mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-10-15 07:20:35 +02:00
replace DirectProduct -> DirectPower
This commit is contained in:
parent
c72067ec37
commit
38e327c385
@ -1,4 +1,4 @@
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export DirectProductGroup, DirectProductGroupElem
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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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@ -75,8 +75,6 @@ elements(G::AddGrp{F}) where F <: AbstractAlgebra.GFField = (G((i-1)*G.obj(1)) f
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order(G::MltGrp{<:AbstractAlgebra.GFField}) = order(G.obj) - 1
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elements(G::MltGrp{F}) where F <: AbstractAlgebra.GFField = (G(i*G.obj(1)) for i in 1:order(G))
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length(G::Union{AddGrp, MltGrp}) = order(G)
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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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@ -100,21 +98,21 @@ end
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###############################################################################
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#
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# DirectProductGroup / DirectProductGroupElem
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# DirectPowerGroup / DirectPowerGroupElem
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#
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###############################################################################
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@doc doc"""
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DirectProductGroup(G::Group, n::Int) <: Group
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DirectPowerGroup(G::Group, n::Int) <: Group
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Implements `n`-fold direct product of `G`. The group operation is
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`*` distributed component-wise, with component-wise identity as neutral element.
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"""
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struct DirectProductGroup{T<:Group} <: Group
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struct DirectPowerGroup{T<:Group} <: Group
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group::T
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n::Int
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end
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struct DirectProductGroupElem{T<:GroupElem} <: GroupElem
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struct DirectPowerGroupElem{T<:GroupElem} <: GroupElem
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elts::Vector{T}
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end
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@ -124,14 +122,14 @@ end
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#
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###############################################################################
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elem_type(::Type{DirectProductGroup{T}}) where {T} =
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DirectProductGroupElem{elem_type(T)}
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elem_type(::Type{DirectPowerGroup{T}}) where {T} =
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DirectPowerGroupElem{elem_type(T)}
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parent_type(::Type{DirectProductGroupElem{T}}) where {T} =
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DirectProductGroup{parent_type(T)}
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parent_type(::Type{DirectPowerGroupElem{T}}) where {T} =
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DirectPowerGroup{parent_type(T)}
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parent(g::DirectProductGroupElem) =
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DirectProductGroup(parent(first(g.elts)), length(g.elts))
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parent(g::DirectPowerGroupElem) =
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DirectPowerGroup(parent(first(g.elts)), length(g.elts))
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###############################################################################
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#
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@ -139,45 +137,45 @@ parent(g::DirectProductGroupElem) =
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#
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###############################################################################
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size(g::DirectProductGroupElem) = size(g.elts)
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Base.IndexStyle(::Type{DirectProductGroupElem}) = Base.LinearFast()
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Base.getindex(g::DirectProductGroupElem, i::Int) = g.elts[i]
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size(g::DirectPowerGroupElem) = size(g.elts)
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Base.IndexStyle(::Type{DirectPowerGroupElem}) = Base.LinearFast()
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Base.getindex(g::DirectPowerGroupElem, i::Int) = g.elts[i]
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function Base.setindex!(g::DirectProductGroupElem{T}, v::T, i::Int) where {T}
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function Base.setindex!(g::DirectPowerGroupElem{T}, v::T, i::Int) where {T}
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parent(v) == parent(g.elts[i]) || throw(DomainError(
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"$g is not an element of $i-th factor of $(parent(G))"))
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g.elts[i] = v
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return g
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end
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function Base.setindex!(g::DirectProductGroupElem{T}, v::S, i::Int) where {T, S}
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function Base.setindex!(g::DirectPowerGroupElem{T}, v::S, i::Int) where {T, S}
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g.elts[i] = parent(g.elts[i])(v)
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return g
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end
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###############################################################################
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#
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# DirectProductGroup / DirectProductGroupElem constructors
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# DirectPowerGroup / DirectPowerGroupElem constructors
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#
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###############################################################################
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function pow(G::Group, H::Group)
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function DirectPower(G::Group, H::Group)
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G == H || throw(DomainError(
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"Direct Powers are defined only for the same groups"))
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return DirectProductGroup(G,2)
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return DirectPowerGroup(G,2)
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end
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pow(H::Group, G::DirectProductGroup) = pow(G,H)
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DirectPower(H::Group, G::DirectPowerGroup) = DirectPower(G,H)
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function pow(G::DirectProductGroup, H::Group)
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function DirectPower(G::DirectPowerGroup, H::Group)
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G.group == H || throw(DomainError(
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"Direct products are defined only for the same groups"))
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return DirectProductGroup(G.group,G.n+1)
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return DirectPowerGroup(G.group,G.n+1)
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end
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function pow(R::T, n::Int) where {T<:AbstractAlgebra.Ring}
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@warn "Creating DirectProduct of the multilplicative group!"
