Call GapObj instead of accessing chi.values (for group characters…

…) or `f.map` (for group homomorphisms) (#3681)

* use `GapObj` instead of `.values` access for group characters
* use `GapObj(f)` not `f.map` for `f::GAPGroupHomomorphism`
  (and replace more `.X` access by `GapObj`)
* replace `GAPTable` for char. tables by `GapObj`
* simplify recursive `GapObj` calls
* more `GapObj` calls using `recursive = true`
* add a `GAP.julia_to_gap(::JSON3.Array, ...)` method until the
  fix from oscar-system/GAP.jl/pull/989 is available

experimental/GModule/GModule.jl

@@ -612,7 +612,7 @@ function Oscar.natural_character(C::GModule{<:Any, <:AbstractAlgebra.FPModule{<:
 
   vals = [GAP.Globals.BrauerCharacterValue(GAP.Obj(map(h, matrix(action(C, representative(x)))))) for x in ccl]
 
-  return Oscar.class_function(modtbl, GAPWrap.ClassFunction(Oscar.GAPTable(modtbl), Oscar.GapObj(vals)))
+  return Oscar.class_function(modtbl, GAPWrap.ClassFunction(GapObj(modtbl), GapObj(vals)))
 end
 
 function Oscar.sub(C::GModule{<:Any, <:AbstractAlgebra.FPModule{T}}, m::MatElem{T}) where {T <: FinFieldElem}
@@ -1528,7 +1528,7 @@ function Oscar.gmodule(::Type{FinGenAbGroup}, C::GModule{T, <:AbstractAlgebra.FP
 end
 
 function Oscar.gmodule(chi::Oscar.GAPGroupClassFunction)
-  f = GAP.Globals.IrreducibleAffordingRepresentation(chi.values)
+  f = GAP.Globals.IrreducibleAffordingRepresentation(GapObj(chi))
   K = abelian_closure(QQ)[1]
   g = GAP.Globals.List(GAP.Globals.GeneratorsOfGroup(GapObj(group(chi))), f)
   z = map(x->matrix(map(y->map(K, y), g[x])), 1:GAP.Globals.Size(g))

experimental/OrthogonalDiscriminants/src/theoretical.jl

@@ -240,7 +240,7 @@ function od_from_p_subgroup(chi::GAPGroupClassFunction, p::Int,
   end
 
   fus = filter(i -> pi[i] != 0, 1:number_of_conjugacy_classes(tbl))
-  res = Oscar.GAPWrap.ELMS_LIST(chi.values, GAP.GapObj(fus))
+  res = Oscar.GAPWrap.ELMS_LIST(GapObj(chi), GapObj(fus))
 
   if l != 0
     # possible shortcut:

experimental/OrthogonalDiscriminants/src/utils.jl

@@ -150,10 +150,10 @@ function possible_permutation_characters_from_sylow_subgroup(tbl::Oscar.GAPGroup
   pos != nothing && return [induced_cyclic(tbl, [pos])[1]]
 
   # Do we have the table of marks?
-  tom = GAP.Globals.TableOfMarks(Oscar.GAPTable(tbl))
+  tom = GAP.Globals.TableOfMarks(GapObj(tbl))
   if tom != GAP.Globals.fail
     pos = findfirst(x -> x == q, Vector{Int}(GAP.Globals.OrdersTom(tom)))
-    return [Oscar.class_function(tbl, GAP.Globals.PermCharsTom(Oscar.GAPTable(tbl), tom)[pos])]
+    return [Oscar.class_function(tbl, GAP.Globals.PermCharsTom(GapObj(tbl), tom)[pos])]
   end
 
   # Does the table have a nontrivial 'p'-core
@@ -193,7 +193,7 @@ function possible_permutation_characters_from_sylow_subgroup(tbl::Oscar.GAPGroup
             for i in npos
               pi[i] = index
             end
-            pi = GAP.Globals.ClassFunction(Oscar.GAPTable(s), GapObj(pi, true))
+            pi = GAP.Globals.ClassFunction(GapObj(s), GapObj(pi, true))
             return [Oscar.class_function(s, pi)^tbl]
           else
             # Try to recurse.
@@ -216,11 +216,11 @@ function possible_permutation_characters_from_sylow_subgroup(tbl::Oscar.GAPGroup
           if cand != nothing
             extcand = []
             for pi in cand
-              pi = GAP.Globals.CompositionMaps(pi.values,
+              pi = GAP.Globals.CompositionMaps(GapObj(pi),
                        GAP.Globals.InverseMap(GapObj(fus)))
               union!(extcand, [Oscar.class_function(tbl, x) for x in
-                                GAP.Globals.PermChars(Oscar.GAPTable(tbl),
-                                  GAP.GapObj(Dict(:torso => pi), true))])
+                                GAP.Globals.PermChars(GapObj(tbl),
+                                  GapObj(Dict(:torso => pi), true))])
             end
             if candlist == nothing
               candlist = extcand

experimental/SymmetricIntersections/src/representations.jl

@@ -234,7 +234,7 @@ end
 Given a class function `chi` on a group `G`, return whether `chi` defines a
 character of `G` (over its codomain).
 """
-is_character(chi::Oscar.GAPGroupClassFunction) = GG.IsCharacter(GAPTable(parent(chi)), chi.values)::Bool
+is_character(chi::Oscar.GAPGroupClassFunction) = GG.IsCharacter(GapObj(parent(chi)), GapObj(chi))::Bool
 
 @doc raw"""
     is_constituent(chi::T, nu::T) where T <: Oscar.GAPGroupClassFunction -> Bool
@@ -502,7 +502,7 @@ function irreducible_affording_representation(RR::RepRing{S, T}, chi::Oscar.GAPG
   H = generators_underlying_group(RR)
 
   # the GAP function which we rely on
-  rep = GG.IrreducibleAffordingRepresentation(chi.values)::GAP.GapObj
+  rep = GG.IrreducibleAffordingRepresentation(GapObj(chi))::GAP.GapObj
 
   # we compute certain images than we will convert then.
   # we use them then to construct the mapping in

src/GAP/oscar_to_gap.jl

@@ -72,3 +72,17 @@ function GAP.julia_to_gap(
 
     return gapset
 end
+
+## TODO: remove the following once GAP.jl has it
+## (This will be the case when the change from
+## https://github.com/oscar-system/GAP.jl/pull/989
+## will be available.)
+using JSON3
+
+function GAP.julia_to_gap(
+    obj::JSON3.Array,
+    recursion_dict::IdDict{Any,Any} = IdDict();
+    recursive::Bool = false)
+
+    return GAP.julia_to_gap(copy(obj), recursion_dict; recursive)
+end