Since both ↑ and ↓ systems are independent (we do not consider spin-flip situations here), we may consider without-loss-of-generality one of these systems. E.g. the ↓-system, in python using itertools we may create an array indexing all possible Molecular Orbitals (MO) and choose N ↓ elements, indicated the occupied MO orbitals. Python's itertools then generates all possible choices, this is exactly what we want for FCI. This yields the an array/matrix Λ ↓Ip , and may be similarly done for Λ ↑Ip .