Some more improvements for OFPModules

src/Modules/ModuleTypes.jl

@@ -584,7 +584,6 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism
     @assert length(a) == ngens(F)
     r = new{typeof(F), typeof(G), Nothing}()
     a=Vector{elem_type(G)}(a)
-    image_module = sub_object(G, a)
     function im_func(x::AbstractFreeModElem)
      # The lines below were an attempt to speed up mapping. 
      # However, it turns out that checking the equality is more 
@@ -610,7 +609,7 @@ When computed, the corresponding matrix (via `matrix()`) and inverse isomorphism
       @assert parent(x) === G
       r.generators_map_to_generators === true && return FreeModElem(coordinates(simplify!(x)), F)
       #c = coordinates(repres(simplify!(x)), image_module)
-      c = coordinates(repres(x), image_module)
+      c = coordinates(repres(x), image_module(r))
       return FreeModElem(c, F)
     end
     r.header = MapHeader{typeof(F), typeof(G)}(F, G, im_func, pr_func)

src/Modules/UngradedModules/FreeMod.jl

@@ -11,7 +11,10 @@ not provide names for the generators, the standard names e_i are used for
 the standard unit vectors.
 """
 function FreeMod(R::AdmissibleOFPModuleRing, n::Int, name::VarName = :e; cached::Bool = false) # TODO cached?
-  return FreeMod{elem_type(R)}(n, R, [Symbol("$name[$i]") for i=1:n])
+   function symb_fun()
+    return [Symbol("$name[$i]") for i=1:n]
+  end
+  return FreeMod{elem_type(R)}(n, R, symb_fun) 
 end
 
 function FreeMod(R::AdmissibleOFPModuleRing, names::Vector{String}; cached::Bool=false)

src/Modules/UngradedModules/FreeModuleHom.jl

@@ -651,3 +651,8 @@ function lift(f::FreeModuleHom, g::FreeModuleHom)
   h = hom(domain(f), domain(g), lifted_imgs)
   return h
 end
+
+@attr SubquoModule{T} function image_module(phi::FreeModuleHom{FreeMod{T}, <:OFPModule{T}, Nothing}) where {T}
+  return sub_object(codomain(phi), images_of_generators(phi))
+end
+

src/Modules/UngradedModules/Hom_and_ext.jl

@@ -4,7 +4,7 @@
 Return true iff `f` is the zero map.
 """
 function iszero(f::OFPModuleHom)
-  return all(iszero, map(f, gens(domain(f))))
+  return all(iszero, images_of_generators(f))
 end
 
 @doc raw"""

src/Modules/UngradedModules/SubQuoHom.jl

@@ -757,6 +757,7 @@ Return the kernel of `a` as an object of type `SubquoModule`.
 Additionally, if `K` denotes this object, return the inclusion map `K` $\to$ `domain(a)`.
 """
 function kernel(h::SubQuoHom)
+  is_zero(codomain(h)) && return domain(h), identity_map(domain(h))
   D = domain(h)
   R = base_ring(D)
   is_graded(h) ? F = graded_free_module(R, degrees_of_generators(D)) : F = FreeMod(R, ngens(D))
@@ -917,7 +918,16 @@ Return the composition `b` $\circ$ `a`.
 """
 function *(h::OFPModuleHom{T1, T2, Nothing}, g::OFPModuleHom{T2, T3, Nothing}) where {T1, T2, T3}
   @assert codomain(h) === domain(g)
-  return hom(domain(h), codomain(g), Vector{elem_type(codomain(g))}([g(h(x)) for x = gens(domain(h))]), check=false)
+  R = base_ring(domain(h))
+  img_gens_coords = sparse_row_type(R)[sparse_row(R) for _ in 1:ngens(domain(h))]
+  img_gens_g = images_of_generators(g)
+  for (k, v) in enumerate(images_of_generators(h))
+    for (i, c) in coordinates(v)
+      Hecke.add_scaled_row!(coordinates(img_gens_g[i]), img_gens_coords[k], c)
+    end
+  end
+  cod = codomain(g)
+  return hom(domain(h), cod, elem_type(cod)[cod(v) for v in img_gens_coords]; check=false)
 end
 
 function *(h::OFPModuleHom{T1, T2, <:Map}, g::OFPModuleHom{T2, T3, <:Map}) where {T1, T2, T3}