Cf work in progress (oscar-system#2682)

* fix some issues with the idel stuff * add simplify option to solve * improve Complex and Symbolic version * slightly more correct reduction code * make simplify also work in QQ * add all_extensions and friends * re-write orbit * typo * replace FreeModule -> FPModule to allow more cases some work... * typo: default argument written badly * deal with GrpAbFinGen vs FreeModule better * allow more general FPModules * try to support FunField in solve... rel ext is missing * support fixex_field(, PermGroup) fur FunField here the precision is a tuple of ints: padic prec and power series prec... * aatempt to imporove the Qt case... not yet complete, rel ext are missing * natural_character (brauer_character) * add sub-G-module and make hom_base more useful * "ray-residue-ring": units of O/I in one step * towards solve / Q(t) * trensor product, natural_module and minor * add tests for Brueckner * trivia and tests * fix examples * first working version of H^3 * add generic differntial - no use yet * actually define q... * Add comment for test * minimal changes to get it to work (again, partly) * make Martin happy: monomials_of_degree * add/ fix extension_field * revert the bad commits * Update experimental/GModule/Cohomology.jl Co-authored-by: Max Horn <[email protected]> * Update Cohomology.jl * Update Cohomology.jl --------- Co-authored-by: Tommy Hofmann <[email protected]> Co-authored-by: Max Horn <[email protected]>
JohnAAbbott · Aug 16, 2023 · 8c97283 · 8c97283
1 parent 4690df2
commit 8c97283
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diff --git a/experimental/GModule/Brueckner.jl b/experimental/GModule/Brueckner.jl
@@ -33,7 +33,7 @@ function reps(K, G::Oscar.GAPGroup)
   if order(G) == 1
     F = free_module(K, 1)
     h = hom(F, F, [F[1]])
-    return [gmodule(F, G, typeof(h)[])]
+    return [gmodule(F, G, typeof(h)[h for i = gens(G)])]
   end
 
   pcgs = GAP.Globals.Pcgs(G.X)
@@ -293,7 +293,7 @@ function Oscar.cokernel(h::Map)
   return quo(codomain(h), image(h)[1])
 end
 
-function Base.iterate(M::Union{Generic.FreeModule{T}, Generic.Submodule{T}}) where T <: FinFieldElem
+function Base.iterate(M::AbstractAlgebra.FPModule{T}) where T <: FinFieldElem
   k = base_ring(M)
   if dim(M) == 0
     return zero(M), iterate([1])
@@ -303,26 +303,32 @@ function Base.iterate(M::Union{Generic.FreeModule{T}, Generic.Submodule{T}}) whe
   return M(elem_type(k)[f[1][i] for i=1:dim(M)]), (f[2], p)
 end
 
-function Base.iterate(::Union{Generic.FreeModule{fqPolyRepFieldElem}, Generic.Submodule{fqPolyRepFieldElem}}, ::Tuple{Int64, Int64})
+function Base.iterate(::AbstractAlgebra.FPModule{fqPolyRepFieldElem}, ::Tuple{Int64, Int64})
   return nothing
 end
 
-function Base.iterate(M::Union{Generic.FreeModule{T}, Generic.Submodule{T}}, st::Tuple{<:Tuple, <:Base.Iterators.ProductIterator}) where T <: FinFieldElem
+function Base.iterate(M::AbstractAlgebra.FPModule{T}, st::Tuple{<:Tuple, <:Base.Iterators.ProductIterator}) where T <: FinFieldElem
   n = iterate(st[2], st[1])
   if n === nothing
     return n
   end
   return M(elem_type(base_ring(M))[n[1][i] for i=1:dim(M)]), (n[2], st[2])
 end
 
-function Base.length(M::Union{Generic.FreeModule{T}, Generic.Submodule{T}}) where T <: FinFieldElem
+function Base.length(M::AbstractAlgebra.FPModule{T}) where T <: FinFieldElem
   return Int(order(base_ring(M))^dim(M))
 end
 
-function Base.eltype(M::Union{Generic.FreeModule{T}, Generic.Submodule{T}}) where T <: FinFieldElem
+function Base.eltype(M::AbstractAlgebra.FPModule{T}) where T <: FinFieldElem
   return elem_type(M)
 end
 
+function Oscar.dim(M::AbstractAlgebra.Generic.DirectSumModule{<:FieldElem})
+  return sum(dim(x) for x = M.m)
+end
+
+Oscar.is_finite(M::AbstractAlgebra.FPModule{<:FinFieldElem}) = true
+
 """
   mp: G ->> Q
   C a F_p[Q]-module
@@ -389,27 +395,30 @@ function lift(C::GModule, mp::Map)
   #projection of G. They are not all surjective. However, lets try:
   k, mk = kernel(s)
   allG = []
-  z = get_attribute(C, :H_two)[1]
+  z = get_attribute(C, :H_two)[1]  #tail (H2) -> cochain
 
   seen = Set{Tuple{elem_type(D), elem_type(codomain(mH2))}}()
   #TODO: the projection maps seem to be rather slow - in particular
   #      as they SHOULD be trivial...
   for x = k
     epi = pDE[1](mk(x)) #the map
-    chn = pDE[2](mk(x)) #the tail data
-    if (epi,mH2(chn)) in seen
+    chn = mH2(pDE[2](mk(x))) #the tail data
+    if (epi,chn) in seen
       continue
     else
-      push!(seen, (epi, mH2(chn)))
+      push!(seen, (epi, chn))
     end
     #TODO: not all "chn" yield distinct groups - the factoring by the 
     #      co-boundaries is missing
     #      not all "epi" are epi, ie. surjective. The part of the thm
     #      is missing...
     # (Thm 15, part b & c) (and the weird lemma)
-    @hassert :BruecknerSQ 2 all(x->all(y->sc(x, y)(chn) == last_c(x, y), gens(N)), gens(N))
+#    @hassert :BruecknerSQ 2 all(x->all(y->sc(x, y)(chn) == last_c(x, y), gens(N)), gens(N))
+
+
     @hassert :BruecknerSQ 2 preimage(z, z(chn)) == chn
     GG, GGinj, GGpro, GMtoGG = Oscar.GrpCoh.extension(PcGroup, z(chn))
+    @assert is_surjective(GGpro)
     if get_assert_level(:BruecknerSQ) > 1
       _GG, _ = Oscar.GrpCoh.extension(z(chn))
       @assert is_isomorphic(GG, _GG)
@@ -432,13 +441,15 @@ function lift(C::GModule, mp::Map)
       return d
     end
     l= [GMtoGG(reduce(gen(G, i)), pro[i](epi)) for i=1:ngens(G)]
+#    @show map(order, l), order(prod(l))
+#    @show map(order, gens(G)), order(prod(gens(G)))
 
-    h = hom(G, GG, gens(G), [GMtoGG(reduce(gen(G, i)), pro[i](epi)) for i=1:ngens(G)])
+    h = hom(G, GG, gens(G), l)
     if !is_surjective(h)
-      @show :darn
+#      @show :darn
       continue
     else
-      @show :bingo
+#      @show :bingo
     end
     push!(allG, h)
   end