Merge branch 'enh/type_ovehaul'

src/DirectProducts.jl

@@ -9,13 +9,14 @@ export DirectProductGroup, DirectProductGroupElem
 ###############################################################################
 
 doc"""
-   DirectProductGroup(factors::Vector{Group}) <: Group
+   DirectProductGroup(G::Group, n::Int) <: Group
-Implements direct product of groups as vector factors. The group operation is
+Implements `n`-fold direct product of `G`. The group operation is
 `*` distributed component-wise, with component-wise identity as neutral element.
 """
 
 immutable DirectProductGroup{T<:Group} <: Group
-   factors::Vector{T}
+   group::T
+   n::Int
 end
 
 immutable DirectProductGroupElem{T<:GroupElem} <: GroupElem
@@ -28,11 +29,14 @@ end
 #
 ###############################################################################
 
-elem_type{T<:Group}(G::DirectProductGroup{T}) = DirectProductGroupElem{elem_type(first(G.factors))}
+elem_type{T<:Group}(G::DirectProductGroup{T}) =
+   DirectProductGroupElem{elem_type(G.group)}
 
-parent_type(::Type{DirectProductGroupElem}) = DirectProductGroup
+parent_type{T<:GroupElem}(::Type{DirectProductGroupElem{T}}) =
+   DirectProductGroup{parent_type(T)}
 
-parent(g::DirectProductGroupElem) = DirectProductGroup([parent(h) for h in g.elts])
+parent(g::DirectProductGroupElem) =
+   DirectProductGroup(parent(first(g.elts)), length(g.elts))
 
 ###############################################################################
 #
@@ -44,8 +48,9 @@ Base.size(g::DirectProductGroupElem) = size(g.elts)
 Base.linearindexing(::Type{DirectProductGroupElem}) = Base.LinearFast()
 Base.getindex(g::DirectProductGroupElem, i::Int) = g.elts[i]
 function Base.setindex!{T<:GroupElem}(g::DirectProductGroupElem{T}, v::T, i::Int)
-   p.part[i] = v
+   parent(v) == parent(first(g.elts)) || throw("$g is not an element of $i-th factor of $(parent(G))")
-   return p
+   g.elts[i] = v
+   return g
 end
 
 ###############################################################################
@@ -54,9 +59,10 @@ end
 #
 ###############################################################################
 
-DirectProductGroup{T<:Group}(G::T, H::T) = DirectProductGroup{T}([G, H])
+function ×(G::Group, H::Group)
-
+   G == H || throw("Direct products are defined only for the same groups")
-×(G::Group, H::Group) = DirectProductGroup([G,H])
+   return DirectProductGroup(G,2)
+end
 
 ###############################################################################
 #
@@ -64,23 +70,25 @@ DirectProductGroup{T<:Group}(G::T, H::T) = DirectProductGroup{T}([G, H])
 #
 ###############################################################################
 
-(G::DirectProductGroup)() = G([H() for H in G.factors])
+doc"""
+    (G::DirectProductGroup)(a::Vector, check::Bool=true)
+> Constructs element of the $n$-fold direct product group `G` by coercing each
+> element of vector `a` to `G.group`. If `check` flag is set to `false` neither
+> check on the correctness nor coercion is performed.
+"""
+function (G::DirectProductGroup)(a::Vector, check::Bool=true)
+   if check
+      G.n == length(a) || throw("Can not coerce to DirectProductGroup: lengths differ")
+      a = G.group.(a)
+   end
+   return DirectProductGroupElem(a)
+end
+
+(G::DirectProductGroup)() = DirectProductGroupElem([G.group() for _ in 1:G.n])
 
 (G::DirectProductGroup)(g::DirectProductGroupElem) = G(g.elts)
 
-doc"""
+(G::DirectProductGroup){T<:GroupElem, N}(a::Vararg{T, N}) = G([a...])
-    (G::DirectProductGroup)(a::Vector; checked=true)
-> Constructs element of the direct product group `G` by coercing each element
-> of vector `a` to the corresponding factor of `G`. If `checked` flag is set to
-> `false` no checks on the correctness are performed.
-
-"""
-function (G::DirectProductGroup){T<:GroupElem}(a::Vector{T})
-   length(a) == length(G.factors) || throw("Cannot coerce $a to $G: they have
-      different number of factors")
-   @assert elem_type(first(G.factors)) == T
-   return DirectProductGroupElem(a)
-end
 
