refactor: computations of primitive embeddings and extensions of ZZLat

Project.toml

@@ -39,7 +39,7 @@ CodecZlib = "0.7.8"
 Compat = "4.13.0"
 Distributed = "1.6"
 GAP = "0.16.3"
-Hecke = "0.39.14"
+Hecke = "0.39.15"
 JSON = "1.0.1"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"

src/Groups/abelian_aut.jl

@@ -355,29 +355,33 @@ julia> order(OT)
 ```
 """
 @attr AutomorphismGroup{TorQuadModule} function orthogonal_group(T::TorQuadModule)
+  return _orthogonal_group(T, _orthogonal_group_gens(T); check=false)
+end
+
+function _orthogonal_group_gens(T::TorQuadModule)
   if is_trivial(abelian_group(T))
-    return _orthogonal_group(T, ZZMatrix[identity_matrix(ZZ, ngens(T))], check = false)
+    return ZZMatrix[identity_matrix(ZZ, ngens(T))]
   elseif is_semi_regular(T)
     # if T is semi-regular, it is isometric to its normal form for which
     # we know how to compute the isometries.
     N, i = normal_form(T)
     j = inv(i)
     gensON_mat = unique(_compute_gens(N))
     gensON = TorQuadModuleMap[hom(N, N, g) for g in gensON_mat]
-    gensOT = TorQuadModuleMap[i * g * j for g in gensON]
-    length(gensOT) > 1 ? filter!(!isone∘matrix, gensOT) : nothing
-    return _orthogonal_group(T, gensOT; check=false)
+    gensOT_mat = ZZMatrix[matrix(i * g * j) for g in gensON]
+    length(gensOT_mat) > 1 ? filter!(!isone, gensOT_mat) : nothing
+    return gensOT_mat
   elseif iszero(gram_matrix_quadratic(T))
     # in that case, we don't have any conditions regarding the
     # quadratic form, so we have all automorphisms coming
     # from the underlying abelian group
-    return _orthogonal_group(T, hom.(gens(automorphism_group(abelian_group(T)))); check=false)
+    return matrix.(gens(automorphism_group(abelian_group(T))))
   else
     # if T is not semi-regular, we distinghuish the cases whether or not
     # it splits its radical quadratic
     i = radical_quadratic(T)[2]
     gensOT_mat = has_complement(i)[1] ? _compute_gens_split_degenerate(T) : _compute_gens_non_split_degenerate(T)
-    return _orthogonal_group(T, gensOT_mat; check=false)
+    return gensOT_mat
   end
 end
 

src/NumberTheory/QuadFormAndIsom.jl

@@ -11,4 +11,5 @@ include("QuadFormAndIsom/finite_group_actions.jl")
 include("QuadFormAndIsom/hermitian_miranda_morrison.jl")
 include("QuadFormAndIsom/enumeration.jl")
 include("QuadFormAndIsom/embeddings.jl")
+include("QuadFormAndIsom/gluing_factory.jl")
 include("QuadFormAndIsom/printings.jl")