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remove MltGrp/AddGrp
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@ -1,100 +1,4 @@
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export DirectPowerGroup, DirectPowerGroupElem
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export MultiplicativeGroup, MltGrp, MltGrpElem
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export AdditiveGroup, AddGrp, AddGrpElem
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###############################################################################
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#
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# MltGrp/MltGrpElem & AddGrp/AddGrpElem
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# (a thin wrapper for multiplicative/additive group of a Ring)
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#
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###############################################################################
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for (Gr, Elem) in [(:MltGrp, :MltGrpElem), (:AddGrp, :AddGrpElem)]
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@eval begin
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struct $Gr{T<:AbstractAlgebra.Ring} <: AbstractAlgebra.Group
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obj::T
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end
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struct $Elem{T<:AbstractAlgebra.RingElem} <: AbstractAlgebra.GroupElem
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elt::T
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end
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==(g::$Elem, h::$Elem) = g.elt == h.elt
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==(G::$Gr, H::$Gr) = G.obj == H.obj
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elem_type(::Type{$Gr{T}}) where T = $Elem{elem_type(T)}
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eltype(::Type{$Gr{T}}) where T = $Elem{elem_type(T)}
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parent_type(::Type{$Elem{T}}) where T = $Gr{parent_type(T)}
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parent(g::$Elem) = $Gr(parent(g.elt))
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length(G::$Gr{<:AbstractAlgebra.Ring}) = order(G.obj)
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end
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end
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MultiplicativeGroup = MltGrp
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AdditiveGroup = AddGrp
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(G::MltGrp)(g::MltGrpElem) = MltGrpElem(G.obj(g.elt))
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function (G::MltGrp)(g)
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r = (G.obj)(g)
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isunit(r) || throw(DomainError(
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"Cannot coerce to multplicative group: $r is not invertible!"))
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return MltGrpElem(r)
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end
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(G::AddGrp)(g) = AddGrpElem((G.obj)(g))
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(G::MltGrp)() = MltGrpElem(G.obj(1))
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(G::AddGrp)() = AddGrpElem(G.obj())
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inv(g::MltGrpElem) = MltGrpElem(inv(g.elt))
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inv(g::AddGrpElem) = AddGrpElem(-g.elt)
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for (Elem, op) in ([:MltGrpElem, :*], [:AddGrpElem, :+])
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@eval begin
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^(g::$Elem, n::Integer) = $Elem(op(g.elt, n))
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function *(g::$Elem, h::$Elem)
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parent(g) == parent(h) || throw(DomainError(
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"Cannot multiply elements of different parents"))
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return $Elem($op(g.elt,h.elt))
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end
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end
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end
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show(io::IO, G::MltGrp) = print(io, "The multiplicative group of $(G.obj)")
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show(io::IO, G::AddGrp) = print(io, "The additive group of $(G.obj)")
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show(io::IO, g::Union{MltGrpElem, AddGrpElem}) = show(io, g.elt)
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gens(F::AbstractAlgebra.Field) = elem_type(F)[gen(F)]
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order(G::AddGrp{<:AbstractAlgebra.GFField}) = order(G.obj)
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order(G::MltGrp{<:AbstractAlgebra.GFField}) = order(G.obj) - 1
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function iterate(G::AddGrp, s=0)
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if s >= order(G)
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return nothing
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else
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g, s = iterate(G.obj,s)
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return G(g), s
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end
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end
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function iterate(G::MltGrp, s=0)
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if s > order(G)
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return nothing
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else
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g, s = iterate(G.obj, s)
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if g == G.obj()
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g, s = iterate(G.obj, s)
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end
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return G(g), s
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end
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end
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###############################################################################
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#
