A first Lie group!

.gitignore

@@ -12,3 +12,4 @@ temp
 tutorials/*.ipynb
 tutorials/*_files/*
 tutorials/_freeze
+.vscode/settings.json

.vale.ini

@@ -0,0 +1,19 @@
+StylesPath = docs/styles
+MinAlertLevel = warning
+Vocab = LieGroups
+
+MinAlertLevel = suggestion
+
+Packages = Google, write-good
+
+[*.md]
+BasedOnStyles = Vale, Google, write-good
+
+[NEWS.md, CONTRIBUTING.md]
+BasedOnStyles = Vale, Google
+Google.Will = false ; given format and really with intend a _will_
+Google.Headings = false ; some might jeally ahabe [] in their headers
+
+
+[*.jl]
+BasedOnStyles = Vale, Google, write-good

.zenodo.json

@@ -1,17 +1,36 @@
 {
+
     "creators": [
+        {
+            "affiliation": "University of California, San Francisco",
+            "name": "Axen, Seth",
+            "orcid": "0000-0003-3933-8247"
+        },
+        {
+            "affiliation": "AGH University of Science and Technology",
+            "name": "Baran, Mateusz",
+            "orcid": "0000-0001-9667-5579"
+        },
         {
             "affiliation": "NTNU Trondheim",
             "name": "Bergmann, Ronny",
             "orcid": "0000-0001-8342-7218"
+        },
+        {
+            "name": "Tu, Yueh-Hua"
+        },
+        {
+            "affiliation": "KTH Royal Institute of Technology",
+            "name": "Verdier, Olivier",
+            "orcid": "0000-0003-3699-6244"
         }
     ],
-    "description": "LieGroups.jl provides a library of Lie groups.",
+    "description": "LieGroups.jl is a library of Lie groups, Lie algebras",
     "keywords": [
-        "Riemannian manifolds",
-        "Lie groups",
-        "Julia",
-        "Programming"
+        "Lie group",
+        "Lie algebra",
+        "manifold",
+        "Julia"
     ],
     "license": "MIT",
     "title": "LieGroups.jl",

NEWS.md

@@ -15,7 +15,7 @@ Everything denoted by “formerly” refers to the previous name in [`Manifolds.
 * `LieGroup` (formerly `GroupManifold`) as well as the concrete groups
   * `AdditiveGroup` (formerly `TranslationGroup`)
 * `AbstractGroupOperation` as well as its concrete subtypes
-  * `AdditiveGroupOperation`
+  * `AdditionGroupOperation` (formerly `AdditionOperation`)
 * `AbstractGroupActionType` with its 2 specific (new) abstract
   * `AbstractLeftGroupActionType`
   * `AbstractRightGroupActionType`
@@ -24,8 +24,6 @@ Everything denoted by “formerly” refers to the previous name in [`Manifolds.
   * `RightGroupOperation` (formerly `RightBackwardAction`)
   * `InverseLeftGroupOperation` (formerly `RightForwardAction`)
   * `InverseRightGroupOperation` (formerly `LeftBackwardAction`)
-* `LieGroups.AbstractGroupOperation` as well as its concrete subtypes
-  * `AdditiveGroupOperation`
 * `apply`and `apply!`
 * `base_manifold` to access the manifold within a Lie group
 * `compose` and `compose!`

Project.toml

@@ -4,12 +4,15 @@ authors = ["Seth Axen <[email protected]>", "Mateusz Baran <mateuszbaran89@gma
 version = "0.1.0"
 
 [deps]
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
 
 [compat]
+LinearAlgebra = "1.6"
 Manifolds = "0.10"
 ManifoldsBase = "0.15.16"
+julia = "1.6"
 
 [extras]
 Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"

Readme.md

@@ -10,8 +10,8 @@
 
 This is a package to rework the Lie group features of [`Manifolds.jl`](https://juliamanifolds.github.io/Manifolds.jl/stable/) in a unified way into a separate package.
 
-This especially also includes a few different choices in default behabiour that
+This especially also includes a few different choices in default behaviour that
 is different from the [`Manifolds.jl`](https://juliamanifolds.github.io/Manifolds.jl/stable/) one. For purely manifold-based operations, any Lie group still is “build upon” a Riemannian manifold.
 