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return DirectProductGroup(R, n)
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function DirectPower(R::AbstractAlgebra.Ring, n::Int)
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@warn "Creating DirectPower of the multilplicative group!"
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return DirectPowerGroup(R, n)
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end
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###############################################################################
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@ -187,25 +185,25 @@ end
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###############################################################################
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@doc doc"""
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(G::DirectProductGroup)(a::Vector, check::Bool=true)
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(G::DirectPowerGroup)(a::Vector, check::Bool=true)
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> Constructs element of the $n$-fold direct product group `G` by coercing each
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> element of vector `a` to `G.group`. If `check` flag is set to `false` neither
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> check on the correctness nor coercion is performed.
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"""
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function (G::DirectProductGroup)(a::Vector, check::Bool=true)
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function (G::DirectPowerGroup)(a::Vector, check::Bool=true)
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if check
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G.n == length(a) || throw(DomainError(
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"Can not coerce to DirectProductGroup: lengths differ"))
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"Can not coerce to DirectPowerGroup: lengths differ"))
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a = (G.group).(a)
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end
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return DirectProductGroupElem(a)
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return DirectPowerGroupElem(a)
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end
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(G::DirectProductGroup)() = DirectProductGroupElem([G.group() for _ in 1:G.n])
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(G::DirectPowerGroup)() = DirectPowerGroupElem([G.group() for _ in 1:G.n])
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(G::DirectProductGroup)(g::DirectProductGroupElem) = G(g.elts)
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(G::DirectPowerGroup)(g::DirectPowerGroupElem) = G(g.elts)
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(G::DirectProductGroup)(a::Vararg{T, N}) where {T, N} = G([a...])
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(G::DirectPowerGroup)(a::Vararg{T, N}) where {T, N} = G([a...])
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###############################################################################
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#
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@ -213,12 +211,12 @@ end
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#
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###############################################################################
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function hash(G::DirectProductGroup, h::UInt)
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return hash(G.group, hash(G.n, hash(DirectProductGroup,h)))
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function hash(G::DirectPowerGroup, h::UInt)
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return hash(G.group, hash(G.n, hash(DirectPowerGroup,h)))
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end
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function hash(g::DirectProductGroupElem, h::UInt)
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return hash(g.elts, hash(parent(g), hash(DirectProductGroupElem, h)))
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function hash(g::DirectPowerGroupElem, h::UInt)
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return hash(g.elts, hash(parent(g), hash(DirectPowerGroupElem, h)))
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end
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###############################################################################
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@ -227,11 +225,11 @@ end
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#
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###############################################################################
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function show(io::IO, G::DirectProductGroup)
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function show(io::IO, G::DirectPowerGroup)
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print(io, "$(G.n)-fold direct product of $(G.group)")
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end
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function show(io::IO, g::DirectProductGroupElem)
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function show(io::IO, g::DirectPowerGroupElem)
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print(io, "[$(join(g.elts,","))]")
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end
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@ -242,20 +240,20 @@ end
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###############################################################################
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@doc doc"""
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==(g::DirectProductGroup, h::DirectProductGroup)
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==(g::DirectPowerGroup, h::DirectPowerGroup)
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> Checks if two direct product groups are the same.
