To add a bit, kudos to root-parent boil-down. Programmers have already the good representation, and call it n-dimensional array, that being a list of lists of lists ... (repeat n times) ... of lists of numbers. The only nuisance is that what programmers call dimension, math people call it rank. It is the sizes of those nested lists what math people call dimensions. It's all set up for a comedy of errors. Also in math the rank is split to make explicit how much of the rank-many arguments are vectors and how many are dual vectors. You'd say something like this is a rank 7 tensor, 3 times covariant (3 vector arguments) and 4 times contravariant (4 dual vector arguments) summing 7 total arguments. I'm assuming a fixed base, so root-parent map determines a number array.