mirror of
https://github.com/kalmarek/Groups.jl.git
synced 2024-12-25 02:05:30 +01:00
replace DirectProduct -> DirectPower
This commit is contained in:
parent
c72067ec37
commit
38e327c385
@ -1,4 +1,4 @@
|
||||
export DirectProductGroup, DirectProductGroupElem
|
||||
export DirectPowerGroup, DirectPowerGroupElem
|
||||
export MultiplicativeGroup, MltGrp, MltGrpElem
|
||||
export AdditiveGroup, AddGrp, AddGrpElem
|
||||
|
||||
@ -75,8 +75,6 @@ elements(G::AddGrp{F}) where F <: AbstractAlgebra.GFField = (G((i-1)*G.obj(1)) f
|
||||
order(G::MltGrp{<:AbstractAlgebra.GFField}) = order(G.obj) - 1
|
||||
elements(G::MltGrp{F}) where F <: AbstractAlgebra.GFField = (G(i*G.obj(1)) for i in 1:order(G))
|
||||
|
||||
length(G::Union{AddGrp, MltGrp}) = order(G)
|
||||
|
||||
function iterate(G::AddGrp, s=0)
|
||||
if s >= order(G)
|
||||
return nothing
|
||||
@ -100,21 +98,21 @@ end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# DirectProductGroup / DirectProductGroupElem
|
||||
# DirectPowerGroup / DirectPowerGroupElem
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
@doc doc"""
|
||||
DirectProductGroup(G::Group, n::Int) <: Group
|
||||
DirectPowerGroup(G::Group, n::Int) <: Group
|
||||
Implements `n`-fold direct product of `G`. The group operation is
|
||||
`*` distributed component-wise, with component-wise identity as neutral element.
|
||||
"""
|
||||
struct DirectProductGroup{T<:Group} <: Group
|
||||
struct DirectPowerGroup{T<:Group} <: Group
|
||||
group::T
|
||||
n::Int
|
||||
end
|
||||
|
||||
struct DirectProductGroupElem{T<:GroupElem} <: GroupElem
|
||||
struct DirectPowerGroupElem{T<:GroupElem} <: GroupElem
|
||||
elts::Vector{T}
|
||||
end
|
||||
|
||||
@ -124,14 +122,14 @@ end
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
elem_type(::Type{DirectProductGroup{T}}) where {T} =
|
||||
DirectProductGroupElem{elem_type(T)}
|
||||
elem_type(::Type{DirectPowerGroup{T}}) where {T} =
|
||||
DirectPowerGroupElem{elem_type(T)}
|
||||
|
||||
parent_type(::Type{DirectProductGroupElem{T}}) where {T} =
|
||||
DirectProductGroup{parent_type(T)}
|
||||
parent_type(::Type{DirectPowerGroupElem{T}}) where {T} =
|
||||
DirectPowerGroup{parent_type(T)}
|
||||
|
||||
parent(g::DirectProductGroupElem) =
|
||||
DirectProductGroup(parent(first(g.elts)), length(g.elts))
|
||||
parent(g::DirectPowerGroupElem) =
|
||||
DirectPowerGroup(parent(first(g.elts)), length(g.elts))
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
@ -139,45 +137,45 @@ parent(g::DirectProductGroupElem) =
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
size(g::DirectProductGroupElem) = size(g.elts)
|
||||
Base.IndexStyle(::Type{DirectProductGroupElem}) = Base.LinearFast()
|
||||
Base.getindex(g::DirectProductGroupElem, i::Int) = g.elts[i]
|
||||
size(g::DirectPowerGroupElem) = size(g.elts)
|
||||
Base.IndexStyle(::Type{DirectPowerGroupElem}) = Base.LinearFast()
|
||||
Base.getindex(g::DirectPowerGroupElem, i::Int) = g.elts[i]
|
||||
|
||||
function Base.setindex!(g::DirectProductGroupElem{T}, v::T, i::Int) where {T}
|
||||
function Base.setindex!(g::DirectPowerGroupElem{T}, v::T, i::Int) where {T}
|
||||
parent(v) == parent(g.elts[i]) || throw(DomainError(
|
||||
"$g is not an element of $i-th factor of $(parent(G))"))
|
||||
g.elts[i] = v
|
||||
return g
|
||||
end
|
||||
|
||||
function Base.setindex!(g::DirectProductGroupElem{T}, v::S, i::Int) where {T, S}
|
||||
function Base.setindex!(g::DirectPowerGroupElem{T}, v::S, i::Int) where {T, S}
|
||||
g.elts[i] = parent(g.elts[i])(v)
|
||||
return g
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
# DirectProductGroup / DirectProductGroupElem constructors
|
||||
# DirectPowerGroup / DirectPowerGroupElem constructors
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function pow(G::Group, H::Group)
|
||||
function DirectPower(G::Group, H::Group)
|
||||
G == H || throw(DomainError(
|
||||
"Direct Powers are defined only for the same groups"))
|
||||
return DirectProductGroup(G,2)
|
||||
return DirectPowerGroup(G,2)
|
||||
end
|
||||
|
||||
pow(H::Group, G::DirectProductGroup) = pow(G,H)
|
||||
DirectPower(H::Group, G::DirectPowerGroup) = DirectPower(G,H)
|
||||
|
||||
function pow(G::DirectProductGroup, H::Group)
|
||||
function DirectPower(G::DirectPowerGroup, H::Group)
|
||||
G.group == H || throw(DomainError(
|
||||
"Direct products are defined only for the same groups"))
|
||||
return DirectProductGroup(G.group,G.n+1)
|
||||
return DirectPowerGroup(G.group,G.n+1)
|
||||
end
|
||||
|
||||
function pow(R::T, n::Int) where {T<:AbstractAlgebra.Ring}
|
||||
@warn "Creating DirectProduct of the multilplicative group!"
