I have two sets of inequalities, say, $Ax \leq 0$ and $Bx \leq 0$. I would like to know if they both define the same polytope. Or, even, whether one is contained in the other.

At the moment I am checking, for each row $a \in A$, whether there exists some $x$ satisfying $ax > 0$ but $Bx \leq 0$. Is there a more efficient approach?

Thanks