  Nuclear matter is studied within the Density Functional Theory (DFT)
framework. Our method employs a finite number of nucleons in a box subject to
periodic boundary conditions, in order to simulate infinite matter and study
its response to an external static potential. We detail both the theoretical
formalism and its computational implementation for pure neutron matter and
symmetric nuclear matter with Skyrme-like Energy Density Functionals (EDFs).
The implementation of spin-orbit, in particular, is carefully discussed. Our
method is applied to the problem of the static response of nuclear matter and
the impact of the perturbation on the energies, densities and level structure
of the system is investigated. Our work is a crucial step in our program of ab
initio-based nuclear EDFs [Phys. Rev. C 104, 024315 (2021)] as it paves the way
towards the goal of constraining the EDF surface terms on ab initio
calculations.