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"""
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function (==)(G::DirectProductGroup, H::DirectProductGroup)
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function (==)(G::DirectPowerGroup, H::DirectPowerGroup)
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G.group == H.group || return false
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G.n == G.n || return false
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return true
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end
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@doc doc"""
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==(g::DirectProductGroupElem, h::DirectProductGroupElem)
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==(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
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> Checks if two direct product group elements are the same.
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"""
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function (==)(g::DirectProductGroupElem, h::DirectProductGroupElem)
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function (==)(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
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g.elts == h.elts || return false
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return true
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end
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@ -267,26 +265,26 @@ end
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###############################################################################
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@doc doc"""
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*(g::DirectProductGroupElem, h::DirectProductGroupElem)
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*(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
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> Return the direct-product group operation of elements, i.e. component-wise
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> operation as defined by `operations` field of the parent object.
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"""
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function *(g::DirectProductGroupElem, h::DirectProductGroupElem, check::Bool=true)
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function *(g::DirectPowerGroupElem, h::DirectPowerGroupElem, check::Bool=true)
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if check
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parent(g) == parent(h) || throw(DomainError(
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"Can not multiply elements of different groups!"))
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end
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return DirectProductGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
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return DirectPowerGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
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end
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^(g::DirectProductGroupElem, n::Integer) = Base.power_by_squaring(g, n)
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^(g::DirectPowerGroupElem, n::Integer) = Base.power_by_squaring(g, n)
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@doc doc"""
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inv(g::DirectProductGroupElem)
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inv(g::DirectPowerGroupElem)
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> Return the inverse of the given element in the direct product group.
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"""
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function inv(g::DirectProductGroupElem{T}) where {T<:GroupElem}
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return DirectProductGroupElem([inv(a) for a in g.elts])
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function inv(g::DirectPowerGroupElem{T}) where {T<:GroupElem}
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return DirectPowerGroupElem([inv(a) for a in g.elts])
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end
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###############################################################################
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@ -313,20 +311,20 @@ function iterate(DPIter::DirectPowerIter, state=0)
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return nothing
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end
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idx = Tuple(CartesianIndices(ntuple(i -> DPIter.orderG, DPIter.N))[state+1])
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return DirectProductGroupElem([DPIter.elts[i] for i in idx]), state+1
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return DirectPowerGroupElem([DPIter.elts[i] for i in idx]), state+1
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end
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eltype(::Type{DirectPowerIter{GrEl}}) where {GrEl} = DirectProductGroupElem{GrEl}
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eltype(::Type{DirectPowerIter{GrEl}}) where {GrEl} = DirectPowerGroupElem{GrEl}
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@doc doc"""
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elements(G::DirectProductGroup)
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elements(G::DirectPowerGroup)
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> Returns `generator` that produces all elements of group `G` (provided that
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> `G.group` implements the `elements` method).
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"""
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elements(G::DirectProductGroup) = DirectPowerIter(G.group, G.n)
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elements(G::DirectPowerGroup) = DirectPowerIter(G.group, G.n)
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@doc doc"""
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order(G::DirectProductGroup)
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order(G::DirectPowerGroup)
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> Returns the order (number of elements) in the group.
