Infinite recursion for `⊕(::ProductSpace, ::ProductSpace)`

[ogauthe]

Hi! I found that ⊕ ends in an infinite recursion when trying to add ProductSpace.

V₁, V₂ = ProductSpace(Rep[SU₂](0=>1)), ProductSpace(Rep[SU₂](1=>1))
⊕(V₁, V₂)  # infinite recursion

This is defined at spaces/vectorspaces.jl:149

⊕(V₁::VectorSpace, V₂::VectorSpace) = ⊕(promote(V₁, V₂)...)

Not sure what should be the behavior here. Maybe the best would be to throw an error for ProductSpace.

[lkdvos]

You shouldn't really be able to add ProductSpace, which is why it wasn't implemented, hence the issue. I somehow thought that promotion should error gracefully when no types changed though

[Jutho]

Can we restrict that method to ElementarySpace subtypes? SumSpace also subtypes that, right?

[lkdvos]

It does, and if not it should :)

[Jutho]

It does, but I am confused looking at this file that it also defines various methods for its own version of ⊕, as well as for TensorKit.:⊕. This seems very confusing?

[Jutho]

Ever considered using something like \boxplus (⊞) for the lazy version that gives you a SumSpace object?

[lkdvos]

I just qualify the names fully in MPSKit 🙃