 ###############################################################################
 #
@@ -94,20 +102,13 @@ function deepcopy_internal(g::DirectProductGroupElem, dict::ObjectIdDict)
 end
 
 function hash(G::DirectProductGroup, h::UInt)
-   return hash(G.factors, hash(DirectProductGroup,h))
+   return hash(G.group, hash(G.n, hash(DirectProductGroup,h)))
 end
 
 function hash(g::DirectProductGroupElem, h::UInt)
    return hash(g.elts, hash(parent(g), hash(DirectProductGroupElem, h)))
 end
 
-doc"""
-    eye(G::DirectProductGroup)
-> Return the identity element for the given direct product of groups.
-
-"""
-eye(G::DirectProductGroup) = G()
-
 ###############################################################################
 #
 #   String I/O
@@ -115,12 +116,11 @@ eye(G::DirectProductGroup) = G()
 ###############################################################################
 
 function show(io::IO, G::DirectProductGroup)
-    println(io, "Direct product of groups")
+    println(io, "$(G.n)-fold direct product of $(G.group)")
-    join(io, G.factors, ", ", " and ")
 end
 
 function show(io::IO, g::DirectProductGroupElem)
-    print(io, "("*join(g.elts,",")*")")
+    print(io, "($(join(g.elts,",")))")
 end
 
 ###############################################################################
@@ -129,65 +129,62 @@ end
 #
 ###############################################################################
 
+doc"""
+    ==(g::DirectProductGroup, h::DirectProductGroup)
+> Checks if two direct product groups are the same.
+"""
 function (==)(G::DirectProductGroup, H::DirectProductGroup)
-    G.factors == H.factors || return false
+    G.group == H.group || return false
+    G.n == G.n || return false
     return true
 end
 
 doc"""
     ==(g::DirectProductGroupElem, h::DirectProductGroupElem)
-> Return `true` if the given elements of direct products are equal, otherwise return `false`.
+> Checks if two direct product group elements are the same.
-
 """
 function (==)(g::DirectProductGroupElem, h::DirectProductGroupElem)
-    parent(g) == parent(h) || return false
     g.elts == h.elts || return false
     return true
 end
 
 ###############################################################################
 #
-#   Binary operators
+#   Group operations
 #
 ###############################################################################
 
-function direct_mult(g::DirectProductGroupElem, h::DirectProductGroupElem)
-   G = parent(g)
-   # G == parent(h) || throw("Can't multiply elements from different groups: $G, $parent(h)")
-   if isa(first(G.factors), Ring)
-      return G(.+(g.elts,h.elts))
-   else
-      return G(.*(g.elts,h.elts))
-   end
-end
-
 doc"""
     *(g::DirectProductGroupElem, h::DirectProductGroupElem)
 > Return the direct-product group operation of elements, i.e. component-wise
 > operation as defined by `operations` field of the parent object.
-
 """
-(*)(g::DirectProductGroupElem, h::DirectProductGroupElem) = direct_mult(g,h)
+# TODO: dirty hack around `+/*` operations
+function *{T<:GroupElem}(g::DirectProductGroupElem{T}, h::DirectProductGroupElem{T}, check::Bool=true)
+   if check
+      parent(g) == parent(h) || throw("Can not multiply elements of different groups!")
+   end
+   return DirectProductGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
+end
 
