Adapt to ManifoldsBase 1.0

[kellertuer]

This depends on JuliaManifolds/ManifoldsBase.jl#221 being merged.

Overall I went through all occurrences of exp and exp! and split/renamed them to expt and expt!, respectively, where necessary.
There are two tricky areas left

• interaction with the MetricManifold, which should carefully be checked
• interaction with solve_exp_ode where I can not yet see why they fail because the error messages basically kill my terminal in length.

Formerly this is breaking, because we drop support for ManifoldsBase 0.15?

Furthermore all occurrences of retract, retract_ and all its follow up functions need to be split for each and every retraction method on every manifold.

• add deprecations for the renamed types from TVector to Tangentvector

[mateuszbaran]

retract rework is more or less done. I have some issues with OrdinaryDiffEq.jl failing to even precompile right now so that part will have to wait a bit. Next part is renaming and injectivity_radius.

[kellertuer]

My rework from the weekend makes all tests pass, so after releasing 1.0, we only have to check for test coverage by now.

[kellertuer]

This should be finished ± checking for code coverage after all the changes to exp/retr.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 96.52%. Comparing base (0c2a7b7) to head (bfd984f).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #781      +/-   ##
==========================================
+ Coverage   96.45%   96.52%   +0.06%     
==========================================
  Files         127      127              
  Lines       11890    11957      +67     
==========================================
+ Hits        11469    11541      +72     
+ Misses        421      416       -5     

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[kellertuer]

Docs are already fixed here locally, checking tutorials already. But will only push after I see how the tests are doing and maybe working on code cov there already.

[kellertuer]

Raised number of ambiguities allowed to 35 – noticed that it is also 35 on 1.11; but we exclude 1.11 from testing ambiguities; so it did not error locally for me. Do we want to keep that exclusion? Do we want to keep the ambiguity test or is the one from Aqua enough? (I just do not remember the arguments maybe).

[mateuszbaran]

Maybe let's keep the exclusion; it prevents spurious failures on CI when a new Julia version is released. The bump in allowed ambiguities should be OK. The Aqua test makes wider exclusions than ours so I'd prefer to keep both.

[kellertuer]

Ok, just means that me running on 1.11 would not see this happening and only CI would fail. But I checked the new ambiguities and they look harmless.

[kellertuer]

We have code coverage – I even fixed a few previously uncovered lines, to slowly increase code cov here.

If it is ok, I would like to merge this and register a new version.

You can merge an register as well of course; for me it would be great in order to continue with the 3 PRs that depend on this.