Mjrodgers ow g modules

experimental/GModule/src/GModule.jl

@@ -1,13 +1,13 @@
 isdefined(Oscar, :word) || function word end
 
 include("Cohomology.jl")
+include("Types.jl")
 include("GaloisCohomology.jl")
 include("GrpExt.jl")
 include("Misc.jl")
 
 module GModuleFromGap
 using Oscar
-using Hecke
 import Hecke: data
 
 #XXX: clash of names!
@@ -43,7 +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
@@ -56,9 +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)
@@ -313,7 +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
 
@@ -496,7 +502,7 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
        k char field
        |
        Q
-     
+
     So: V is given as G -> GL(n, K)
     This is represented by
       sigma: Gal(K/k)^2 -> K a 2-chain
@@ -520,7 +526,7 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
       split by A in GL(n, K)
       Now, technically, A V A^-1 has values in Gl(n, E)
     Step 7:
-      Replacing V -> A V A^-1 changes 
+      Replacing V -> A V A^-1 changes
                 X_g -> A^g X A^-1
       As A V A^-1 is in GL(n, E), A^g X A^-1 can be normlized (mult. by
       scalar in K) to be in Gl(n, E)
@@ -543,7 +549,7 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
     d = reduce(lcm, [x[2] for x = ld], init = 1)
 
     s = subfields(base_ring(V))
-    
+
     s = [x for x in s if degree(x[1]) >= d*degree(k)]
     sort!(s, lt = (a,b) -> degree(a[1]) < degree(b[1]))
     for (m, mm) in s
@@ -600,7 +606,7 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
       #we need Gal(E/k) as the quotient of A/U
       q, mq = quo(domain(mA), U)
       X = Dict( g => map_entries(mA(preimage(mq, g)), AA) * X[preimage(mq, g)] * AAi for g = q)
-      for (g, x) = X  
+      for (g, x) = X
         lf = findfirst(!iszero, x)
         x *= inv(x[lf])
         X[g] = map_entries(pseudo_inv(mm), x)
@@ -636,7 +642,7 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
       LD = Dict{AbsSimpleNumFieldOrderIdeal, Int}()
       LI = Dict{AbsSimpleNumFieldEmbedding, Int}()
       for (p, d) = ld
-        if p == -1 
+        if p == -1
           @assert d == 2
           if signature(k)[2] == 0
             for e = real_embeddings(k)
@@ -659,21 +665,21 @@ function _minimize(V::GModule{<:Oscar.GAPGroup, <:AbstractAlgebra.FPModule{AbsSi
       C, mC = automorphism_group(PermGroup, EF)
       gE = mE_EF(E[1])
       hBC = hom(C, B, [[b for b = B if mC(c)(gE) == mE_EF(mB(b)(E[1]))][1] for c = gens(C)])
-      gF = mF_EF(F[1])    
-      U, mU = sub(C, [c for c = C if mC(c)(gF) == gF])    
+      gF = mF_EF(F[1])
+      U, mU = sub(C, [c for c = C if mC(c)(gF) == gF])
       MEF = MultGrp(EF)
       #inflate
       s = Dict{NTuple{2, elem_type(U)}, elem_type(MEF)}((f, g) => MEF(mE_EF(s[(hBC(f), hBC(g))])) for f = U for g = U)
 
-          
+
       D = gmodule(U, [hom(MEF, MEF, mC(mU(x))) for x = gens(U)])
       Sigma = CoChain{2,PermGroupElem, MultGrpElem{AbsSimpleNumFieldElem}}(D, s)
 
       fl, mu = Oscar.GaloisCohomology_Mod.is_coboundary(Sigma)
       @assert fl
       #inflate X
       X = Dict( g => map_entries(mE_EF, X[preimage(h, hBC(mU(g)))]) *mu(g).data for g = U)
-      @hassert :MinField 1 isone_cochain(X, mU*mC)  
+      @hassert :MinField 1 isone_cochain(X, mU*mC)
       @vtime :MinField 2 BB, BBi = hilbert90_generic(X, mU*mC)
       c = content_ideal(BB)
       sd = Hecke.short_elem(inv(c))
@@ -697,7 +703,8 @@ end
 function irreducible_modules(::QQField, G::Oscar.GAPGroup)
   #if cyclo is not minimal, this is not irreducible
   z = irreducible_modules(CyclotomicField, G)
-  return [gmodule(QQ, descent_to_minimal_degree_field(m)) for m in z]
+  temp = map(x -> galois_orbit_sum(character(x)), z)
+  return [gmodule(QQ, descent_to_minimal_degree_field(z[i])) for i in unique(i -> temp[i], 1:length(temp))]
 end
 
 function irreducible_modules(::ZZRing, G::Oscar.GAPGroup)
@@ -926,7 +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
 