|
||||
return DirectProductGroup(R, n)
|
||||
function DirectPower(R::AbstractAlgebra.Ring, n::Int)
|
||||
@warn "Creating DirectPower of the multilplicative group!"
|
||||
return DirectPowerGroup(R, n)
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
@ -187,25 +185,25 @@ end
|
||||
###############################################################################
|
||||
|
||||
@doc doc"""
|
||||
(G::DirectProductGroup)(a::Vector, check::Bool=true)
|
||||
(G::DirectPowerGroup)(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)
|
||||
function (G::DirectPowerGroup)(a::Vector, check::Bool=true)
|
||||
if check
|
||||
G.n == length(a) || throw(DomainError(
|
||||
"Can not coerce to DirectProductGroup: lengths differ"))
|
||||
"Can not coerce to DirectPowerGroup: lengths differ"))
|
||||
a = (G.group).(a)
|
||||
end
|
||||
return DirectProductGroupElem(a)
|
||||
return DirectPowerGroupElem(a)
|
||||
end
|
||||
|
||||
(G::DirectProductGroup)() = DirectProductGroupElem([G.group() for _ in 1:G.n])
|
||||
(G::DirectPowerGroup)() = DirectPowerGroupElem([G.group() for _ in 1:G.n])
|
||||
|
||||
(G::DirectProductGroup)(g::DirectProductGroupElem) = G(g.elts)
|
||||
(G::DirectPowerGroup)(g::DirectPowerGroupElem) = G(g.elts)
|
||||
|
||||
(G::DirectProductGroup)(a::Vararg{T, N}) where {T, N} = G([a...])
|
||||
(G::DirectPowerGroup)(a::Vararg{T, N}) where {T, N} = G([a...])
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
@ -213,12 +211,12 @@ end
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function hash(G::DirectProductGroup, h::UInt)
|
||||
return hash(G.group, hash(G.n, hash(DirectProductGroup,h)))
|
||||
function hash(G::DirectPowerGroup, h::UInt)
|
||||
return hash(G.group, hash(G.n, hash(DirectPowerGroup,h)))
|
||||
end
|
||||
|
||||
function hash(g::DirectProductGroupElem, h::UInt)
|
||||
return hash(g.elts, hash(parent(g), hash(DirectProductGroupElem, h)))
|
||||
function hash(g::DirectPowerGroupElem, h::UInt)
|
||||
return hash(g.elts, hash(parent(g), hash(DirectPowerGroupElem, h)))
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
@ -227,11 +225,11 @@ end
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
function show(io::IO, G::DirectProductGroup)
|
||||
function show(io::IO, G::DirectPowerGroup)
|
||||
print(io, "$(G.n)-fold direct product of $(G.group)")
|
||||
end
|
||||
|
||||
function show(io::IO, g::DirectProductGroupElem)
|
||||
function show(io::IO, g::DirectPowerGroupElem)
|
||||
print(io, "[$(join(g.elts,","))]")
|
||||
end
|
||||
|
||||
@ -242,20 +240,20 @@ end
|
||||
###############################################################################
|
||||
|
||||
@doc doc"""
|
||||
==(g::DirectProductGroup, h::DirectProductGroup)
|
||||
==(g::DirectPowerGroup, h::DirectPowerGroup)
|
||||
> Checks if two direct product groups are the same.