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@ -72,129 +72,9 @@
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@test elem_type(G×G×G) == DirectPowerGroupElem{3, elem_type(G)}
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@test parent_type(typeof((G×G)(g,g^2))) == Groups.DirectPowerGroup{2, typeof(G)}
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@test parent(DirectPowerGroupElem((g,g^2,g^3))) == DirectPowerGroup(G,3)
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F = AdditiveGroup(GF(13))
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@test elem_type(F×F) ==
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DirectPowerGroupElem{2, Groups.AddGrpElem{AbstractAlgebra.gfelem{Int}}}
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@test parent_type(typeof((F×F)(1,5))) ==
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Groups.DirectPowerGroup{2, Groups.AddGrp{AbstractAlgebra.GFField{Int}}}
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parent((F×F)(1,5)) == DirectPowerGroup(F,2)
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F = MultiplicativeGroup(GF(13))
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@test elem_type(F×F) ==
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DirectPowerGroupElem{2, Groups.MltGrpElem{AbstractAlgebra.gfelem{Int}}}
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@test parent_type(typeof((F×F)(1,5))) ==
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Groups.DirectPowerGroup{2, Groups.MltGrp{AbstractAlgebra.GFField{Int}}}
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parent((F×F)(1,5)) == DirectPowerGroup(F,2)
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end
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@testset "Additive/Multiplicative groups" begin
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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^3 + x + 1, "a")
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G = PermutationGroup(3)
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@testset "MltGrp basic functionality" begin
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Gr = MltGrp(F)
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@test Gr(a) isa MltGrpElem
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g = Gr(a)
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@test deepcopy(g) isa MltGrpElem
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@test inv(g) == Gr(a^-1)
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@test Gr() == Gr(1)
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@test inv(g)*g == Gr()
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end
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@testset "AddGrp basic functionality" begin
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Gr = AddGrp(F)
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@test Gr(a) isa AddGrpElem
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g = Gr(a)
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@test deepcopy(g) isa AddGrpElem
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@test inv(g) == Gr(-a)
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@test Gr() == Gr(0)
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@test inv(g)*g == Gr()
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end
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end
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@testset "Direct Product of Multiplicative Groups" begin
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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^3 + x + 1, "a")
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FF = Groups.DirectPowerGroup(MltGrp(F),2)
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@test FF([a,1]) isa GroupElem
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@test FF([a,1]) isa DirectPowerGroupElem
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@test FF([a,1]) isa DirectPowerGroupElem{2, MltGrpElem{elem_type(F)}}
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@test_throws DomainError FF(1,0)
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@test_throws DomainError FF([0,1])
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@test_throws DomainError FF([1,0])
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@test MltGrp(F) isa AbstractAlgebra.Group
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@test MltGrp(F) isa MultiplicativeGroup
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@test DirectPowerGroup(MltGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectPowerGroup(MltGrp(F), 2) isa DirectPowerGroup{2, MltGrp{typeof(F)}}
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F, a = NumberField(x^3 + x + 1, "a")
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FF = DirectPowerGroup(MltGrp(F), 2)
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@test FF(a,a+1) == FF([a,a+1])
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@test FF([1,a+1])*FF([a,a]) == FF(a,a^2+a)
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x, y = FF([1,a]), FF([a^2,1])
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@test x*y == FF([a^2, a])
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@test inv(x) == FF([1,-a^2-1])
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@test parent(x) == FF
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end
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@testset "Direct Product of Additive Groups" begin
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R, x = PolynomialRing(QQ, "x")
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F, a = NumberField(x^3 + x + 1, "a")
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# Additive Group
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@test AddGrp(F) isa AbstractAlgebra.Group
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@test AddGrp(F) isa AdditiveGroup
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@test DirectPowerGroup(AddGrp(F), 2) isa AbstractAlgebra.Group
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@test DirectPowerGroup(AddGrp(F), 2) isa DirectPowerGroup{2, AddGrp{typeof(F)}}
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FF = DirectPowerGroup(AdditiveGroup(F), 2)
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@test FF([0,a]) isa AbstractAlgebra.GroupElem
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@test FF(F(0),a) isa DirectPowerGroupElem
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@test FF(0,0) isa DirectPowerGroupElem{2, AddGrpElem{elem_type(F)}}
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@test FF(F(1),a+1) == FF([1,a+1])