-###############################################################################
+function *{T<:RingElem}(g::DirectProductGroupElem{T}, h::DirectProductGroupElem{T}, check::Bool=true)
-#
+   if check
-#   Inversion
+      parent(g) == parent(h) || throw("Can not multiply elements of different groups!")
-#
+   end
-###############################################################################
+   return DirectProductGroupElem(g.elts + h.elts)
+end
 
 doc"""
     inv(g::DirectProductGroupElem)
 > Return the inverse of the given element in the direct product group.
-
 """
-# TODO: dirty hack around `+` operation
+# TODO: dirty hack around `+/*` operation
-function inv(g::DirectProductGroupElem)
+function inv{T<:GroupElem}(g::DirectProductGroupElem{T})
-    G = parent(g)
-   if isa(first(G.factors), Ring)
-      return DirectProductGroupElem([-a for a in g.elts])
-   else
    return DirectProductGroupElem([inv(a) for a in g.elts])
 end
+
+function inv{T<:RingElem}(g::DirectProductGroupElem{T})
+   return DirectProductGroupElem(-g.elts)
 end
 
 ###############################################################################
@@ -198,15 +195,15 @@ end
 
 doc"""
     elements(G::DirectProductGroup)
-> Returns `Task` that produces all elements of group `G` (provided that factors
+> Returns `generator` that produces all elements of group `G` (provided that
-> implement the elements function).
+> `G.group` implements the `elements` method).
-
 """
 # TODO: can Base.product handle generators?
 #   now it returns nothing's so we have to collect ellements...
 function elements(G::DirectProductGroup)
-    cartesian_prod = Base.product([collect(elements(H)) for H in G.factors]...)
+    elts = collect(elements(G.group))
-    return (G(collect(elt)) for elt in cartesian_prod)
+    cartesian_prod = Base.product([elts for _ in 1:G.n]...)
+    return (DirectProductGroupElem([elt...]) for elt in cartesian_prod)
 end
 
 doc"""
@@ -214,4 +211,4 @@ doc"""
 > Returns the order (number of elements) in the group.
 
 """
-order(G::DirectProductGroup) = prod([order(H) for H in G.factors])
+order(G::DirectProductGroup) = order(G.group)^G.n

src/WreathProducts.jl

@@ -7,35 +7,38 @@ export WreathProduct, WreathProductElem
 ###############################################################################
 
 doc"""
-    WreathProduct <: Group
+    WreathProduct{T<:Group} <: Group
-> Implements Wreath product of a group N by permutation (sub)group P < Sₖ,
+> Implements Wreath product of a group $N$ by permutation (sub)group $P < S_k$,
 > usually written as $N \wr P$.
 > The multiplication inside wreath product is defined as
->    (n, σ) * (m, τ) = (n*ψ(σ)(m), σ*τ),
+>    $$(n, \sigma) * (m, \tau) = (n\psi(\sigma)(m), \sigma\tau),$$
-> where ψ:P → Aut(Nᵏ) is the permutation representation of Sₖ restricted to P.
+> where $\psi:P → Aut(N^k)$ is the permutation representation of $S_k$
+> restricted to $P$.
 
 # Arguments:
-* `::Group` : the single factor of group N
+* `::Group` : the single factor of group $N$
-* `::PermutationGroup` : full PermutationGroup
+* `::PermGroup` : full `PermutationGroup`
 """
+immutable WreathProduct{T<:Group} <: Group
+   N::DirectProductGroup{T}
+   P::PermGroup
 
-type WreathProduct <: Group
+   function WreathProduct(G::Group, P::PermGroup)
-   N::DirectProductGroup
+      N = DirectProductGroup(G, P.n)
-   P::PermutationGroup
-
-   function WreathProduct(G::Group, P::PermutationGroup)
-      N = DirectProductGroup(typeof(G)[G for _ in 1:P.n])
       return new(N, P)
    end
 end
 
-type WreathProductElem <: GroupElem
+immutable WreathProductElem{T<:GroupElem} <: GroupElem
-   n::DirectProductGroupElem
+   n::DirectProductGroupElem{T}
    p::perm
-   parent::WreathProduct
+   # parent::WreathProduct
 
-   function WreathProductElem(n::DirectProductGroupElem, p::perm)
+   function WreathProductElem(n::DirectProductGroupElem, p::perm,
-      length(n.elts) == parent(p).n
+      check::Bool=true)
+      if check
+         length(n.elts) == parent(p).n || throw("Can't form WreathProductElem: lengths differ")
+      end
       return new(n, p)
    end
 end
@@ -46,11 +49,12 @@ end
 #
 ###############################################################################
 
