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We provide an algorithm for evolving general spin-$s$ Gross-Pitaevskii /non-linear Schr\"odinger systems carrying a variety of interactions, where the$2s+1$ components of the `spinor' field represent the differentspin-multiplicity states. We consider many nonrelativistic interactions up toquartic order in the Schr\"odinger field (both short and long-range, andspin-dependent and spin-independent interactions), including explicitspin-orbit couplings. The algorithm allows for spatially varying externaland/or self-generated vector potentials that couple to the spin density of thefield. Our work can be used for scenarios ranging from laboratory systems suchas spinor Bose-Einstein condensates (BECs), to cosmological/astrophysicalsystems such as self-interacting bosonic dark matter. As examples, we provideresults for two different setups of spin-$1$ BECs that employ a varyingmagnetic field and spin-orbit coupling, respectively, and also collisions ofspin-$1$ solitons in dark matter. Our symplectic algorithm is second-orderaccurate in time, and is extensible to the known higher-order accurate methods.

i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems