Hi @eeshan9815
if you or @dpsanders feel motivated to implement topological (Lefshetz) index computation (see e.g. the discussion in here) in IntervalRootFinding, feel free to ask me any questions.
This is really less complicated than it sounds (no need to chase commutative diagrams; just count roots with “topological multiplicity”, which is the sign of the determinant of the jacobian; the only tricky part is computing the multiplicity for maybe-roots with maybe-non-invertible jacobian)
But I’m not familiar with the codebase, am not an active user of the JuliaIntervals world, and do not plan to implement this myself in the near future. I am working on some other computational topology stuff though, so there might be overlap.
Otherwise, welcome and have a nice summer!