-elem_type(::WreathProduct) = WreathProductElem
+elem_type{T<:Group}(::WreathProduct{T}) = WreathProductElem{elem_type(T)}
 
-parent_type(::WreathProductElem) = WreathProduct
+parent_type{T<:GroupElem}(::Type{WreathProductElem{T}}) =
+   WreathProduct{parent_type(T)}
 
-parent(g::WreathProductElem) = g.parent
+parent(g::WreathProductElem) = WreathProduct(parent(g.n[1]), parent(g.p))
 
 ###############################################################################
 #
@@ -58,7 +62,10 @@ parent(g::WreathProductElem) = g.parent
 #
 ###############################################################################
 
-# converts???
+WreathProduct{T<:Group}(G::T, P::PermGroup) = WreathProduct{T}(G, P)
+
+WreathProductElem{T<:GroupElem}(n::DirectProductGroupElem{T},
+   p::perm, check::Bool=true) = WreathProductElem{T}(n, p, check)
 
 ###############################################################################
 #
@@ -67,39 +74,31 @@ parent(g::WreathProductElem) = g.parent
 ###############################################################################
 
 function (G::WreathProduct)(g::WreathProductElem)
-   try
+   n = try
       G.N(g.n)
    catch
       throw("Can't coerce $(g.n) to $(G.N) factor of $G")
    end
-   try
+   p = try
       G.P(g.p)
    catch
       throw("Can't coerce $(g.p) to $(G.P) factor of $G")
    end
-   elt = WreathProductElem(G.N(g.n), G.P(g.p))
+   return WreathProductElem(n, p)
-   elt.parent = G
-   return elt
 end
 
 doc"""
     (G::WreathProduct)(n::DirectProductGroupElem, p::perm)
 > Creates an element of wreath product `G` by coercing `n` and `p` to `G.N` and
 > `G.P`, respectively.
-
 """
-function (G::WreathProduct)(n::DirectProductGroupElem, p::perm)
+(G::WreathProduct)(n::DirectProductGroupElem, p::perm) = WreathProductElem(n,p)
-   result = WreathProductElem(n,p)
-   result.parent = G
-   return result
-end
 
-(G::WreathProduct)() = G(G.N(), G.P())
+(G::WreathProduct)() = WreathProductElem(G.N(), G.P(), false)
 
 doc"""
     (G::WreathProduct)(p::perm)
 > Returns the image of permutation `p` in `G` via embedding `p -> (id,p)`.
-
 """
 (G::WreathProduct)(p::perm) = G(G.N(), p)
 
@@ -107,7 +106,6 @@ doc"""
     (G::WreathProduct)(n::DirectProductGroupElem)
 > Returns the image of `n` in `G` via embedding `n -> (n,())`. This is the
 > embedding that makes sequence `1 -> N -> G -> P -> 1` exact.
-
 """
 (G::WreathProduct)(n::DirectProductGroupElem) = G(n, G.P())
 
@@ -118,8 +116,7 @@ doc"""
 ###############################################################################
 
 function deepcopy_internal(g::WreathProductElem, dict::ObjectIdDict)
-   G = parent(g)
+   return WreathProductElem(deepcopy(g.n), deepcopy(g.p), false)
-   return G(deepcopy(g.n), deepcopy(g.p))
 end
 
 function hash(G::WreathProduct, h::UInt)
@@ -127,7 +124,7 @@ function hash(G::WreathProduct, h::UInt)
 end
 
 function hash(g::WreathProductElem, h::UInt)
-   return hash(g.n, hash(g.p, hash(parent(g), h)))
+   return hash(g.n, hash(g.p, hash(WreathProductElem, h)))
 end
 
 ###############################################################################
@@ -137,12 +134,10 @@ end
 ###############################################################################
 
 function show(io::IO, G::WreathProduct)
-   print(io, "Wreath Product of $(G.N.factors[1]) and $(G.P)")
+   print(io, "Wreath Product of $(G.N.group) by $(G.P)")
 end
 
 function show(io::IO, g::WreathProductElem)
-   # println(io, "Element of WreathProduct over $T of size $(size(X)):")
-   # show(io, "text/plain", matrix_repr(X))
    print(io, "($(g.n)≀$(g.p))")
 end
 