@@ -936,7 +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}})
@@ -1324,14 +1333,14 @@ function Oscar.is_coboundary(c::CoChain{1,PermGroupElem,MultGrpElem{AbsSimpleNum
   cnt = 0
   while true
     local Y
-    while true 
+    while true
       Y = rand(K, -5:5)
       iszero(Y) || break
     end
     cnt += 1
     S = sum(mA(emb(g))(Y)*c((g,)).data for g = G)
       is_zero(S) || return true, mK(S)
-    if cnt > 10 
+    if cnt > 10
       error("should not happen")
     end
   end

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

@@ -0,0 +1,93 @@
+mutable struct GModuleHom{ G, T1, T2} <: Map{GModule{G, T1}, GModule{G, T2}, OscarMap, GModuleHom}
+
+  GM1::GModule{G, T1}
+  GM2::GModule{G, T2}
+  module_map::Map{T1, T2}
+
+  function GModuleHom(
+    M1::GModule,
+    M2::GModule,
+    mp::Map;
+    check::Bool = false
+    ) 
+    # Need to require that
+    #   1. Both GModules have the same group
+    #   2. The group action is respected
+    @req M1.G === M2.G "groups need to be identical"
+    @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 #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
+
+    return new{typeof(M1.G), typeof(M1.M), typeof(M2.M)}(M1, M2, mp)
+  end
+end
+
+function hom(M1::GModule{T}, M2::GModule{T}, mp::Map; check::Bool = true) where T <: AbstractAlgebra.Group
+  return GModuleHom(M1, M2, mp; check) 
+end
+
+function hom(M1::GModule{T}, M2::GModule{T}, mp::MatElem; check::Bool = true) where T <: AbstractAlgebra.Group
+  return GModuleHom(M1, M2, hom(M1.M, M2.M, mp); check) 
+end
+
+domain(M::GModuleHom) = M.GM1
+codomain(M::GModuleHom) = M.GM2
+parent(M::GModuleHom) = Hecke.MapParent(domain(M), codomain(M), "homomorphisms")
+
+mutable struct GModuleElem{T}
+  parent::GModule
+  data::T
+end
+
+parent(a::GModuleElem) = a.parent
+
+function (C::GModule)(a::Union{ModuleElem, FinGenAbGroupElem})
+  @req parent(a) === C.M "wrong parent for $a"
+  return GModuleElem(C, a)
+end
+
+function ==(a::GModuleElem, b::GModuleElem)
+  @req parent(a) === parent(b) "parents differ"
+  return a.data == b.data
+end
+
+function hash(a::GModuleElem, u::UInt)
+  return hash(a.data, u)
+end
+
+function +(a::GModuleElem, b::GModuleElem)
+  @req parent(a) === parent(b) "parents differ"
+  return GModuleElem(parent(a), a.data + b.data)
+end
+
+function -(a::GModuleElem, b::GModuleElem)
+  @req parent(a) === parent(b) "parents differ"
+  return GModuleElem(parent(a), a.data - b.data)
+end
+
+function -(a::GModuleElem)
+  return GModuleElem(parent(a), -a.data)
+end
+
+function *(a::GModuleElem, g::GroupElem)
+  @req parent(a).G === parent(g) "group element has wrong parent"
+  return GModuleElem(parent(a), action(parent(a), g, a.data))
+end
+
+function (A::GModuleHom)(a::GModuleElem)
+  @req parent(a) === domain(A) "element has wrong parent"
+  return GModuleElem(codomain(A), A.module_map(a.data))
+end
+
+function kernel(A::GModuleHom)
+  return sub(A, kernel(A.module_map)[2])
+end
+
+function image(A::GModuleHom)
+  return sub(A, image(A.module_map)[2])
+end
+