Katrin (#1315)

* cornercase: lattice did not handle identical input

triggered by some weird GrpAb stuff of Katrin:
  f:G -> H
then doing
  preimage(f, H)
(why I do not remember), but then no common over structure for H and H
was found

* check parent of group elem in ray_class_group_map

Also from Katrin: she got intersting results due to using elements
in the wrong abelian group: she had a non-trivial group with 10
generators the first 5 being trivial, the RCG had only 5.
disc_exp on her non-trivial elements always resulted in trivial ideals
due to the wrong parent. The code would only use the first 5
coefficients of the group elements...

src/GrpAb/Lattice.jl

@@ -517,6 +517,10 @@ end
 # "overgroup" M. If so, the second return value is M and the third and fourth
 # return values describe the map from G to M and H to M respectively.
 function can_map_into_overstructure(L::RelLattice{T, D}, G::T, H::T) where {T, D}
+  if G === H
+    return true, G, L.make_id(G)::D, L.make_id(G)::D
+  end
+
   if !(G in keys(L.weak_vertices) && H in keys(L.weak_vertices))
     return false, G, L.zero, L.zero
   end

src/NumFieldOrd/NfOrd/RayClassGrp.jl

@@ -197,6 +197,7 @@ function class_as_ray_class(C::GrpAbFinGen, mC::MapClassGrp, exp_class::Function
     local expo_map
     let mQ = mQ, exp_class = exp_class
       function expo_map(el::GrpAbFinGenElem)
+        @assert parent(el) === codomain(mQ)
         return exp_class(mQ\el)
       end
     end
@@ -237,8 +238,9 @@ function empty_ray_class(m::NfOrdIdl)
   X = abelian_group(Int[])
 
   local exp
-  let O = O
+  let O = O, X = X
     function exp(a::GrpAbFinGenElem)
+      @assert parent(a) === X
       return FacElem(Dict(ideal(O,1) => ZZRingElem(1)))
     end
   end
@@ -478,8 +480,9 @@ function n_part_class_group(mC::Hecke.MapClassGrp, n::Integer)
   if is_coprime(exponent(C), n)
     G = abelian_group(ZZRingElem[])
     local exp1
-    let O = O
+    let O = O, G = G
       function exp1(a::GrpAbFinGenElem)
+        @assert parent(a) === G
         return ideal(O, one(O))
       end
     end
@@ -507,6 +510,7 @@ function n_part_class_group(mC::Hecke.MapClassGrp, n::Integer)
   local exp2
   let O = O, G = G
     function exp2(a::GrpAbFinGenElem)
+      @assert parent(a) === G
       new_coeff = zero_matrix(FlintZZ, 1, ngens(C))
       for i = 1:ngens(G)
         new_coeff[1, i+ind-1] = a[i]*diff
@@ -909,6 +913,7 @@ function ray_class_group(m::NfOrdIdl, inf_plc::Vector{<:InfPlc} = Vector{InfPlc{
   local expo
   let C = C, O = O, groups_and_maps = groups_and_maps, exp_class = exp_class, eH = eH, H = H, K = K, Dgens = Dgens, X = X, p = p
     function expo(a::GrpAbFinGenElem)
+      @assert parent(a) === X
       b = GrpAbFinGenElem(C, sub(a.coeff, 1:1, 1:ngens(C)))
       res = exp_class(b)
       for i = 1:nG
@@ -978,6 +983,7 @@ function ray_class_groupQQ(O::NfOrd, modulus::Int, inf_plc::Bool, n_quo::Int)
     end
 
     function expon1(a::GrpAbFinGenElem)
+      @assert parent(a) === domain(mU)
       x=mU(a)
       return FacElem(Dict{NfOrdIdl, ZZRingElem}(ideal(O,lift(x)) => 1))
     end
@@ -997,6 +1003,7 @@ function ray_class_groupQQ(O::NfOrd, modulus::Int, inf_plc::Bool, n_quo::Int)
     end
 
     function expon2(a::GrpAbFinGenElem)
+      @assert parent(a) === domain(mU)
       x=mU(a)
       return FacElem(Dict{NfOrdIdl, ZZRingElem}(ideal(O,lift(x)) => 1))
     end
@@ -1016,6 +1023,7 @@ function ray_class_groupQQ(O::NfOrd, modulus::Int, inf_plc::Bool, n_quo::Int)
     end
 
     function expon(a::GrpAbFinGenElem)
+      @assert parent(a) === codomain(mQ)
       x=mU(mQ\a)
       return FacElem(Dict{NfOrdIdl, ZZRingElem}(ideal(O,x) => 1))
     end

test/GrpAb/Lattice.jl

@@ -138,5 +138,9 @@
     Q2, mQ2 = quo(G, [G[1]], true, L)
     b, GG, MHHH, MHH = @inferred Hecke.can_map_into_overstructure(L, Q, Q2)
     @test !b
+
+    b, GG, _, _ = @inferred Hecke.can_map_into_overstructure(L, Q, Q)
+    @test b
+    @test GG === Q
   end
 end