proof of comcept: use map in restriction

experimental/GModule/src/GModule.jl

@@ -8,7 +8,6 @@ include("Misc.jl")
 
 module GModuleFromGap
 using Oscar
-using Hecke
 import Hecke: data
 
 #XXX: clash of names!
@@ -44,7 +43,7 @@ julia> C = gmodule(CyclotomicField, C);
 julia> h = subfields(base_ring(C), degree = 2)[1][2];
 
 julia> restriction_of_scalars(C, h)
-G-module for G acting on vector space of dimension 4 over number field
+(G-module for G acting on vector space of dimension 4 over number field, Map: C -> g-module for G acting on vector space of dimension 4 over number field)
 
 julia> restriction_of_scalars(C, QQ)
 G-module for G acting on vector space of dimension 8 over QQ
@@ -57,9 +56,15 @@ function restriction_of_scalars(M::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.F
   @assert codomain(phi) == base_ring(M)
   d = divexact(degree(codomain(phi)), degree(domain(phi)))
   F = free_module(domain(phi), dim(M)*d)
-  _, _, rep = relative_field(phi)
+  _, coord, rep = relative_field(phi)
 
-  return GModule(F, group(M), [hom(F, F, hvcat(dim(M), [rep(x) for x in transpose(matrix(y))]...)) for y in M.ac])
+  D = GModule(F, group(M), [hom(F, F, hvcat(dim(M), [rep(x) for x in transpose(matrix(y))]...)) for y in M.ac])
+  #the blow-up function is not a "nice" module hom as tis is used
+  #to make from a K-Module to e.g. a QQ-module, so the map
+  #will be QQ-linear and we'd need to get QQ-gens from a K-module
+  #also: pre-image is not working (not implemented) (needs more info from
+  #relative_field)
+  return D, hom(M, D, MapFromFunc(M.M, D.M, x->D.M(vcat([coord(t) for t = x.v[1,:]]...))); check = false)
 end
 
 function restriction_of_scalars(C::GModule{<:Any, <:AbstractAlgebra.FPModule{AbsSimpleNumFieldElem}}, ::QQField)
@@ -314,7 +319,7 @@ function maximal_submodule_bases(M::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.
   return res
 end
 
-function maximal_submodules(M::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{<:FinFieldElem}})
+function Oscar.maximal_submodules(M::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{<:FinFieldElem}})
   return [sub(M, s) for s = maximal_submodule_bases(M)]
 end
 
@@ -928,7 +933,8 @@ function Oscar.sub(C::GModule{<:Any, <:AbstractAlgebra.FPModule{T}}, m::MatElem{
 
   y = GAP.Globals.MTX.InducedActionSubmoduleNB(g, x)
   F = free_module(k, nrows(b))
-  return gmodule(F, Group(C), [hom(F, F, matrix([preimage(h, x[i, j]) for i in 1:GAPWrap.NrRows(x), j in 1:GAPWrap.NrCols(x)])) for x = y.generators]), hom(F, C.M, b)
+  D = gmodule(F, Group(C), [hom(F, F, matrix([preimage(h, x[i, j]) for i in 1:GAPWrap.NrRows(x), j in 1:GAPWrap.NrCols(x)])) for x = y.generators])
+  return D, hom(C, D, b)
   return b
 end
 
@@ -938,7 +944,8 @@ function Oscar.sub(M::GModule{<:Any, <:AbstractAlgebra.FPModule{T}}, f::Abstract
   @assert codomain(f) == M.M
   S = domain(f)
   Sac = [hom(S, S, [preimage(f, h(f(x))) for x in gens(S)]) for h in M.ac]
-  return gmodule(S, M.G, Sac)
+  D = gmodule(S, M.G, Sac)
+  return D, hom(D, M, f)
 end
 
 function gmodule(k::Nemo.FinField, C::GModule{<:Any, <:AbstractAlgebra.FPModule{<:FinFieldElem}})

experimental/GModule/src/Misc.jl

@@ -245,6 +245,9 @@ Hecke.restrict(::Hecke.NumFieldEmb, ::Map{QQField, AbsSimpleNumField}) = complex
 function relative_field(m::Map{<:AbstractAlgebra.Field, <:AbstractAlgebra.Field})
   k = domain(m)
   K = codomain(m)
+  if k == base_field(K)
+    return defining_polynomial(K), Hecke.coordinates, representation_matrix
+  end
   @assert base_field(k) == base_field(K)
   kt, t = polynomial_ring(k, cached = false)
   f = defining_polynomial(K)

experimental/GModule/src/Types.jl

@@ -17,7 +17,8 @@ mutable struct GModuleHom{ G, T1, T2} <: Map{GModule{G, T1}, GModule{G, T2}, Osc
     @req domain(mp) === M1.M && codomain(mp) === M2.M "map need to map 1st module into 2nd"
     #not every hom is a G-Hom...that is what check is supposed to do - eventually
     #see 2.
-    if check
+    if check #only works if mp is a morphism so that "*" and "==" are doing
+      #s.th. useful
       @assert all(g->action(M1, g)*mp == mp*action(M2, g), gens(M1.G))
     end
 
@@ -33,8 +34,8 @@ function hom(M1::GModule{T}, M2::GModule{T}, mp::MatElem; check::Bool = true) wh
   return GModuleHom(M1, M2, hom(M1.M, M2.M, mp); check) 
 end
 
-domain(M::GModuleHom) = M.Gm1
-codomain(M::GModuleHom) = M.Gm2
+domain(M::GModuleHom) = M.GM1
+codomain(M::GModuleHom) = M.GM2
 parent(M::GModuleHom) = Hecke.MapParent(domain(M), codomain(M), "homomorphisms")
 
 mutable struct GModuleElem{T}
@@ -79,7 +80,7 @@ end
 
 function (A::GModuleHom)(a::GModuleElem)
   @req parent(a) === domain(A) "element has wrong parent"
-  return GModuleElem(codomain(A), A.module_map(a))
+  return GModuleElem(codomain(A), A.module_map(a.data))
 end
 
 function kernel(A::GModuleHom)