-See [#5](https://github.com/JuliaManifolds/LieGroups.jl/issues/5) for an overview of fatures that are plannned.
+See [#5](https://github.com/JuliaManifolds/LieGroups.jl/issues/5) for an overview of features that we plan to implement.
 Feel free to add to this list with opening further issues.

docs/make.jl

@@ -117,10 +117,14 @@ makedocs(;
         "Home" => "index.md",
         "About" => "about.md",
         (tutorials_in_menu ? [tutorials_menu] : [])...,
-        "An Interface for Lie Groups" => "interface.md",
+        "An Interface for ..." => [
+            "A Lie group and algebra" => "interface/group.md",
+            "A group operation" => "interface/operations.md",
+            "A group action" => "interface/actions.md",
+        ],
         "Lie groups" => [
             "List of Lie Groups" => "groups/index.md",
-            "Additive group" => "groups/additive.md",
+            "Translation group" => "groups/translation.md",
         ],
         "Contributing to LieGroups.jl" => "contributing.md",
         "Notation" => "notation.md",

docs/src/groups/index.md

@@ -1,5 +1,7 @@
-# Alphabetical List of Lie groups
+# An overview of Lie groups
+
+# Alphabetical list of Lie groups
 
 | Group | Manifold | ``∘`` | Comment |
 |:------|:---------|:---------:|:------|
-| [`AdditiveGroup`](@ref) | [`Euclidean`](@extref `Manifolds.Euclidean`) | [`+`](@ref AdditiveGroupOperation) | |
+| [`TranslationGroup`](@ref) | [`Euclidean`](@extref `Manifolds.Euclidean`) | [`+`](@ref AdditionGroupOperation) | |

docs/src/groups/translation.md

@@ -0,0 +1,13 @@
+# The Lie group of translations on an Euclidean space
+
+```@docs
+TranslationGroup
+```
+
+## Functions
+
+```@autodocs
+Modules = [LieGroups]
+Pages = ["groups/translation_group.jl"]
+Order = [:function]
+```

docs/src/interface/actions.md

@@ -0,0 +1,33 @@
+# An Interface Actions on Lie groups
+
+```@autodocs
+Modules = [LieGroups]
+Pages = ["group_action_interface.jl"]
+Order = [:type]
+```
+
+## Functions for Lie group actions
+
+```@autodocs
+Modules = [LieGroups]
+Pages = ["group_action_interface.jl"]
+Order = [:function]
+```
+
+# Generic Lie group actions
+
+For certain types of actions, a general implementation can be provided.
+These interfaces are documented here.
+
+```@autodocs
+Modules = [LieGroups]
+Pages = ["group_operation_action.jl"]
+Order = [:type, :function]
+```
+
+## Literature
+
+```@bibliography
+Pages = ["actions.md"]
+Canonical=false
+```

docs/src/interface/group.md

@@ -0,0 +1,45 @@
+# The interface for Lie Groups and Lie algebras
+
+```@docs
+LieGroup
+LieAlgebra
+```
+
+## Functions on Lie Groups
+
+```@docs
+adjoint
+adjoint!
+base_manifold
+conjugate
+conjugate!
+diff_conjugate
+diff_conjugate!
+exp
+exp!
+identity_element
+identity_element!
+is_identity
+isapprox
+is_point(::LieGroup, ::Any)
+is_vector(::LieGroup, ::Any)
+is_vector(::LieGroup{𝔽,O}, ::Identity{O}, ::Any) where {𝔽,O}
+log
+log!
+```
+
+
+## Functions on Lie algebras
+
+```@docs
+is_point(::LieAlgebra, ::Any)
+lie_bracket
+lie_bracket!
+```
+
+## Literature
+
+```@bibliography
+Pages = ["group.md"]
+Canonical=false
+```

docs/src/interface/operations.md

@@ -0,0 +1,29 @@
+
+# Lie group operations
+
+```@docs
+AbstractGroupOperation
+Identity
+compose
+compose!
+diff_inv
+diff_inv!
+diff_left_compose
+diff_left_compose!
+diff_right_compose
+diff_right_compose!
+inv_left_compose
+inv_left_compose!
+inv_right_compose
+inv_right_compose!
+inv(::LieGroup, ::Any)
+inv!
+```
+
+For some generic group operations, an easy generic implementation can be provided. This section lists these specific cases and what is implemented for these.
+
+## Additive Group operation
+
+```@docs
+AdditionGroupOperation
+```

docs/src/references.md

@@ -1,7 +1,7 @@
 # Literature
 
 This is all literature mentioned / referenced in the `LieGroups.jl` documentation.
-Usually you find a small reference section at the end of every documentation page
+You find a small reference section at the end of every documentation page
 that contains the corresponding references as well.
 
 ```@bibliography