|
||||
"""
|
||||
function (==)(G::DirectProductGroup, H::DirectProductGroup)
|
||||
function (==)(G::DirectPowerGroup, H::DirectPowerGroup)
|
||||
G.group == H.group || return false
|
||||
G.n == G.n || return false
|
||||
return true
|
||||
end
|
||||
|
||||
@doc doc"""
|
||||
==(g::DirectProductGroupElem, h::DirectProductGroupElem)
|
||||
==(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
|
||||
> Checks if two direct product group elements are the same.
|
||||
"""
|
||||
function (==)(g::DirectProductGroupElem, h::DirectProductGroupElem)
|
||||
function (==)(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
|
||||
g.elts == h.elts || return false
|
||||
return true
|
||||
end
|
||||
@ -267,26 +265,26 @@ end
|
||||
###############################################################################
|
||||
|
||||
@doc doc"""
|
||||
*(g::DirectProductGroupElem, h::DirectProductGroupElem)
|
||||
*(g::DirectPowerGroupElem, h::DirectPowerGroupElem)
|
||||
> Return the direct-product group operation of elements, i.e. component-wise
|
||||
> operation as defined by `operations` field of the parent object.
|
||||
"""
|
||||
function *(g::DirectProductGroupElem, h::DirectProductGroupElem, check::Bool=true)
|
||||
function *(g::DirectPowerGroupElem, h::DirectPowerGroupElem, check::Bool=true)
|
||||
if check
|
||||
parent(g) == parent(h) || throw(DomainError(
|
||||
"Can not multiply elements of different groups!"))
|
||||
end
|
||||
return DirectProductGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
|
||||
return DirectPowerGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
|
||||
end
|
||||
|
||||
^(g::DirectProductGroupElem, n::Integer) = Base.power_by_squaring(g, n)
|
||||
^(g::DirectPowerGroupElem, n::Integer) = Base.power_by_squaring(g, n)
|
||||
|
||||
@doc doc"""
|
||||
inv(g::DirectProductGroupElem)
|
||||
inv(g::DirectPowerGroupElem)
|
||||
> Return the inverse of the given element in the direct product group.
|
||||
"""
|
||||
function inv(g::DirectProductGroupElem{T}) where {T<:GroupElem}
|
||||
return DirectProductGroupElem([inv(a) for a in g.elts])
|
||||
function inv(g::DirectPowerGroupElem{T}) where {T<:GroupElem}
|
||||
return DirectPowerGroupElem([inv(a) for a in g.elts])
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
@ -313,20 +311,20 @@ function iterate(DPIter::DirectPowerIter, state=0)
|
||||
return nothing
|
||||
end
|
||||
idx = Tuple(CartesianIndices(ntuple(i -> DPIter.orderG, DPIter.N))[state+1])
|
||||
return DirectProductGroupElem([DPIter.elts[i] for i in idx]), state+1
|
||||
return DirectPowerGroupElem([DPIter.elts[i] for i in idx]), state+1
|
||||
end
|
||||
|
||||
eltype(::Type{DirectPowerIter{GrEl}}) where {GrEl} = DirectProductGroupElem{GrEl}
|
||||
eltype(::Type{DirectPowerIter{GrEl}}) where {GrEl} = DirectPowerGroupElem{GrEl}
|
||||
|
||||
@doc doc"""
|
||||
elements(G::DirectProductGroup)
|
||||
elements(G::DirectPowerGroup)
|
||||
> Returns `generator` that produces all elements of group `G` (provided that
|
||||
> `G.group` implements the `elements` method).
|
||||
"""
|
||||
elements(G::DirectProductGroup) = DirectPowerIter(G.group, G.n)
|
||||
elements(G::DirectPowerGroup) = DirectPowerIter(G.group, G.n)
|
||||
|
||||
@doc doc"""
|
||||
order(G::DirectProductGroup)
|
||||
order(G::DirectPowerGroup)
|
||||
> Returns the order (number of elements) in the group.
