Replace manifold.default_point_type by manifold.point_ndim

[luisfpereira]

manifold.default_point_type is a property relying on manifold.shape. It is nice to still have a property with this information because it simplifies a bit the code in a lot of parts of the library.

Nevertheless, following @ninamiolane suggestion, manifold.point_ndim may be a better naming because we will have an integer instead of a string (easier to avoid types) and point shapes greater than 2 will be captured differently.

Are you aligned with this @ninamiolane?

[johnharveymath]

I would suggest that this particular variable name might cause confusion with manifold.dimension.

Perhaps manifold.point_repr_depth or manifold.point_coord_depth or manifold.point_array_depth or manifold.shape_depth? I think 'depth' is a good word for indicating how many dimensions an array has without using the word 'dimension'. Something that makes it clear that it is not a mathematical property of the manifold but a property of how we are representing or co-ordinatizing points of the manifold. manifold.shape_depth might be my favourite because it suggests, accurately, that the property is derived from manifold.shape.

[luisfpereira]

Thanks for the suggestion @johnharveymath.

I like the suffix ndim because it connects to the method we are interested in gs.array (gs.ndim). Would point_repr_ndim be more clear? I think depth does not ring a bell for people used to work with arrays.

We are also thinking about renaming manifold.shape to manifold.point_shape (or, following partially your suggestion manifold.point_repr_shape).

What do you think?

[johnharveymath]

That makes sense as a reason to use ndim. And yes, I'm not a fan of manifold.shape. When I saw it first I had no idea what it might be. The other possibilities are more informative.

My concern about something like point_repr_ndim is that if you gave me a 3x3 array and said it represented a point in SO(3), then asked me that I thought point_repr_ndim should be, my gut answer would be 9, not 2.

What about array_ndim and array_shape (or point_array_ndim and point_array_shape), making clear that it is the dimension and shape of the array that we are talking about?