@@ -159,7 +154,6 @@ function (==)(G::WreathProduct, H::WreathProduct)
 end
 
 function (==)(g::WreathProductElem, h::WreathProductElem)
-   parent(g) == parent(h) || return false
    g.n == h.n || return false
    g.p == h.p || return false
    return true
@@ -167,45 +161,32 @@ end
 
 ###############################################################################
 #
-#   Binary operators
+#   Group operations
 #
 ###############################################################################
 
-function wreath_multiplication(g::WreathProductElem, h::WreathProductElem)
-   parent(g) == parent(h) || throw("Can not multiply elements from different
-      groups!")
-   G = parent(g)
-   w = G.N((h.n).elts[inv(g.p).d])
-   return G(g.n*w, g.p*h.p)
-end
-
 doc"""
     *(g::WreathProductElem, h::WreathProductElem)
 > Return the wreath product group operation of elements, i.e.
 >
-> g*h = (g.n*g.p(h.n), g.p*h.p),
+> `g*h = (g.n*g.p(h.n), g.p*h.p)`,
 >
-> where g.p(h.n) denotes the action of `g.p::perm` on
+> where `g.p(h.n)` denotes the action of `g.p::perm` on
 > `h.n::DirectProductGroupElem` via standard permutation of coordinates.
 """
-(*)(g::WreathProductElem, h::WreathProductElem) = wreath_multiplication(g,h)
+function *(g::WreathProductElem, h::WreathProductElem)
-
+   w = DirectProductGroupElem((h.n).elts[inv(g.p).d])
-
+   return WreathProductElem(g.n*w, g.p*h.p, false)
-###############################################################################
+end
-#
-#   Inversion
-#
-###############################################################################
 
 doc"""
     inv(g::WreathProductElem)
 > Returns the inverse of element of a wreath product, according to the formula
->   g^-1 = (g.n, g.p)^-1 = (g.p^-1(g.n^-1), g.p^-1).
+>   `g^-1 = (g.n, g.p)^-1 = (g.p^-1(g.n^-1), g.p^-1)`.
 """
 function inv(g::WreathProductElem)
-   G = parent(g)
+   w = DirectProductGroupElem(inv(g.n).elts[g.p.d])
-   w = G.N(inv(g.n).elts[g.p.d])
+   return WreathProductElem(w, inv(g.p), false)
-   return G(w, inv(g.p))
 end
 
 ###############################################################################
@@ -218,7 +199,7 @@ matrix_repr(g::WreathProductElem) = Any[matrix_repr(g.p) g.n]
 
 function elements(G::WreathProduct)
    iter = Base.product(collect(elements(G.N)), collect(elements(G.P)))
-   return (G(n)*G(p) for (n,p) in iter)
+   return (WreathProductElem(n, p, false) for (n,p) in iter)
 end
 
 order(G::WreathProduct) = order(G.P)*order(G.N)

