Any additional methods that are provided will _not work_ if they do
not have access to the RefFrame objects (in order to know how to
transform between coordinates). Your proposal does not explain how
these RefFrame objects will be accessed.

Because of this, the only advantage of subclassing Add and Mul that I
see is that it will have garbage checks (which as I mentioned can be
postponed to precondition checks in any of the functions to be
implemented). On the other hand it keeps all the disadvantages
mentioned by Matthew (Add and Mul make many assumptions, that you will
keep by subclassing them).

So, if you want new container classes for any of the reasons mentioned
by Matthew, subclassing Add and Mul does not seem the right way - you
should start from Basic as it is done in MatExpr. On the other hand,
as I mentioned in the last two paragraph, I do not think you have
given appropriate reasons for creating new container classes.

If the main reason for new container classes is garbage checks you can
just use MatExpr (its add, mul, matsymbol, etc).

This MatExpr approach has another unrelated advantage: the author of
MatExpr (Matthew) has both addressed most (probably not all) of the
issues that are problematic for diffgeom, mechanics or quantum in
terms of following sympy conventions and he is still very active
within the project so you will be able to question him for details
(sorry to volunteer you like that, Matthew ;)

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