Introduce ZeroVector

[kellertuer]

Here is a first draft to close #279 .

There are still quite a few TODOs in the zero_vector.jl file – mainly which functions to implement and which not.
For me Riemann_tensor, sectional_curvature and angle do not make much sense, but maybe one could “error more gracefully” there still.

The general modelling here is to do all these on “level 1” of our design scheme – for a few cases one could check whether level 2 makes more sense. A main challenge is probably to avoid ambiguities.

I also refactored the code a bit in places where all variables would fit on one line – since Runic allows for that while JuliaFormatter did not and put every variable on its own line.

Lets discuss also whether further methods are missing – and check whether it breaks something in Manifolds.jl or Manopt.jl.

[kellertuer]

Documentation is also still missing, though there it is maybe enough to add the docs of the type to the vector space page.

[kellertuer]

That is what I feared. A “straight-forward” plain approach introduces 200+ ambiguities. So we probably need something more clever than this PR.

[mateuszbaran]

I fear properly adding it everywhere would require a very careful and time-consuming ambiguity hunting. I personally think ZeroVector has a fairly narrow utility and I would be fine with it not being supported by most (or even nearly all) of our functions. Solving all of these ambiguities will most likely not be worth the small gain it would give.

[kellertuer]

That is why I stopped at that point yesterday. I am not sure which narrow utility you have in mind. Could you then continue here and minimise it again?

[mateuszbaran]

So far there is exactly one example of actual utility, in Manopt.jl 😄 . To me it's more about "let's not make a separate ZeroVector type in case we notice a second example in a different package".

[kellertuer]

That is very narrow 😄

But then lets document that carefully that it is clear that the zero vector does not (necessarily, automatically) work in “any tangent vector position”.

[kellertuer]

I now added a careful technical note, that the type has to be considered on every manifold separately since it has to be implemented on layer 3, and kept those functions that do not cause ambiguities (+, -, *, allocate, and zero_vector with an optional allocate=true positional third argument).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (e36b1a0) to head (9cc2a29).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

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  Coverage   100.00%   100.00%           
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  Files           34        34           
  Lines         3802      3813   +11     
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+ Hits          3802      3813   +11     

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[mateuszbaran]

OK, everything else looks fine.

[kellertuer]

Should this also be a new version?

[mateuszbaran]

I think we can tag a new release after merging this.

[kellertuer]

Great. I set the date in the news and will merge when the tests pass – and register after merge.