add docstrings for acting_group and action_function (oscar-system…

…#3432)

docs/src/Groups/action.md

@@ -52,10 +52,14 @@ A G-set provides an explicit bijection between the elements of the set and
 the corresponding set of positive integers on which the induced permutation
 group acts,
 see [`action_homomorphism(Omega::GSetByElements{T}) where T<:GAPGroup`](@ref).
+Note that the explicit elements of a G-set `Omega` can be obtained using
+`collect(Omega)`.
 
 ```@docs
 gset(G::GAPGroup, fun::Function, Omega)
 permutation
+acting_group(Omega::GSetByElements)
+action_function(Omega::GSetByElements)
 action_homomorphism(Omega::GSetByElements{T}) where T<:GAPGroup
 orbit(Omega::GSetByElements{<:GAPGroup}, omega::T) where T
 orbit(G::PermGroup, omega)

src/Groups/gsets.jl

@@ -69,8 +69,40 @@ function Base.show(io::IO, x::GSetByElements)
   end
 end
 
-# TODO: document `acting_group`, `action_function`
+"""
+    acting_group(Omega::GSetByElements)
+
+Return the group `G` acting on `Omega`.
+
+# Examples
+```jldoctest
+julia> G = symmetric_group(4);
+
+julia> acting_group(gset(G, [1])) == G
+true
+```
+"""
 acting_group(Omega::GSetByElements) = Omega.group
+
+@doc raw"""
+    action_function(Omega::GSetByElements)
+
+Return the function $f: \Omega \times G \to \Omega$ that defines the G-set.
+
+# Examples
+```jldoctest
+julia> G = symmetric_group(4);
+
+julia> action_function(gset(G, [1])) == ^
+true
+
+julia> action_function(gset(G, [[1, 2]])) == on_tuples
+true
+
+julia> action_function(gset(G, on_sets, [[1, 2]])) == on_sets
+true
+```
+"""
 action_function(Omega::GSetByElements) = Omega.action_function
 
 # The following works for all G-set types that support attributes
@@ -241,7 +273,7 @@ function ^(omega::ElementOfGSet, g::T) where {T<:AbstractAlgebra.GroupElem}
     return ElementOfGSet(Omega, fun(omega.obj, g))
 end
 
-==(omega1::ElementOfGSet, omega2::ElementOfGSet) = 
+==(omega1::ElementOfGSet, omega2::ElementOfGSet) =
   ((omega1.gset == omega2.gset) && (omega1.obj == omega2.obj))
 
 function Base.hash(omega::ElementOfGSet, h::UInt)

src/exports.jl

@@ -182,6 +182,7 @@ export acting_domain
 export acting_group
 export acting_subgroup
 export action
+export action_function
 export action_homomorphism
 export add_edge!
 export add_gluing!