|
||||
"""
|
||||
order(G::DirectProductGroup) = order(G.group)^G.n
|
||||
order(G::DirectPowerGroup) = order(G.group)^G.n
|
||||
@ -72,7 +72,7 @@ include("FreeGroup.jl")
|
||||
include("FPGroups.jl")
|
||||
include("AutGroup.jl")
|
||||
|
||||
include("DirectProducts.jl")
|
||||
include("DirectPower.jl")
|
||||
include("WreathProducts.jl")
|
||||
|
||||
###############################################################################
|
||||
|
||||
@ -20,21 +20,21 @@ export WreathProduct, WreathProductElem
|
||||
* `P::Generic.PermGroup` : full `PermutationGroup`
|
||||
"""
|
||||
struct WreathProduct{T<:Group, I<:Integer} <: Group
|
||||
N::DirectProductGroup{T}
|
||||
N::DirectPowerGroup{T}
|
||||
P::Generic.PermGroup{I}
|
||||
|
||||
function WreathProduct{T, I}(Gr::T, P::Generic.PermGroup{I}) where {T, I}
|
||||
N = DirectProductGroup(Gr, Int(P.n))
|
||||
N = DirectPowerGroup(Gr, Int(P.n))
|
||||
return new(N, P)
|
||||
end
|
||||
end
|
||||
|
||||
struct WreathProductElem{T<:GroupElem, I<:Integer} <: GroupElem
|
||||
n::DirectProductGroupElem{T}
|
||||
n::DirectPowerGroupElem{T}
|
||||
p::Generic.perm{I}
|
||||
# parent::WreathProduct
|
||||
|
||||
function WreathProductElem{T, I}(n::DirectProductGroupElem{T}, p::Generic.perm{I},
|
||||
function WreathProductElem{T, I}(n::DirectPowerGroupElem{T}, p::Generic.perm{I},
|
||||
check::Bool=true) where {T, I}
|
||||
if check
|
||||
length(n.elts) == length(p.d) || throw(DomainError(
|
||||
@ -65,7 +65,7 @@ parent(g::WreathProductElem) = WreathProduct(parent(g.n[1]), parent(g.p))
|
||||
|
||||
WreathProduct(G::T, P::Generic.PermGroup{I}) where {T, I} = WreathProduct{T, I}(G, P)
|
||||
|
||||
WreathProductElem(n::DirectProductGroupElem{T}, p::Generic.perm{I}, check=true) where {T,I} = WreathProductElem{T,I}(n, p, check)
|
||||
WreathProductElem(n::DirectPowerGroupElem{T}, p::Generic.perm{I}, check=true) where {T,I} = WreathProductElem{T,I}(n, p, check)
|
||||
|
||||
###############################################################################
|
||||
#
|
||||
@ -88,11 +88,11 @@ function (G::WreathProduct)(g::WreathProductElem)
|
||||
end
|
||||
|
||||
@doc doc"""
|
||||
(G::WreathProduct)(n::DirectProductGroupElem, p::Generic.perm)
|
||||
(G::WreathProduct)(n::DirectPowerGroupElem, p::Generic.perm)
|
||||
> Creates an element of wreath product `G` by coercing `n` and `p` to `G.N` and
|
||||
> `G.P`, respectively.
|
||||
"""
|
||||
(G::WreathProduct)(n::DirectProductGroupElem, p::Generic.perm) = WreathProductElem(n,p)
|
||||
(G::WreathProduct)(n::DirectPowerGroupElem, p::Generic.perm) = WreathProductElem(n,p)
|
||||
|
||||
(G::WreathProduct)() = WreathProductElem(G.N(), G.P(), false)
|
||||
|
||||
@ -103,11 +103,11 @@ end
|
||||
(G::WreathProduct)(p::Generic.perm) = G(G.N(), p)
|
||||
|
||||
@doc doc"""
|
||||
(G::WreathProduct)(n::DirectProductGroupElem)
|
||||
(G::WreathProduct)(n::DirectPowerGroupElem)
|
||||
> 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())
|
||||
(G::WreathProduct)(n::DirectPowerGroupElem) = G(n, G.P())
|
||||
|
||||
(G::WreathProduct)(n,p) = G(G.N(n), G.P(p))
|
||||
|
||||
@ -163,7 +163,7 @@ end
|
||||
#
|
||||
###############################################################################
|
||||
|
||||
(p::perm)(n::DirectProductGroupElem) = DirectProductGroupElem(n.elts[p.d])
|
||||
(p::perm)(n::DirectPowerGroupElem) = DirectPowerGroupElem(n.elts[p.d])
|
||||
|
||||
@doc doc"""
|
||||
*(g::WreathProductElem, h::WreathProductElem)
|
||||
@ -172,7 +172,7 @@ end
|
||||
> `g*h = (g.n*g.p(h.n), g.p*h.p)`,
|
||||
>
|
||||
> where `g.p(h.n)` denotes the action of `g.p::Generic.perm` on
|
||||
> `h.n::DirectProductGroupElem` via standard permutation of coordinates.
|
||||
> `h.n::DirectPowerGroupElem` via standard permutation of coordinates.
|
||||
"""
|
||||
function *(g::WreathProductElem, h::WreathProductElem)
|
||||
return WreathProductElem(g.n*g.p(h.n), g.p*h.p, false)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user