Given a convex polytope with integral vertices presented in half-space description is there a way to test in
polynomial time or
polynomial hierarchy
if polytope has integral volume?
Finding volume to desired approximation is in $PSPACE$.
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$\begingroup$ If it helps, $(\dim P)! \operatorname{vol}(P)$ is necessarily an integer $\endgroup$– Avi SteinerCommented Jul 21, 2019 at 19:15
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$\begingroup$ @AviSteiner Denominator has to be smooth integer and so related to diophantine approximation? Could you clarify your comment? To be integral denominator has to be $1$. Perhaps there is something here. $\endgroup$– TurboCommented Aug 8, 2019 at 7:23
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