test/DirectProd-tests.jl

@@ -0,0 +1,83 @@
+@testset "DirectProducts" begin
+   using Nemo
+
+   G = PermutationGroup(3)
+   g = G([2,3,1])
+   F, a = FiniteField(2,3,"a")
+
+   @testset "Constructors" begin
+      @test isa(Groups.DirectProductGroup(G,2), Nemo.Group)
+      @test isa(G×G, Nemo.Group)
+      @test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Nemo.PermGroup})
+
+      GG = Groups.DirectProductGroup(G,2)
+
+      @test GG == Groups.DirectProductGroup(G,2)
+
+      @test Groups.DirectProductGroupElem([G(), G()]) == GG()
+      @test GG(G(), G()) == GG()
+
+      @test isa(GG([g, g^2]), GroupElem)
+      @test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Nemo.perm})
+
+      h = GG([g,g^2])
+
+      @test h == GG(h)
+
+      @test isa(GG(g, g^2), GroupElem)
+      @test isa(GG(g, g^2), Groups.DirectProductGroupElem)
+
+      @test_throws String GG(g,g,g)
+      @test GG(g,g^2) == h
+
+      @test size(h) == (2,)
+      @test h[1] == g
+      @test h[2] == g^2
+      h[2] = G()
+      @test h == GG(g, G())
+   end
+
+   GG = Groups.DirectProductGroup(G,2)
+   FF = Groups.DirectProductGroup(F,2)
+
+   @testset "Types" begin
+      @test elem_type(GG) == Groups.DirectProductGroupElem{elem_type(G)}
+      @test elem_type(FF) == Groups.DirectProductGroupElem{elem_type(F)}
+      @test parent_type(typeof(GG(g,g^2))) == Groups.DirectProductGroup{typeof(G)}
+      @test parent_type(typeof(FF(a,a^2))) == Groups.DirectProductGroup{typeof(F)}
+
+      @test isa(FF([0,1]), GroupElem)
+      @test isa(FF([0,1]), Groups.DirectProductGroupElem)
+      @test isa(FF([0,1]), Groups.DirectProductGroupElem{elem_type(F)})
+      @test_throws MethodError FF(1,0)
+   end
+
+   @testset "Group arithmetic" begin
+      g = G([2,3,1])
+      h = GG([g,g^2])
+
+      @test h^2 == GG(g^2,g)
+      @test h^6 == GG()
+
+      @test h*h == h^2
+
+      @test h*inv(h) == GG()
+
+      @test FF([0,a])*FF([a,1]) == FF(a,1+a)
+      x, y = FF([1,a]), FF([a^2,1])
+      @test x*y == FF([a^2+1, a+1])
+      @test inv(x) == FF([1,a])
+   end
+
+   @testset "Misc" begin
+      @test order(GG) == 36
+      @test order(FF) == 64
+
+      @test isa([elements(GG)...], Vector{Groups.DirectProductGroupElem{elem_type(G)}})
+      elts = [elements(GG)...]
+
+      @test length(elts) == 36
+      @test all([g*inv(g) for g in elts] .== GG())
+      @test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
+   end
+end

test/FreeGroup-tests.jl

@@ -1,7 +1,9 @@
+
 @testset "Groups.FreeSymbols" begin
    s = Groups.FreeSymbol("s")
    t = Groups.FreeSymbol("t")
-   @testset "defines" begin
+
+   @testset "constructors" begin
       @test isa(Groups.FreeSymbol("aaaaaaaaaaaaaaaa"), Groups.GSymbol)
       @test Groups.FreeSymbol("abc").pow == 1
       @test isa(s, Groups.FreeSymbol)
@@ -23,10 +25,10 @@
    end
 end
 
-@testset "FreeGroupElems" begin
+@testset "FreeGroupSymbols manipulation" begin
    s = Groups.FreeSymbol("s")
    t = Groups.FreeSymbol("t", -2)
-   @testset "defines" begin
+
    @test isa(Groups.GWord(s), Groups.GWord)
    @test isa(Groups.GWord(s), FreeGroupElem)
    @test isa(FreeGroupElem(s), Groups.GWord)
@@ -35,18 +37,7 @@ end
    @test isa(Vector{FreeGroupElem}([s,t]), Vector{FreeGroupElem})
    @test length(FreeGroupElem(s)) == 1
    @test length(FreeGroupElem(t)) == 2
-   end
 
-   @testset "eltary functions" begin
-      G = FreeGroup(["s", "t"])
-      s = G(s)
-      t = G(t)
-      @test Vector{Groups.GWord}([s,t]) == [Groups.GWord(s), Groups.GWord(t)]
-
-      @test (s*s).symbols == (s^2).symbols
-
-      @test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
-   end
 end
 
 @testset "FreeGroup" begin
@@ -64,6 +55,11 @@ end
    s, t = Nemo.gens(G)
 
    @testset "internal arithmetic" begin
+
+      @test Vector{Groups.GWord}([s,t]) == [Groups.GWord(s), Groups.GWord(t)]
+      @test (s*s).symbols == (s^2).symbols
+      @test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
+
       t_symb = Groups.FreeSymbol("t")
       tt = deepcopy(t)
       @test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=true)) ==
@@ -96,7 +92,7 @@ end
       @test Groups.reduce!(w).symbols ==Vector{Groups.FreeSymbol}([])
    end
 
