Mateusz Baran

Yes, sure, that would make sense.

This is an interesting idea. We do have `in` in Manifolds.jl and `eltype` should be doable but it looks like the main point about DomainSets.jl (correct me if I'm wrong)...

I see, then at least it would be useful to extend both DomainSets.jl and Manifolds.jl to work in bases constructed from eigenvectors of Laplace-Beltrami operator or something similar. I think...

Note that mapping to R^n is often quite far from the best you can do to integrate over a manifold: https://www-user.tu-chemnitz.de/~potts/workgroup/graef/quadrature/index.php.en .

High dimensionality shouldn't be an issue, points and weights could be recomputed. What kind of manifolds would you be interested in?

Intersection of Bayesian models and manifolds is a fairly broad subject with many tools like RMHMC or Riemannian symplectic integrators :sweat_smile: . I think the discussion would be more productive...

I think using `repeat` rather than `fill` would be more appropriate here. > * the current form generates a few ambiguities, but it follows our idea to have M first;...

> Oh, I was not aware of that, what is that meaning? ```julia julia> fill(PowerManifold(Circle(), 3), 4) 4-element Vector{PowerManifold{ℝ, Circle{ℝ}, Tuple{Int64}, ArrayPowerRepresentation}}: PowerManifold(Circle(ℝ), 3) PowerManifold(Circle(ℝ), 3) PowerManifold(Circle(ℝ), 3) PowerManifold(Circle(ℝ), 3)...

> We can also use both reapeat and fill, but I fear they actually would do the same basically then? I prefer `repeat` but I'm also OK with `fill` as...

And yes, there is no reason to have both `fill` and `repeat`.