Make inj/proj of products groups consistent with other products objects

docs/src/Groups/products.md

@@ -17,8 +17,10 @@ number_of_factors(G::DirectProductGroup)
 cartesian_power(G::GAPGroup, n::Int)
 inner_cartesian_power(G::T, n::Int; morphisms=false) where T<: GAPGroup
 factor_of_direct_product(G::DirectProductGroup, j::Int)
-embedding(G::DirectProductGroup, j::Int)
-projection(G::DirectProductGroup, j::Int)
+canonical_injection(G::DirectProductGroup, j::Int)
+canonical_injections(G::DirectProductGroup)
+canonical_projection(G::DirectProductGroup, j::Int)
+canonical_projections(G::DirectProductGroup)
 write_as_full(G::DirectProductGroup)
 is_full_direct_product(G::DirectProductGroup)
 ```
@@ -32,8 +34,8 @@ normal_subgroup(G::SemidirectProductGroup)
 acting_subgroup(G::SemidirectProductGroup)
 homomorphism_of_semidirect_product(G::SemidirectProductGroup)
 is_full_semidirect_product(G::SemidirectProductGroup)
-embedding(G::SemidirectProductGroup, n::Int)
-projection(G::SemidirectProductGroup)
+canonical_injection(G::SemidirectProductGroup, n::Int)
+canonical_projection(G::SemidirectProductGroup)
 ```
 
 ## Wreath products
@@ -45,6 +47,7 @@ normal_subgroup(W::WreathProductGroup)
 acting_subgroup(W::WreathProductGroup)
 homomorphism_of_wreath_product(G::WreathProductGroup)
 is_full_wreath_product(G::WreathProductGroup)
-projection(W::WreathProductGroup)
-embedding(W::WreathProductGroup, n::Int)
+canonical_projection(W::WreathProductGroup)
+canonical_injection(W::WreathProductGroup, n::Int)
+canonical_injections(W::WreathProductGroup)
 ```

src/Groups/directproducts.jl

@@ -149,14 +149,15 @@ end
 Return the `j`-th factor of `G`.
 """
 function factor_of_direct_product(G::DirectProductGroup, j::Int)
-  @req j in 1:length(G.L) "index not valid"
+  @req j in 1:number_of_factors(G) "index not valid"
   return G.L[j]
 end
 
 """
-    embedding(G::DirectProductGroup, j::Int)
+    canonical_injection(G::DirectProductGroup, j::Int)
 
-Return the embedding of the `j`-th component of `G` into `G`, for `j` = 1,...,#factors of `G`.
+Return the injection of the `j`-th component of `G` into `G`, for `j` = 1,...,#factors of `G`.
+It is not defined for proper subgroups of direct products.
 
 # Examples
 ```jldoctest
@@ -166,51 +167,61 @@ Permutation group of degree 3 and order 6
 julia> K = symmetric_group(2)
 Permutation group of degree 2 and order 2
 
-julia> G = direct_product(H,K)
+julia> G = direct_product(H, K)
 Direct product of
  Permutation group of degree 3 and order 6
  Permutation group of degree 2 and order 2
 
-julia> emb1 = embedding(G,1)
+julia> inj1 = canonical_injection(G, 1)
 Group homomorphism
   from permutation group of degree 3 and order 6
   to direct product of
    Permutation group of degree 3 and order 6
    Permutation group of degree 2 and order 2
 
-julia> h = perm(H,[2,3,1])
+julia> h = perm(H, [2,3,1])
 (1,2,3)
 
-julia> emb1(h)
+julia> inj1(h)
 (1,2,3)
 
-julia> emb2 = embedding(G,2)
+julia> inj2 = canonical_injection(G, 2)
 Group homomorphism
   from permutation group of degree 2 and order 2
   to direct product of
    Permutation group of degree 3 and order 6
    Permutation group of degree 2 and order 2
 
-julia> k = perm(K,[2,1])
+julia> k = perm(K, [2,1])
 (1,2)
 
-julia> emb2(k)
+julia> inj2(k)
 (4,5)
 
