Mateusz Baran

Hm, OK, we can keep the old variant but I'd like to document its requirements regarding the basis then -- they are not obvious to me at least.

Good idea, incidentally this is quite high on my priority list as well (though I expect to mostly need Jacobians). > The first is, what I think [pymanopt](https://github.com/pymanopt/pymanopt) does, the...

> Why would you classify ChainRules.jl's forward mode support as experimental? ChainRules just hit v1.0, which signals that its API is very stable. By comparison, ForwarDiff has not yet hit...

Here is the quick sketch or a `rrule` for `distance` I've made on Slack. I think it's worth saving from the Slack hole: ```julia function ChainRulesCore.rrule(::typeof(distance), M::AbstractManifold, p, q) d...

I'm not even sure what would I recommend reading here, usually GPU support is done from the other side than I'd prefer to do it here: each manifold is implemented...

Related thing: https://github.com/JuliaGPU/KernelAbstractions.jl .

@kellertuer could you take a look if my approach to scalars for vector spaces makes sense? There may be some holes related to scalars of tangent spaces of complex manifolds....

Some code lines: - Here is the new definition of `VectorSpaceType`: https://github.com/JuliaManifolds/Manifolds.jl/pull/202/files#diff-c6389631d82343df20214336402283efR26 . It is now parametrized by number system. I replaced the constants `TangentSpace` and `CotangentSpace` by functions since...

Now after some discussion in https://discourse.julialang.org/t/ann-tensoralgebra-jl-taking-covariance-seriously/43587 I'm starting to think that perhaps adding a number system argument to vector spaces wasn't a good idea. After all it can be deduced...

I've read some parts of the Absil's book and reevaluated (again) the plans here. It looks like the most important missing component are affine connections and that's what I've started...