Is base_manifold supposed to commute with ProductManifold?

[olivierverdier]

It is currently not the case, but perhaps it is supposed to work that way?
Example:

G = SpecialOrthogonal(3)
M = ConnectionManifold(G, CartanSchoutenZero())
base_manifold(M) # Rotations(3)

MM = ProductManifold(M, M)
base_manifold(MM) # MM, but I would have expected ProductManifold(Rotations(3), Rotations(3))

[kellertuer]

Uh, interesting!

For now, the idea is, that it “undecorates”

• it gives you the manifold of a tangent space
• it gives you the base manifold if you have a metric decorator, the validation manifold (that performs checks), ...
• if it not decorated it is of course its own base manifold
  In that sense the Lie group is also decorated and the base is the plain manifold without the Lie structure.

So for now the answer to the question is: No.

I think it could permute, but while it is a philosophical question whether it should (or one of: does someone need it and we provide it in the package for that reason), the larger problem might be the realisation,
since this would have to work for all decorators and recursively? I mean you could do (× is implemented associative and would create a 4-factor product manifold ... but:)

ProductManifold(ProductManifold(ProductManifold(M,M), M), M)

for your case, which would require a (careful) recursive base manifold case.

I personally do not have a strong opinion here. It should be done very carefully and would be a breaking change.

[kellertuer]

Since base_manifold is really more this technical “strip decorators” idea – maybe a new function like plain_manifold would be the thing you look for? One could then even introduce which features to “strip” (maybe keep a metric?)

That way the technical ‘“undecorate” action would stay as is (we do not have to care about all side effects changing this function would introduce) and we have a “more high level” function doing these more fine granular (and commuting) things.

[olivierverdier]

Yes, I think I will use this implementation in my code, this will suffice for my needs, I think.

plain_manifold(M::ProductManifold) = ProductManifold(plain_manifold.(M.manifolds)...)
plain_manifold(M) = base_manifold(M)

[kellertuer]

An alternative could be to use a keyword argument with the base_manifold like recursive to add your case.