-julia> emb1(h)*emb2(k)
+julia> inj1(h)*inj2(k)
 (1,2,3)(4,5)
 ```
 """
-function embedding(G::DirectProductGroup, j::Int)
-  @req j in 1:length(G.L) "index not valid"
-  @req G.isfull "Embedding is not defined for proper subgroups of direct products"
+function canonical_injection(G::DirectProductGroup, j::Int)
+  @req j in 1:number_of_factors(G) "index not valid"
+  @req G.isfull "Injection is not defined for proper subgroups of direct products"
   f = GAPWrap.Embedding(G.X, j)
   gr = G.L[j]
   return GAPGroupHomomorphism(gr, G, f)
 end
 
 """
-    projection(G::DirectProductGroup, j::Int)
+    canonical_injections(G::DirectProductGroup)
+
+Return the injection of the `j`-th component of `G` into `G`, for all `j` = 1,...,#factors of `G`.
+It is not defined for proper subgroups of direct products.
+"""
+function canonical_injections(G::DirectProductGroup)
+  return [canonical_injection(G, j) for j in 1:number_of_factors(G)]
+end
+
+"""
+    canonical_projection(G::DirectProductGroup, j::Int)
 
 Return the projection of `G` into the `j`-th component of `G`, for `j` = 1,...,#factors of `G`.
 
@@ -222,19 +233,19 @@ Permutation group of degree 3 and order 6
 julia> K = symmetric_group(2)
 Permutation group of degree 2 and order 2
 
-julia> G = direct_product(H,K)
+julia> G = direct_product(H, K)
 Direct product of
  Permutation group of degree 3 and order 6
  Permutation group of degree 2 and order 2
 
-julia> proj1 = projection(G,1)
+julia> proj1 = canonical_projection(G, 1)
 Group homomorphism
   from direct product of
    Permutation group of degree 3 and order 6
    Permutation group of degree 2 and order 2
   to permutation group of degree 3 and order 6
 
-julia> proj2 = projection(G,2)
+julia> proj2 = canonical_projection(G, 2)
 Group homomorphism
   from direct product of
    Permutation group of degree 3 and order 6
@@ -251,15 +262,26 @@ julia> proj2(g)
 (1,2)
 ```
 """
-function projection(G::DirectProductGroup, j::Int)
+function canonical_projection(G::DirectProductGroup, j::Int)
   @req j in 1:number_of_factors(G) "index not valid"
   f = GAPWrap.Projection(G.Xfull, j)
   p = GAPWrap.RestrictedMapping(f, G.X)
   return GAPGroupHomomorphism(G, factor_of_direct_product(G, j), p)
 end
 
+"""
+    canonical_projection(G::DirectProductGroup)
+
+Return the projection of `G` into the `j`-th component of `G`, for all `j` = 1,...,#factors of `G`.
+"""
+function canonical_projections(G::DirectProductGroup)
+  return [canonical_projection(G, j) for j in 1:number_of_factors(G)]
+end
+
+
+
 function (G::DirectProductGroup)(V::AbstractVector{<:GAPGroupElem})
-  @req length(V) == length(G.L) "Wrong number of entries"
+  @req length(V) == number_of_factors(G) "Wrong number of entries"
   arr = [GAPWrap.Image(GAPWrap.Embedding(G.Xfull, i), V[i].X) for i in 1:length(V)]
   xgap = prod(arr)
   @req xgap in G.X "Element not in the group"
@@ -301,7 +323,7 @@ function write_as_full(G::DirectProductGroup)
   if G.isfull
     return G
   else
-    LK = [image(projection(G, j))[1] for j in 1:length(G.L)]
+    LK = [image(canonical_projection(G, j))[1] for j in 1:number_of_factors(G)]
     H = direct_product(LK)
     # index(H,G)==1 does not work because it does not recognize G as a subgroup of H
     @req order(H) == order(G) "G is not a direct product of groups"
@@ -379,13 +401,13 @@ Return whether `G` is a semidirect product of two groups, instead of a proper su
 is_full_semidirect_product(G::SemidirectProductGroup) = G.isfull
 
 """
-    embedding(G::SemidirectProductGroup, n::Int)
+    canonical_injection(G::SemidirectProductGroup, n::Int)
 
-Return the embedding of the `n`-th component of `G` into `G`, for `n` = 1,2.
+Return the injection of the `n`-th component of `G` into `G`, for `n` = 1,2.
 It is not defined for proper subgroups of semidirect products.
 """
-function embedding(G::SemidirectProductGroup, n::Int)
-  @req G.isfull "Embedding not defined for proper subgroups of semidirect products"
+function canonical_injection(G::SemidirectProductGroup, n::Int)
+  @req G.isfull "Injection not defined for proper subgroups of semidirect products"
   if n == 1
     f = GAPWrap.Embedding(G.X, 2)
     gr = G.N
@@ -399,11 +421,11 @@ function embedding(G::SemidirectProductGroup, n::Int)
 end
 
 """
-    projection(G::SemidirectProductGroup)
+    canonical_projection(G::SemidirectProductGroup)
 
