That depends very much on how K and L are defined. The code to calculate whether any possible cross-section of K is greater than the corresponding cross-sectio

That depends very much on how K and L are defined. The code to calculate whether any possible cross-section of K is greater than the corresponding cross-section of L is trivial if they are both (hyper)spheres. If they are polyhedra (polytopes), then it would be a lot more involved. And if their boundaries are defined by even more complicated surfaces, it could be fiendishly difficult. The relationship between declarative statements about infinite families of continuous objects, and imperative code that can be implemented on a discrete computer in finite time, tends to be very very non-trivial.