Merge branch 'kellertuer/general-linear-group' of github.com:JuliaMan…

…ifolds/LieGroups.jl into kellertuer/general-linear-group

# Conflicts:
#	docs/src/tutorials/transition.md

NEWS.md

@@ -14,6 +14,7 @@ Everything denoted by “formerly” refers to the previous name in [`Manifolds.
 * `LieAlgebra`
 * `LieGroup` (formerly `GroupManifold`) as well as the concrete groups
   * `TranslationGroup`
+  * `GeneralLinearGroup` (formerly `GeneralLinear`)
 * `AbstractGroupOperation` as well as its concrete subtypes
   * `AdditionGroupOperation` (formerly `AdditionOperation`)
 * `AbstractGroupActionType` with its 2 specific (new) abstract

docs/make.jl

@@ -102,7 +102,7 @@ end
 tutorials_menu =
     "How to..." => [
         "🚀 Get Started with LieGroups.jl" => "tutorials/getstarted.md",
-        "Transistion from `GroupManifolds`" => "tutorials/transition.md",
+        "Transition from `GroupManifolds`" => "tutorials/transition.md",
     ]
 # (e) finally make docs
 bib = CitationBibliography(joinpath(@__DIR__, "src", "references.bib"); style=:alpha)
@@ -123,7 +123,7 @@ makedocs(;
         "About" => "about.md",
         (tutorials_in_menu ? [tutorials_menu] : [])...,
         "Lie groups" => [
-            "List of Lie Groups" => "groups/index.md",
+            "List of Lie groups" => "groups/index.md",
             "General Linear" => "groups/general_linear.md",
             "Translation group" => "groups/translation.md",
         ],

docs/src/tutorials/transition.md

@@ -1,6 +1,6 @@
 # Transition from `GroupManifolds` in `Manifolds.jl`
 
-One predecessor of `LieGroups.jl` are the [`GroupManifold`](@extref `Manifolds.GroupManifold`)s in `Manifoldsjl`.
+One predecessor of `LieGroups.jl` are the [`GroupManifold`](@extref `Manifolds.GroupManifold`)s in `Manifolds.jl`.
 While this package provides the same features, one reason for a new package is,
 that a “restart” offers the opportunity to put the main focus for the functions in this package
 really on Lie groups.
@@ -25,7 +25,7 @@ The list is alphabetical, but first lists types, then functions
 | `LeftForwardAction` | [`LeftGroupOperation`](@ref)
 | `RightBackwardAction` | [`RightGroupOperation`](@ref) | |
 | `LeftBackwardAction` | [`InverseRightGroupOperation`](@ref) | note that this is now also aa [`AbstractLeftGroupActionType`](@ref) |
-| | [`LieAlgebra`](@ref)`(G)` | new to emphasize its menifold- and vector structure as well as for a few dispatch methods. |
+| | [`LieAlgebra`](@ref)`(G)` | new alias to emphasize its manifold- and vector structure as well as for a few dispatch methods. |
 | `GroupManifold(M, op)` | [`LieGroup`](@ref)`(M, op)` | |
 | `RightForwardAction` | [`InverseLeftGroupOperation`](@ref) | note that this is an [`AbstractRightGroupActionType`](@ref) |
 | `adjoint` | [`adjoint`](@ref) | now implemented with a default, when you provide [`diff_conjugate!`](@ref).
@@ -44,9 +44,9 @@ The list is alphabetical, but first lists types, then functions
 | `switch_direction(A)` | [`inv`](@ref inv(::AbstractGroupAction))`(A)` | switches from an action to its inverse action (formerly the direction forward/backward, sometimes even left/right, do not confuse with the side left/right). |
 | `switch_side(A)` | [`switch`](@ref switch(::AbstractGroupAction))`(A)` | switches from a left action to its corresponding right action. |
 | `translate(G, g, h)` | [`compose`](@ref)`(G, g, h)` | unified to `compose` |
-| `translate_diff(G, g, X, c)` | [`diff_left_compose`](@ref)`(G, g, h, X)`, [`diff_right_compose`](@ref)`(G, g, h, X)` | for compose ``∘(g,h)` we specify now whether we take the derivative with respect to the left (`g`) or right (`h`) argument
+| `translate_diff(G, g, X, c)` | [`diff_left_compose`](@ref)`(G, g, h, X)`, [`diff_right_compose`](@ref)`(G, g, h, X)` | for compose ``∘(g, h)`` we specify now whether we take the derivative with respect to the left (`g`) or right (`h`) argument |
 |`VeeOrthogonalBasis` | [`LieAlgebraOrthogonalBasis`](@ref) | |
 
