Tests: adjoint_action

- at Identity
- remove some unused adjoint_action! implementations

ext/ManifoldsTestExt/tests_group.jl

@@ -553,6 +553,10 @@ function test_group(
             adjoint_action(G, g_pts[2], adjoint_action(G, g_pts[2], X, RightAction())),
             X,
         )
+        # adjoint action at identity
+        for conv in [LeftAction(), RightAction()]
+            isapprox(TangentSpace(G, identity_element(G)), adjoint_action(G, e, Xe_pts[1]), Xe_pts[1])
+        end
         if test_mutating
             Z = allocate(X)
             adjoint_action!(G, Z, g_pts[2], X)

src/groups/circle_group.jl

@@ -166,7 +166,6 @@ end
 adjoint_action(::RealCircleGroup, p, X) = X
 adjoint_action(::RealCircleGroup, p, X, ::ActionDirection) = X
 
-adjoint_action!(::RealCircleGroup, Y, p, X) = copyto!(Y, X)
 adjoint_action!(::RealCircleGroup, Y, p, X, ::ActionDirection) = copyto!(Y, X)
 
 for AD in [LeftAction, RightAction]

src/groups/group.jl

@@ -467,16 +467,6 @@ end
 function adjoint_action!(G::AbstractDecoratorManifold, Y, p, X)
     return adjoint_action!(G, Y, p, X, LeftAction())
 end
-function adjoint_action!(
-    ::TraitList{<:IsGroupManifold},
-    G::AbstractDecoratorManifold,
-    Y,
-    p,
-    X,
-)
-    BG = base_group(G)
-    return adjoint_action!(BG, Y, p, X, LeftAction())
-end
 # fall back method: the right action is defined from the left action
 function adjoint_action!(
     ::TraitList{<:IsGroupManifold},