Hi Sebastian,

I haven't given this as much thought as it deserves, but thought I
would comment from the astropy perspective, where we both have direct
subclasses of `ndarray` (`Quantity`, `Column`, `MaskedColumn`) and
classes that store their data internally as ndarray (subclass)
instances (`Time`, `SkyCoord`, ...).

One comment would be that if one were to introduce a special method,
one should perhaps think a bit more broadly, and capture more than the
indexing methods with it. I wonder about this because for the
array-holding classes mentioned above, we initially just had
`__getitem__`, which got the relevant items from the underlying
arrays, and then constructed a new instance with those. But recently
we realised that methods like `reshape`, `transpose`, etc., require
essentially the same steps, and so we constructed a new
`ShapedLikeNDArray` mixin, which provides all of those [1] as long as
one defines a single `_apply` method. (Indeed, it turns out that the
same technique works without any real change for some numpy functions
such as `np.broadcast_to`.)

That said, in the actual ndarray subclasses, we have not found a need
to overwrite any of the reshaping methods, since those methods are all
handled OK via `__array_finalize__`. We do overwrite `__getitem__`
(and `item`) as we need to take care of scalars. And we would
obviously have to overwrite `oindex`, etc., as well, for the same
reason, so in that respect a common method might be useful.

However, perhaps it is worth considering that the only reason we need
to overwrite them in the first place, unlike what is the case for all
the shape-changing methods, is that scalar output does not get put
through `__array_finalize__`. Might it be an idea to have the new
indexing methods return array scalars instead of normal ones so we can
get rid of this?

All the best,

Marten

[1] https://github.com/astropy/astropy/blob/master/astropy/utils/misc.py#L856
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