Work through the tipps from vale.

CONTRIBUTING.md

@@ -1,53 +1,51 @@
 # Contributing to `LieGroups.jl`
 
 First, thanks for taking the time to contribute.
-Any contribution is appreciated and welcome.
+We appreciate and welcome any contribution.
 
 The following is a set of guidelines to [`LieGroups.jl`](https://juliamanifolds.github.io/LieGroups.jl/).
 
 #### Table of contents
 
 - [Contributing to `LieGroups.jl`](#Contributing-to-manoptjl)
       - [Table of Contents](#Table-of-Contents)
-  - [I just have a question](#I-just-have-a-question)
-  - [How can I file an issue?](#How-can-I-file-an-issue)
-  - [How can I contribute?](#How-can-I-contribute)
+  - [How to just ask a question](#I-just-have-a-question)
+  - [How to file an issue](#How-can-I-file-an-issue)
+  - [How to contribute](#How-can-I-contribute)
   - [Code style](#Code-style)
 
-## I just have a question
+## How to just ask a question
 
 The developer can most easily be reached in the Julia Slack channel [#manifolds](https://julialang.slack.com/archives/CP4QF0K5Z).
 You can apply for the Julia Slack workspace [here](https://julialang.org/slack/) if you haven't joined yet.
 You can also ask your question on [discourse.julialang.org](https://discourse.julialang.org).
 
-## How can I file an issue?
+## How to file an issue
 
 If you found a bug or want to propose a feature, please open an issue in within the [GitHub repository](https://github.com/JuliaManifolds/LieGroups.jl/issues).
 
-## How can I contribute?
+## How to contribute
 
-Currently we are still consolidating most details and defaults, but feel free to contribute to these discussions within this repository.
+Currently most details are still work-in-progress.
+Feel free to contribute ideas, features you would like to see, Lie groups you want to have or would like to contribute, or any other idea for `LieGroups.jl`. For these, use either the [discussions](https://github.com/JuliaManifolds/LieGroups.jl/discussions) or [issues](https://github.com/JuliaManifolds/LieGroups.jl/issues) in the [GitHub repository](https://github.com/JuliaManifolds/LieGroups.jl)
 
 ## Code style
 
-Try to follow the [documentation guidelines](https://docs.julialang.org/en/v1/manual/documentation/) from the Julia documentation as well as [Blue Style](https://github.com/invenia/BlueStyle).
-Run [`JuliaFormatter.jl`](https://github.com/domluna/JuliaFormatter.jl) on the repository in the way set in the `.JuliaFormatter.toml` file, which enforces a number of conventions consistent with the Blue Style.
+Please follow the [documentation guidelines](https://docs.julialang.org/en/v1/manual/documentation/) from the Julia documentation as well as [Blue Style](https://github.com/invenia/BlueStyle).
+Run [`JuliaFormatter.jl`](https://github.com/domluna/JuliaFormatter.jl) on the repository running `using JuliaFormatter; format(".")` on the main folder of the project.
 
 Please follow a few internal conventions:
 
-- Any implemented function should be accompanied by its mathematical formulae if a closed form exists.
-- A Lie group, a Lie group action or a Lie algebra should be implemented in it own file
+- Include the mathematical formulae for any implemented function if a closed form exists.
+- Define a Lie group, a Lie group action, or a Lie algebra in its own file. Include all related functions in the same file
 - an alphabetical order of functions in every file is preferable.
 - The preceding implies that the mutating variant of a function follows the non-mutating variant.
-- usually, both the allocating and the mutating variants of a function should be documented. For avoiding duplication, one doc string attached to both is preferrable
+- Document both the allocating and the mutating variants of a function. To avoid duplication, attach one doc string defined before both functions and attach it to both.
 - There should be no dangling `=` signs.
-- Always add a newline between things of different types (struct/method/const).
-- Always add a newline between methods for different functions (including allocating/mutating variants).
+- Add a newline between things of different types (struct/method/const).
+- Add a newline between methods for different functions (including allocating/mutating variants).
 - Prefer to have no newline between methods for the same function; when reasonable, merge the documentation strings.
 - All `import`/`using`/`include` should be in the main module file.
-- `import` is discouraged and the explicit full name, like `Base.exp` should be used when implementing functions
-
-Concerning documentation
-
+- Avoid using `import` and use the explicit full name, like `Base.exp`, when implementing functions, that extend functions of other packages.
 - if possible provide both mathematical formulae and literature references using [DocumenterCitations.jl](https://juliadocs.org/DocumenterCitations.jl/stable/) and BibTeX where possible
 - Always document all input variables and keyword arguments

docs/styles/config/vocabularies/LieGroups/accept.txt

@@ -1,4 +1,5 @@
 julia
+Julia
 LieGroups.jl
 Lie algebra
 Lie algebras

src/documentation_glossary.jl

@@ -9,7 +9,7 @@
 # * links
 # * notes
 #
-# to keep naming, notation, and formatting in a unifed way
+# to keep naming, notation, and formatting in a unified way
 
 # In general every dictionary here can be either `:Symbol-> String` or `:Symbol -> Dictionary enrties`
 
@@ -28,7 +28,7 @@ if that entrs is
 * a function, it is called with `args...` and `kwargs...` passed
 * a dictionary, then the arguments and keyword arguments are passed to this dictionary, assuming `args[1]` is a symbol
 """
-#Do not attach the doc string here for now, since there is no internals section in the documenttion yet
+#Do not attach the doc string here for now, since there is no internals section in the documentation yet
 glossary(s::Symbol, args...; kwargs...) = glossary(_manopt_glossary, s, args...; kwargs...)
 function glossary(g::_LIEGROUPS_DOC_TYPE, s::Symbol, args...; kwargs...)
     return glossary(g[s], args...; kwargs...)