ag.algebraic geometry – Could somebody can suggests a way to determine if a parallelogram contains another parallelogram?

I thought one way to do this.
Using the algorithm which determine if a point is inside a parallelogram,
one can determine if the polygon contains the point within a 2N step (N=2 for parallogram)
I want to do this for n-dimensional pallelotope but I guess it will take 2^N check for every vertex of the n-parallelotope.
Could somebody can suggest a better way, which is computationally faster (in a polynomial time, not exponential)?