 Return the projection of `G` into the second component of `G`.
 """
-function projection(G::SemidirectProductGroup)
+function canonical_projection(G::SemidirectProductGroup)
   f = GAPWrap.Projection(G.Xfull)
   p = GAPWrap.RestrictedMapping(f, G.X)
   return GAPGroupHomomorphism(G, acting_subgroup(G), p)
@@ -571,23 +593,24 @@ Return whether `G` is a wreath product of two groups, instead of a proper subgro
 is_full_wreath_product(G::WreathProductGroup) = G.isfull
 
 """
-    projection(G::WreathProductGroup)
+    canonical_projection(G::WreathProductGroup)
 
 Return the projection of `wreath_product(G,H)` onto the permutation group `H`.
 """
-function projection(W::WreathProductGroup)
+function canonical_projection(W::WreathProductGroup)
   #  @req W.isfull "Projection not defined for proper subgroups of wreath products"
   f = GAPWrap.Projection(W.Xfull)
   p = GAPWrap.RestrictedMapping(f, W.X)
   return GAPGroupHomomorphism(W, acting_subgroup(W), p)
 end
 
 """
-    embedding(G::WreathProductGroup, n::Int)
+    canonical_injection(G::WreathProductGroup, n::Int)
 
-Return the embedding of the `n`-th component of `G` into `G`.
+Return the injection of the `n`-th component of `G` into `G`.
+It is not defined for proper subgroups of wreath products.
 """
-function embedding(W::WreathProductGroup, n::Int)
+function canonical_injection(W::WreathProductGroup, n::Int)
   @req W.isfull "Embedding not defined for proper subgroups of wreath products"
   @req n <= GAP.Globals.NrMovedPoints(GAPWrap.Image(W.a.map)) + 1 "n is too big"
   f = GAPWrap.Embedding(W.Xfull, n)
@@ -599,6 +622,16 @@ function embedding(W::WreathProductGroup, n::Int)
   return GAPGroupHomomorphism(C, W, f)
 end
 
+"""
+    canonical_injections(G::WreathProductGroup)
+
+Return the injection of the `n`-th component of `G` into `G` for all `n`.
+It is not defined for proper subgroups of wreath products.
+"""
+function canonical_injections(W::WreathProductGroup)
+  return [canonical_injection(W, n) for n in 1:GAP.Globals.NrMovedPoints(GAPWrap.Image(W.a.map)) + 1]
+end
+
 Base.show(io::IO, x::WreathProductGroup) = print(io, String(GAPWrap.StringViewObj(x.X)))
 
 #TODO : to be fixed

src/deprecations.jl

@@ -529,7 +529,7 @@ Base.@deprecate_binding has_is_isomorphic_with_alternating_group has_is_isomorph
 Base.@deprecate_binding set_is_isomorphic_with_alternating_group set_is_isomorphic_to_alternating_group
 
 Base.@deprecate_binding are_algebraically_independent is_algebraically_independent_with_relations
-          
+
 Base.@deprecate ambient_ring(U::AbsMultSet) ring(U)
 
 # Deprecated after 0.15
@@ -561,3 +561,10 @@ Base.@deprecate_binding ToricGlueingData ToricGluingData
 
 Base.@deprecate_binding jacobi_matrix jacobian_matrix
 Base.@deprecate_binding jacobi_ideal jacobian_ideal
+
+@deprecate embedding(G::DirectProductGroup, j::Int) canonical_injection(G, j)
+@deprecate projection(G::DirectProductGroup, j::Int) canonical_projection(G, j)
+@deprecate embedding(G::SemidirectProductGroup, n::Int) canonical_injection(G, n)
+@deprecate projection(G::SemidirectProductGroup) canonical_projection(G)
+@deprecate embedding(W::WreathProductGroup, n::Int) canonical_injection(W, n)
+@deprecate projection(W::WreathProductGroup) canonical_projection(W)

test/Groups/directproducts.jl

@@ -16,21 +16,21 @@
 
    G,emb,proj = direct_product(S,C; morphisms=true)
    @test G==direct_product(S,C)
-   @test emb[1]==embedding(G,1)
-   @test emb[2]==embedding(G,2)
-   @test proj[1]==projection(G,1)
-   @test proj[2]==projection(G,2)
+   @test emb[1]==canonical_injection(G,1)
+   @test emb[2]==canonical_injection(G,2)
+   @test proj[1]==canonical_projection(G,1)
+   @test proj[2]==canonical_projection(G,2)
 
