Mateusz Baran

OK, I will check how to implement the duplicated cost case during the weekend.

I changed it so that duplicates are allowed and tests are passing locally. Let me know if you notice any issues.

I've added `get_cost_and_differential` to optimize the LineSearches extension. Is that OK?

Yes, I think the SPD should just be an alias for real-coefficient HPD.

No problem, this change is largely independent of the core work of implementing complex HPD.

Good idea. In the context of this paper I think it would be appropriate to make a new `

But we don't need the ambient space here, `p0 + v0 + Δ` is in a parametrization. > So in theory, this _is_ super straight forward, if you have an...

I mean you add parameters of `p` in the selected parametrization and coordinates of a tangent vector in the induced basis.

Yes, ideally an atlas would be needed. I think our support for that is good enough, see for example `EmbeddedTorus`. We have an example of working with `InducedBasis` and in-chart...

Sure, we need more atlases. But IMO this is the right way of implementing this feature.