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@test FF([F(1),a+1])*FF([a,a]) == FF(1+a,2a+1)
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x, y = FF([1,a]), FF([a^2,1])
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@test x*y == FF(a^2+1, a+1)
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@test inv(x) == FF([F(-1),-a])
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@test parent(x) == FF
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end
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@testset "Misc" begin
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F = GF(5)
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FF = DirectPowerGroup(AdditiveGroup(F),2)
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@test order(FF) == 25
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elts = vec(collect(FF))
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@test length(elts) == 25
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@test all([g*inv(g) == FF() for g in elts])
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@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
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FF = DirectPowerGroup(MultiplicativeGroup(F), 3)
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@test order(FF) == 64
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elts = vec(collect(FF))
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@test length(elts) == 64
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@test all([g*inv(g) == FF() for g in elts])
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@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
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G = PermutationGroup(3)
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GG = Groups.DirectPowerGroup(G,3)
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@test order(GG) == 216
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@ -64,40 +64,26 @@
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end
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@testset "Group arithmetic" begin
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B4 = Groups.WreathProduct(AdditiveGroup(GF(3)), PermutationGroup(4))
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B4 = Groups.WreathProduct(PermutationGroup(3), PermutationGroup(4))
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x = B4((0,1,2,0), perm"(1,2,3)(4)")
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@test inv(x) == B4((1,0,2,0), perm"(1,3,2)(4)")
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id, a, b = perm"(3)", perm"(1,2)(3)", perm"(1,2,3)"
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y = B4((1,0,1,2), perm"(1,4)(2,3)")
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@test inv(y) == B4((1,2,0,2), perm"(1,4)(2,3)")
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x = B4((id,a,b,id), perm"(1,2,3)(4)")
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@test inv(x) == B4((inv(b),id, a,id), perm"(1,3,2)(4)")
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@test x*y == B4((0,2,0,2), perm"(1,3,4)(2)")
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y = B4((a,id,a,b), perm"(1,4)(2,3)")
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@test inv(y) == B4((inv(b), a,id, a), perm"(1,4)(2,3)")
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@test y*x == B4((1,2,2,2), perm"(1,4,2)(3)")
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@test x*y == B4((id,id,b*a,b), perm"(1,3,4)(2)")
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@test y*x == B4(( a, b, id,b), perm"(1,4,2)(3)")
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@test inv(x)*y == B4((inv(b)*a,a,a,b), perm"(1,2,4)(3)")
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@test y*inv(x) == B4((a,a,a,id), perm"(1,4,3)(2)")
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@test inv(x)*y == B4((2,1,2,2), perm"(1,2,4)(3)")
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@test y*inv(x) == B4((1,2,1,0), perm"(1,4,3)(2)")
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@test (x*y)^6 == ((x*y)^2)^3
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end
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@testset "Iteration" begin
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B3_a = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
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@test order(B3_a) == 3^3*6
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@test collect(B3_a) isa Vector{
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WreathProductElem{3, AddGrpElem{AbstractAlgebra.gfelem{Int}}, perm{Int}}}
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B3_m = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test order(B3_m) == 2^3*6
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@test collect(B3_m) isa Vector{
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WreathProductElem{3, MltGrpElem{AbstractAlgebra.gfelem{Int}}, perm{Int}}}
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@test length(Set([B3_a, B3_m, B3_a])) == 2
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Wr = WreathProduct(PermutationGroup(2),PermutationGroup(4))
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elts = collect(Wr)
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@ -108,18 +94,5 @@
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@test all([g*inv(g) == Wr() for g in elts])
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@test all(inv(g*h) == inv(h)*inv(g) for g in elts for h in elts)
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end
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@testset "Misc" begin
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B3_a = Groups.WreathProduct(AdditiveGroup(GF(3)), S_3)
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@test string(B3_a) == "Wreath Product of The additive group of Finite field F_3 by Permutation group over 3 elements"
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@test string(B3_a(perm"(1,3)")) == "([0,0,0]≀(1,3))"
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B3_m = Groups.WreathProduct(MultiplicativeGroup(GF(3)), S_3)
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@test string(B3_m) == "Wreath Product of The multiplicative group of Finite field F_3 by Permutation group over 3 elements"
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@test string(B3_m(perm"(1,3)")) == "([1,1,1]≀(1,3))"
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end
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end
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