    x = rand(G)
    @test x in G
-   @test projection(G,1)(x) in S
-   @test projection(G,2)(x) in C
-   @test embedding(G,1)(rand(S)) in G
-   @test embedding(G,2)(rand(C)) in G
-   @test x==G(projection(G,1)(x), projection(G,2)(x))
-   @test x==embedding(G,1)(projection(G,1)(x))*embedding(G,2)(projection(G,2)(x))
-   S1 = image(embedding(G,1))[1]
-   C1 = image(embedding(G,2))[1]
+   @test canonical_projection(G,1)(x) in S
+   @test canonical_projection(G,2)(x) in C
+   @test canonical_injection(G,1)(rand(S)) in G
+   @test canonical_injection(G,2)(rand(C)) in G
+   @test x==G(canonical_projection(G,1)(x), canonical_projection(G,2)(x))
+   @test x==canonical_injection(G,1)(canonical_projection(G,1)(x))*canonical_injection(G,2)(canonical_projection(G,2)(x))
+   S1 = image(canonical_injection(G,1))[1]
+   C1 = image(canonical_injection(G,2))[1]
    @test intersect(G,S1)[1]==S1
    @test is_isomorphic(S1,S)
    @test is_isomorphic(quo(G,S1)[1],C)
@@ -150,20 +150,20 @@ end
    @test is_subset(H, G)
    @test index(G,H)==4
    @test !is_full_semidirect_product(H)
-   @test projection(G)(x)==projection(H)(x)
+   @test canonical_projection(G)(x)==canonical_projection(H)(x)
    @test H==center(G)[1]
    y=G(Q[1],one(C))
    K = sub(G,gens(G))[1]
 #   @test is_full_semidirect_product(K)
    K = sub(G,[y])[1]
    @test K==sub(y)[1]
    @test K==sub(y)[1]
-   @test y == embedding(G,1)(Q[1])
-   @test_throws ArgumentError embedding(G,3)(Q[1])
-   @test codomain(projection(K))==C
-   @test order(image(projection(K))[1])==1
-   @test embedding(G,2)*projection(G)==id_hom(C)
-   @test image(embedding(G,1))[1]==kernel(projection(G))[1]
+   @test y == canonical_injection(G,1)(Q[1])
+   @test_throws ArgumentError canonical_injection(G,3)(Q[1])
+   @test codomain(canonical_projection(K))==C
+   @test order(image(canonical_projection(K))[1])==1
+   @test canonical_injection(G,2)*canonical_projection(G)==id_hom(C)
+   @test image(canonical_injection(G,1))[1]==kernel(canonical_projection(G))[1]
 end
 
 
@@ -186,13 +186,13 @@ end
    @test rand(W) isa elem_type(WreathProductGroup)
    f1 = C[1]
    x = W(f1,one(C),f1,one(C),cperm([1,4,2]))
-   @test embedding(W,1)(f1)==W(f1,one(C),one(C),one(C),one(H))
-   @test embedding(W,4)(f1)==W(one(C),one(C),one(C),f1,one(H))
-   @test_throws ArgumentError embedding(W,7)(f1) in W
-   @test embedding(W,5)(cperm([1,4,2]))==W(one(C),one(C),one(C),one(C),cperm([1,4,2]))
-   @test projection(W)(x)==cperm([1,4,2])
-   @test codomain(projection(W))==H
-   @test domain(embedding(W,2))==C
+   @test canonical_injection(W,1)(f1)==W(f1,one(C),one(C),one(C),one(H))
+   @test canonical_injection(W,4)(f1)==W(one(C),one(C),one(C),f1,one(H))
+   @test_throws ArgumentError canonical_injection(W,7)(f1) in W
+   @test canonical_injection(W,5)(cperm([1,4,2]))==W(one(C),one(C),one(C),one(C),cperm([1,4,2]))
+   @test canonical_projection(W)(x)==cperm([1,4,2])
+   @test codomain(canonical_projection(W))==H
+   @test domain(canonical_injection(W,2))==C
    K = sub(W,gens(W))[1]
 #   @test is_full_wreath_product(K)
    K = sub(W,[x])[1]
@@ -202,7 +202,7 @@ end
    @test order(K)==6
    @test is_cyclic(K)
    @test index(W,K)==8
-   @test_throws ArgumentError embedding(K,1)(f1) in K
+   @test_throws ArgumentError canonical_injection(K,1)(f1) in K
 
    C = cyclic_group(3)
    a = hom(C,H,[C[1]],[cperm([1,2,4])])
@@ -212,8 +212,8 @@ end
    @test is_isomorphic(normal_subgroup(W),C)
    @test is_isomorphic(acting_subgroup(W),C)
    @test homomorphism_of_wreath_product(W)==a
-   @test embedding(W,1)(C[1]) in W
+   @test canonical_injection(W,1)(C[1]) in W
    @test W(C[1],one(C),one(C),C[1]) isa elem_type(WreathProductGroup)
-   @test image(projection(W))[1]==C
-   @test_throws ArgumentError embedding(W,5)(C[1])
+   @test image(canonical_projection(W))[1]==C
+   @test_throws ArgumentError canonical_injection(W,5)(C[1])
 end