This expansion can also be easily verified using the relation between |n m| and the GMM matrices in Eq. 2-Eq. 4. Note that Eq. 11 has an explicit separation of the trace and traceless parts of the potential, due to the traceless generators in Eqs. 2-4 where Tr e [ Ŝi ] = 0. Enforcing this separation in the MMST mapping formalism can significantly improve the stability and accuracy of the dynamics. In the SU (N ) mapping formalism, this is intrinsically enforced.