Try to sort out the homs (#1488)

* Try to sort out the homs

* Add deprecations

* chore: Bump version and AA compat

Project.toml

@@ -1,6 +1,6 @@
 name = "Hecke"
 uuid = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
-version = "0.31.2"
+version = "0.31.3"
 
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
@@ -28,7 +28,7 @@ GAPExt = "GAP"
 PolymakeExt = "Polymake"
 
 [compat]
-AbstractAlgebra = "^0.41.0"
+AbstractAlgebra = "^0.41.3"
 Dates = "1.6"
 Distributed = "1.6"
 GAP = "0.9.6, 0.10, 0.11"

src/Deprecations.jl

@@ -266,3 +266,6 @@ end
 @deprecate reduce_full(A::SMat{T}, g::SRow{T}, trafo::Type{Val{N}}) where {N, T} reduce_full(A, g, Val(N))
 @deprecate gens(A::GroupAlgebra, return_full_basis::Type{Val{T}}) where T gens(A, Val(T))
 @deprecate gens(A::AbstractAssociativeAlgebra, return_full_basis::Type{Val{T}}; thorough_search::Bool = false) where T gens(A, Val(T); thorough_search)
+
+@deprecate hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup, FinGenAbGroup}}) hom_direct_sum(G, H, A)
+@deprecate hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}}) hom_tensor(G, H, A)

src/GrpAb/GrpAbFinGen.jl

@@ -840,13 +840,13 @@ function matrix(M::Generic.IdentityMap{FinGenAbGroup})
 end
 
 @doc raw"""
-    hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup, FinGenAbGroup}}) -> Map
+    hom_direct_sum(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup, FinGenAbGroup}}) -> Map
 
 Given groups $G$ and $H$ that are created as direct products as well
 as a matrix $A$ containing maps $A[i,j] : G_i \to H_j$, return
 the induced homomorphism.
 """
-function hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup, FinGenAbGroup}})
+function hom_direct_sum(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup, FinGenAbGroup}})
   r, c = size(A)
   if c == 1
     dG = [G]
@@ -866,6 +866,26 @@ function hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Matrix{ <: Map{FinGenAbGroup
   return h
 end
 
+"""
+    hom_direct_sum(G::FinGenAbGroup, H::FinGenAbGroup, V::Vector{<:Map{FinGenAbGroup, FinGenAbGroup}})
+
+For groups `G = prod G_i` and `H = prod H_i` as well as maps `V_i: G_i -> H_i`,
+build the induced map from `G -> H`.
+"""
+function hom_direct_sum(G::FinGenAbGroup, H::FinGenAbGroup, V::Vector{<:Map{FinGenAbGroup, FinGenAbGroup}})
+  dG = get_attribute(G, :direct_product)
+  dH = get_attribute(H, :direct_product)
+
+  if dG === nothing || dH === nothing
+    error("both groups need to be direct products")
+  end
+  @assert length(V) == length(dG) == length(dH)
+
+  @assert all(i -> domain(V[i]) == dG[i] && codomain(V[i]) == dH[i], 1:length(V))
+  h = hom(G, H, cat([matrix(V[i]) for i=1:length(V)]..., dims=(1,2)), check = !true)
+  return h
+end
+
 function _flat(G::FinGenAbGroup)
   s = get_attribute(G, :direct_product)
   if s === nothing
@@ -981,13 +1001,13 @@ end
 ⊗(G::FinGenAbGroup...) = tensor_product(G..., task = :none)
 
 @doc raw"""
-    hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}}) -> Map
+    hom_tensor(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}}) -> Map
 
 Given groups $G = G_1 \otimes \cdots \otimes G_n$ and
 $H = H_1 \otimes \cdot \otimes H_n$ as well as maps
 $\phi_i: G_i\to H_i$, compute the tensor product of the maps.
 """
-function hom(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}})
+function hom_tensor(G::FinGenAbGroup, H::FinGenAbGroup, A::Vector{ <: Map{FinGenAbGroup, FinGenAbGroup}})
   tG = get_attribute(G, :tensor_product)
   tG === nothing && error("both groups must be tensor products")
   tH = get_attribute(H, :tensor_product)

src/exports.jl

@@ -400,6 +400,8 @@ export hnf
 export hnf!
 export hnf_extend!
 export hom
+export hom_direct_sum
+export hom_tensor
 export homogeneous_equation
 export howell_form
 export hyperbolic_plane_lattice

test/GrpAb/GrpAbFinGen.jl

@@ -348,8 +348,8 @@
     T, p = tensor_product(G, G)
     D = direct_product(G, G, task = :none)
     for i=1:5
-      Th = hom(T, T, map(mH, [rand(H) for x = 1:2])) #induced map in tensor product
-      Dh = hom(D, D, map(mH, rand(H, (2,2)))) #induced map on direct prod
+      Th = hom_tensor(T, T, map(mH, [rand(H) for x = 1:2])) #induced map in tensor product
+      Dh = hom_direct_sum(D, D, map(mH, rand(H, (2,2)))) #induced map on direct prod
     end
     #=