Most personal computers in 2016 have 4-8 Gbytes of RAM, meaning that this calculation would be way out of reach. There are supercomputers that can handle applications using 500 Gbytes of memory, but we can quickly reduce the total memory required by applying some physical arguments. In addition to vanishing elements with repeated indices, mentioned above, elements that do not obey certain symmetries are also zero. Almost all realistic two-body forces preserve some quantities due to symmetries in the interaction. For example, an interaction with rotational symmetry will conserve angular momentum. This means that a two-body ket state \( \vert rs\rangle \), which has some set of quantum numbers, will retain quantum numbers corresponding to the interaction symmetries after being acted on by \( \hat{v} \). This state is then projected onto \( \vert pq\rangle \) with its own set of quantum numbers. Thus \( \langle pq|v|rs\rangle \) is only non-zero if \( \vert pq\rangle \) and \( \vert rs\rangle \) share the same quantum numbers that are preserved by \( \hat{v} \). In addition, because the cluster operators represent excitations due to the interaction, \( t_{ij}^{ab} \) is only non-zero if \( \vert ij\rangle \) has the same relevant quantum numbers as \( \vert ab\rangle \).