-   @testset "binary/inv operations" begin
+   @testset "Group operations" begin
       @test parent(s) == G
       @test parent(s) === parent(deepcopy(s))
       @test isa(s*t, FreeGroupElem)

test/WreathProd-tests.jl

@@ -0,0 +1,85 @@
+@testset "WreathProducts" begin
+   S_3 = PermutationGroup(3)
+   F, a = FiniteField(2,3,"a")
+   b = S_3([2,3,1])
+
+   @testset "Constructors" begin
+      @test isa(Groups.WreathProduct(F, S_3), Nemo.Group)
+      @test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct)
+      @test isa(Groups.WreathProduct(F, S_3), Groups.WreathProduct{Nemo.FqNmodFiniteField})
+
+      aa = Groups.DirectProductGroupElem([a^0 ,a, a^2])
+
+      @test isa(Groups.WreathProductElem(aa, b), Nemo.GroupElem)
+      @test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem)
+      @test isa(Groups.WreathProductElem(aa, b), Groups.WreathProductElem{typeof(a)})
+
+      B3 = Groups.WreathProduct(F, S_3)
+
+      @test B3.N == Groups.DirectProductGroup(F, 3)
+      @test B3.P == S_3
+
+      @test B3(aa, b) == Groups.WreathProductElem(aa, b)
+      @test B3(b) == Groups.WreathProductElem(B3.N(), b)
+      @test B3(aa) == Groups.WreathProductElem(aa, S_3())
+
+      g = B3(aa, b)
+
+      @test g.p == b
+      @test g.n == aa
+      h = deepcopy(g)
+
+      @test hash(g) == hash(h)
+
+      g.n[1] = a
+
+      @test g.n[1] == a
+      @test g != h
+
+      @test hash(g) != hash(h)
+   end
+
+   @testset "Types" begin
+      B3 = Groups.WreathProduct(F, S_3)
+
+      @test elem_type(B3) == Groups.WreathProductElem{elem_type(F)}
+
+      @test parent_type(typeof(B3())) == Groups.WreathProduct{parent_type(typeof(B3.N.group()))}
+
+      @test parent(B3()) == Groups.WreathProduct(F,S_3)
+      @test parent(B3()) == B3
+   end
+
+   @testset "Group arithmetic" begin
+      B3 = Groups.WreathProduct(F, S_3)
+
+      x = B3(B3.N([1,0,0]), B3.P([2,3,1]))
+      y = B3(B3.N([0,1,1]), B3.P([2,1,3]))
+
+      @test x*y == B3(B3.N([0,0,1]), B3.P([3,2,1]))
+      @test y*x == B3(B3.N([0,0,1]), B3.P([1,3,2]))
+
+      @test inv(x) == B3(B3.N([0,0,1]), B3.P([3,1,2]))
+      @test inv(y) == B3(B3.N([1,0,1]), B3.P([2,1,3]))
+
+      @test inv(x)*y == B3(B3.N([1,1,1]), B3.P([1,3,2]))
+      @test y*inv(x) == B3(B3.N([0,1,0]), B3.P([3,2,1]))
+
+   end
+
+   @testset "Misc" begin
+      B3 = Groups.WreathProduct(FiniteField(2,1,"a")[1], S_3)
+      @test order(B3) == 48
+
+      Wr = WreathProduct(PermutationGroup(2),S_3)
+
+      @test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Nemo.perm}})
+
+      elts = [elements(Wr)...]
+
+      @test length(elts) == order(Wr)
+      @test all([g*inv(g) for g in elts] .== Wr())
+      @test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
+   end
+
+end

test/runtests.jl

@@ -6,4 +6,6 @@ using Base.Test
 @testset "Groups" begin
    include("FreeGroup-tests.jl")
    include("AutGroup-tests.jl")
+   include("DirectProd-tests.jl")
+   include("WreathProd-tests.jl")
 end