feat: add regular_character (#3393)

docs/src/Groups/group_characters.md

@@ -140,6 +140,7 @@ orders_centralizers
 orders_class_representatives
 ordinary_table(tbl::GAPGroupCharacterTable)
 trivial_character(tbl::GAPGroupCharacterTable)
+regular_character(tbl::GAPGroupCharacterTable)
 ```
 
 ## Construct group characters from groups
@@ -150,6 +151,7 @@ natural_character(G::Union{MatrixGroup{QQFieldElem}, MatrixGroup{AbsSimpleNumFie
 natural_character(G::MatrixGroup{T, MT}) where T <: FinFieldElem where MT
 natural_character(rho::GAPGroupHomomorphism)
 trivial_character(G::GAPGroup)
+regular_character(G::GAPGroup)
 ```
 
 ## Operations for group characters

src/Groups/group_characters.jl

@@ -1673,7 +1673,7 @@ function class_function(tbl::GAPGroupCharacterTable, values::GapObj)
     return GAPGroupClassFunction(tbl, values)
 end
 
-function class_function(tbl::GAPGroupCharacterTable, values::Vector{<:QQAbElem})
+function class_function(tbl::GAPGroupCharacterTable, values::Vector{<:Union{Integer, ZZRingElem, Rational, QQFieldElem, QQAbElem}})
     gapvalues = GapObj([GAP.Obj(x) for x in values])
     return GAPGroupClassFunction(tbl, GAPWrap.ClassFunction(GAPTable(tbl), gapvalues))
 end
@@ -1683,7 +1683,7 @@ function class_function(G::GAPGroup, values::GapObj)
     return GAPGroupClassFunction(character_table(G), values)
 end
 
-function class_function(G::GAPGroup, values::Vector{<:QQAbElem})
+function class_function(G::GAPGroup, values::Vector{<:Union{Integer, ZZRingElem, Rational, QQFieldElem, QQAbElem}})
     return class_function(character_table(G), values)
 end
 
@@ -1724,6 +1724,48 @@ function trivial_character(G::GAPGroup)
     return class_function(G, [val for i in 1:Int(number_of_conjugacy_classes(G))])
 end
 
+@doc raw"""
+    regular_character(G::GAPGroup)
+
+Return the regular character of `G`.
+
+# Examples
+```jldoctest
+julia> G = symmetric_group(3);
+
+julia> values(regular_character(G))
+3-element Vector{QQAbElem{AbsSimpleNumFieldElem}}:
+ 6
+ 0
+ 0
+```
+"""
+function regular_character(G::GAPGroup)
+  return regular_character(character_table(G))
+end
+
+@doc raw"""
+    regular_character(tbl::GAPGroupCharacterTable)
+
+Return the regular character of `tbl`.
+
+# Examples
+```jldoctest
+julia> tbl = character_table(symmetric_group(3));
+
+julia> values(regular_character(tbl))
+3-element Vector{QQAbElem{AbsSimpleNumFieldElem}}:
+ 6
+ 0
+ 0
+```
+"""
+function regular_character(tbl::GAPGroupCharacterTable)
+  val = ZZRingElem[0 for i in 1:length(tbl)]
+  val[1] = order(group(tbl))
+  return class_function(tbl, val)
+end
+
 @doc raw"""
     natural_character(G::PermGroup)
 

src/exports.jl

@@ -1265,6 +1265,7 @@ export register_morphism!
 export regular_120_cell
 export regular_24_cell
 export regular_600_cell
+export regular_character
 export regular_triangulation
 export regular_triangulations
 export relations

test/Groups/group_characters.jl

@@ -844,6 +844,10 @@ end
   @test tr == t[end]
   @test tr == trivial_character(g)
   @test !is_faithful(tr)
+  re = regular_character(g)
+  @test coordinates(re) == degree.(t)
+  re = regular_character(t)
+  @test coordinates(re) == degree.(t)
   chi = t[2]
   @test chi isa Oscar.GAPGroupClassFunction
   @test chi[4] == t[2,4]