Make GivensQ subtype AbstractQ, use API

[dkarrasch]

This makes this package future-proof for JuliaLang/julia#46196 and JuliaLang/julia#46874. This closes #4. Starting with the AbstractQ API in Julia v1.10, many need not be defined anymore. In fact, eltype promotion is then additionally handled by the fallback.

[SebastianAment]

Thank you for putting this up @dkarrasch! The current version fails on Julia 1.6 because this error:

Expression: F.Q \ Qx ≈ x
  MethodError: no method matching lu!(::UpdatableQRFactorizations.GivensQ{Float64, Vector{LinearAlgebra.Givens{Float64}}}, ::Val{true}; check=true)

Is there a more recent stable Julia version or a different fix that would support this?

[dkarrasch]

Ok, I fixed the issue on v1.6. Unfortunately, switching from Factorization to AbstractQ introduces quite some method ambiguities, which is due to the horrible API for AbstractQ. With the current state of the PR, this packages, however, is ambiguity-free on v1.10. The ambiguities don't show up in the tests because only strided arrays are used, so that usage seems safe.