathcal{H}$-polytope $P$ in $\mathbb{R}^d$ and $4$ orthogonal vectors $v_1, ..., v_4 \in \mathbb{R}^d$, compute the projection of $P$ to the subspace ...