Mateusz Baran

I've made an issue about it: https://github.com/JuliaTesting/Aqua.jl/issues/290 .

Manopt.jl is currently in the process of adding such workaround: https://github.com/JuliaManifolds/Manopt.jl/pull/236 . Essentially it's wrapping points in one-element vectors. It's not ideal for performance, especially in the case of `mean`,...

I think this is a good idea. Right now our definitions are somewhat messy. I will keep this in mind for the next round of group cleanup.

The problem here is providing default that work for groups with left-invariant tangent vector representation (basically all our groups except semidirect products), while not giving wrong results for the groups...

> There are four solutions, I emphasize the effort to be put and the backward compatibility breaking: I think this is a good summary of options. In Manifolds.jl we do...

I checked to be sure and it looks like we ended up in an inconsistent state somehow. Manifold structure is implemented without left-invariance, but at least part of group code...

OK. Using a different tangent vector representation for `exp_lie` doesn't seem to make sense though? `exp_lie` is different from `exp` because it is conceptually a different operation.

Sure, I was just asking if you maybe remember something about CircleGroup. Changing implementation of `exp` to use `exp_lie` would be very tricky because `exp` needs to be available on...

> Hang on, `exp_lie` and `log_lie` should only work on the tangent space at identity and therefore be independent of the way tangent vectors are stored? (although they depend on...

Using `CartanSchoutenMinus` as the default connection for Lie groups would be a significant breaking change but it does make sense.