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"""
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order(G::DirectProductGroup) = order(G.group)^G.n
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order(G::DirectPowerGroup) = order(G.group)^G.n
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@ -72,7 +72,7 @@ include("FreeGroup.jl")
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include("FPGroups.jl")
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include("AutGroup.jl")
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include("DirectProducts.jl")
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include("DirectPower.jl")
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include("WreathProducts.jl")
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###############################################################################
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@ -20,21 +20,21 @@ export WreathProduct, WreathProductElem
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* `P::Generic.PermGroup` : full `PermutationGroup`
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"""
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struct WreathProduct{T<:Group, I<:Integer} <: Group
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N::DirectProductGroup{T}
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N::DirectPowerGroup{T}
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P::Generic.PermGroup{I}
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function WreathProduct{T, I}(Gr::T, P::Generic.PermGroup{I}) where {T, I}
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N = DirectProductGroup(Gr, Int(P.n))
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N = DirectPowerGroup(Gr, Int(P.n))
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return new(N, P)
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end
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end
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struct WreathProductElem{T<:GroupElem, I<:Integer} <: GroupElem
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n::DirectProductGroupElem{T}
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n::DirectPowerGroupElem{T}
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p::Generic.perm{I}
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# parent::WreathProduct
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function WreathProductElem{T, I}(n::DirectProductGroupElem{T}, p::Generic.perm{I},
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function WreathProductElem{T, I}(n::DirectPowerGroupElem{T}, p::Generic.perm{I},
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check::Bool=true) where {T, I}
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if check
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length(n.elts) == length(p.d) || throw(DomainError(
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@ -65,7 +65,7 @@ parent(g::WreathProductElem) = WreathProduct(parent(g.n[1]), parent(g.p))
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WreathProduct(G::T, P::Generic.PermGroup{I}) where {T, I} = WreathProduct{T, I}(G, P)
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WreathProductElem(n::DirectProductGroupElem{T}, p::Generic.perm{I}, check=true) where {T,I} = WreathProductElem{T,I}(n, p, check)
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WreathProductElem(n::DirectPowerGroupElem{T}, p::Generic.perm{I}, check=true) where {T,I} = WreathProductElem{T,I}(n, p, check)
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###############################################################################
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#
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@ -88,11 +88,11 @@ function (G::WreathProduct)(g::WreathProductElem)
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end
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@doc doc"""
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(G::WreathProduct)(n::DirectProductGroupElem, p::Generic.perm)
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(G::WreathProduct)(n::DirectPowerGroupElem, p::Generic.perm)
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> Creates an element of wreath product `G` by coercing `n` and `p` to `G.N` and
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> `G.P`, respectively.
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"""
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(G::WreathProduct)(n::DirectProductGroupElem, p::Generic.perm) = WreathProductElem(n,p)
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(G::WreathProduct)(n::DirectPowerGroupElem, p::Generic.perm) = WreathProductElem(n,p)
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(G::WreathProduct)() = WreathProductElem(G.N(), G.P(), false)
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@ -103,11 +103,11 @@ end
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(G::WreathProduct)(p::Generic.perm) = G(G.N(), p)
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@doc doc"""
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(G::WreathProduct)(n::DirectProductGroupElem)
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(G::WreathProduct)(n::DirectPowerGroupElem)
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> Returns the image of `n` in `G` via embedding `n -> (n,())`. This is the
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> embedding that makes sequence `1 -> N -> G -> P -> 1` exact.
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"""
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(G::WreathProduct)(n::DirectProductGroupElem) = G(n, G.P())
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(G::WreathProduct)(n::DirectPowerGroupElem) = G(n, G.P())
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(G::WreathProduct)(n,p) = G(G.N(n), G.P(p))
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@ -163,7 +163,7 @@ end
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#
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###############################################################################
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(p::perm)(n::DirectProductGroupElem) = DirectProductGroupElem(n.elts[p.d])
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(p::perm)(n::DirectPowerGroupElem) = DirectPowerGroupElem(n.elts[p.d])
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@doc doc"""
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*(g::WreathProductElem, h::WreathProductElem)
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@ -172,7 +172,7 @@ end
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> `g*h = (g.n*g.p(h.n), g.p*h.p)`,
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>
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> where `g.p(h.n)` denotes the action of `g.p::Generic.perm` on
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> `h.n::DirectProductGroupElem` via standard permutation of coordinates.
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> `h.n::DirectPowerGroupElem` via standard permutation of coordinates.
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"""
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function *(g::WreathProductElem, h::WreathProductElem)
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return WreathProductElem(g.n*g.p(h.n), g.p*h.p, false)
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