 # Notable changes
 
-* The [`GeneralLinearGroup`](@ref) (formerly `GeneralLinear`) switched to using its Lie algebra to represent tangent vectors
+* The [`GeneralLinearGroup`](@ref) (formerly `GeneralLinear`) switched to using its Lie algebra to represent tangent vectors.

src/documentation_glossary.jl

@@ -85,7 +85,7 @@ define!(
         _tex(:Set, elem * raw"\ " * _tex(Symbol("$(size)")) * raw"|\ " * "$(cond)", size),
 )
 define!(:LaTeX, :sum, raw"\sum")
-define!(:LaTeX, :transp, raw"\mathm{T}")
+define!(:LaTeX, :transp, raw"\mathrm{T}")
 #
 # ---
 # Mathematics and semantic symbols

src/group_operations/multiplication_operation.jl

@@ -101,22 +101,23 @@ function diff_conjugate!(
 end
 
 _doc_diff_inv_mult = """
-    diff_inv(G::LieGroup{𝔽,<:AbstractMultiplicationGroupOperation},, p, X)
+    diff_inv(G::LieGroup{𝔽,<:AbstractMultiplicationGroupOperation}, g, X)
+    diff_inv!(G::LieGroup{𝔽,<:AbstractMultiplicationGroupOperation}, Y, g, X)
 
-Compute the value of differential ``Dι_{$(_math(:G))}(g)[X] of matrix inversion ``ι_{$(_math(:G))}(g) := g^{-1}`` at ``X ∈ 𝔤``
+Compute the value of differential ``Dι_{$(_math(:G))}(g)[X]`` of matrix inversion ``ι_{$(_math(:G))}(g) := g^{-1}`` at ``X ∈ 𝔤``
 in the [`LieAlgebra`](@ref) ``𝔤`` of the [`LieGroup`](@ref) `G`.
 
 The formula is given by
 
 ```math
-Dι_{$(_math(:G))}(g)[X] = -g^{$(_tex(:transp))}Xp^{-1},
+Dι_{$(_math(:G))}(g)[X] = -g^{$(_tex(:transp))}Xg^{-1},
 ```
 
 which stems from using the differential of the inverse from [Giles:2008](@cite) given by
-``D(g^-1)[X] = -g^{-1}Xg^{-1}`` composed with the push forward of the left composition
+``D(g^{-1})[X] = -g^{-1}Xg^{-1}`` composed with the push forward of the left composition
 ``Dλ_$(_math(:e))(g)[X] = gX`` mapping from the Liea algebra into the tangent space at ``g``,
 and its adjoint ``D^*λ_$(_math(:e))(g)[X] = g^{$(_tex(:transp))}X``.
-Then we get ``g^{$(_tex(:transp))}(g^{-1}(gX)g^{-1})`` which simplifies to ``-g^{$(_tex(:transp))}Xp^{-1}`` from above.
+Then we get ``g^{$(_tex(:transp))}(g^{-1}(gX)g^{-1})`` which simplifies to ``-g^{$(_tex(:transp))}Xg^{-1}`` from above.
 """
 
 @doc "$(_doc_diff_inv_mult)"

src/interface.jl

@@ -446,7 +446,7 @@ ManifoldsBase.get_vector!(G::LieGroup, X, g, c, B::ManifoldsBase.AbstractBasis)
 
 _doc_hat = """
     hat(G::LieGroup, c)
-    hat(G::LieGroup, X, c)
+    hat!(G::LieGroup, X, c)
 
 Compute the hat map ``(⋅)^̂ `` that maps a vector of coordinates ``c_i``
 with respect to a certain basis to an tangent vector in the Lie algebra
@@ -761,7 +761,7 @@ end
 
 _doc_vee = """
     vee(G::LieGroup, X)
-    vee(G::LieGroup, c, X)
+    vee!(G::LieGroup, c, X)
 
 Compute the vee map ``(⋅)^̂ `` that maps a tangent vector `X` from the [`LieAlgebra`](@ref)
 to its coordinates with respect to a certain bvasis in the Lie algebra