Try to sort out the homs

Project.toml

@@ -25,12 +25,12 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.41.2"
+AbstractAlgebra = "0.41.3"
 AlgebraicSolving = "0.4.11"
 Distributed = "1.6"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.10.2"
-Hecke = "0.31.0"
+Hecke = "0.31.3"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"

experimental/GModule/Cohomology.jl

@@ -380,8 +380,8 @@ function Oscar.direct_product(C::GModule...; task::Symbol = :none)
   @assert all(x->x.G == G, C)
   mM, pro, inj = direct_product([x.M for x = C]..., task = :both)
 
-  mC = gmodule(G, [hom(mM, mM, [action(C[i], g) for i=1:length(C)]) for g = gens(G)])
-  mC.iac = [hom(mM, mM, [action(C[i], inv(g)) for i=1:length(C)]) for g = gens(G)]
+  mC = gmodule(G, [hom_direct_sum(mM, mM, [action(C[i], g) for i=1:length(C)]) for g = gens(G)])
+  mC.iac = [hom_direct_sum(mM, mM, [action(C[i], inv(g)) for i=1:length(C)]) for g = gens(G)]
 
   if task == :none
     return mC
@@ -403,7 +403,7 @@ function Oscar.tensor_product(C::GModule{<:Any, FinGenAbGroup}...; task::Symbol
   @assert all(x->x.G == C[1].G, C)
 
   T, mT = Oscar.tensor_product([x.M for x = C]...; task = :map)
-  TT = gmodule(T, C[1].G, [hom(T, T, [action(C[i], g) for i=1:length(C)]) for g = gens(C[1].G)])
+  TT = gmodule(T, C[1].G, [hom_tensor(T, T, [action(C[i], g) for i=1:length(C)]) for g = gens(C[1].G)])
   if task == :map
     return TT, mT
   else

experimental/GModule/Misc.jl

@@ -247,27 +247,6 @@ Hecke.extend(::Hecke.QQEmb, mp::MapFromFunc{QQField, AbsSimpleNumField}) = compl
 
 Hecke.restrict(::Hecke.NumFieldEmb, ::Map{QQField, AbsSimpleNumField}) = complex_embeddings(QQ)[1]
 
-"""
-    hom(G::FinGenAbGroup, H::FinGenAbGroup, V::Vector{<:Map{FinGenAbGroup, FinGenAbGroup}})
-
-For groups `G = prod G_i` and `H = prod H_i` as well as maps `V_i: G_i -> H_i`,
-build the induced map from `G -> H`.
-"""
-function Oscar.hom(G::FinGenAbGroup, H::FinGenAbGroup, V::Vector{<:Map{FinGenAbGroup, FinGenAbGroup}})
-  dG = get_attribute(G, :direct_product)
-  dH = get_attribute(H, :direct_product)
-
-  if dG === nothing || dH === nothing
-    error("both groups need to be direct products")
-  end
-  @assert length(V) == length(dG) == length(dH)
-
-  @assert all(i -> domain(V[i]) == dG[i] && codomain(V[i]) == dH[i], 1:length(V))
-  h = hom(G, H, cat([matrix(V[i]) for i=1:length(V)]..., dims=(1,2)), check = !true)
-  return h
-
-end
-
 #XXX: have a type for an implicit field - in Hecke?
 #     add all(?) the other functions to it
 function relative_field(m::Map{<:AbstractAlgebra.Field, <:AbstractAlgebra.Field})

experimental/LieAlgebras/src/LieAlgebras.jl

@@ -45,8 +45,9 @@ import ..Oscar:
   gen,
   gens,
   height,
-  hom_tensor,
   hom,
+  hom_direct_sum,
+  hom_tensor,
   ideal,
   identity_map,
   image,
@@ -131,7 +132,6 @@ export exterior_power
 export fundamental_weight
 export fundamental_weights
 export general_linear_lie_algebra
-export hom_direct_sum
 export induced_map_on_symmetric_power
 export induced_map_on_tensor_power
 export is_cartan_matrix
@@ -260,7 +260,6 @@ export exterior_power
 export fundamental_weight
 export fundamental_weights
 export general_linear_lie_algebra
-export hom_direct_sum
 export induced_map_on_symmetric_power
 export induced_map_on_tensor_power
 export is_cartan_matrix