We define the successor data commutator (SDC)
[m,n] = mn’ – m’n = m(n+1) – (m+1)n = m-n
These successor and data operator commutator are 2 different approaches. The operator commutator is applied to some test data on the right. For successor it is applies to a number. For the derivative, it is applied to a function.
The data commutator is not applied to test data.
Project: Evaluate [m,[n,p]]. What identities can you find for this? Are their cyclic identities? Jacobi identity?
Project: Discuss which is more useful, the successor data or operator commutator.