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mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-12-25 18:15:29 +01:00

iterate directly over groups (removes elements)

This commit is contained in:
kalmarek 2019-01-02 15:49:52 +01:00
parent 4dcc9121a0
commit 44f08716d2
2 changed files with 48 additions and 36 deletions

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@ -26,6 +26,7 @@ for (Gr, Elem) in [(:MltGrp, :MltGrpElem), (:AddGrp, :AddGrpElem)]
eltype(::Type{$Gr{T}}) where T = $Elem{elem_type(T)} eltype(::Type{$Gr{T}}) where T = $Elem{elem_type(T)}
parent_type(::Type{$Elem{T}}) where T = $Gr{parent_type(T)} parent_type(::Type{$Elem{T}}) where T = $Gr{parent_type(T)}
parent(g::$Elem) = $Gr(parent(g.elt)) parent(g::$Elem) = $Gr(parent(g.elt))
length(G::$Gr{<:AbstractAlgebra.Ring}) = order(G.obj)
end end
end end
@ -70,10 +71,9 @@ show(io::IO, g::Union{MltGrpElem, AddGrpElem}) = show(io, g.elt)
gens(F::AbstractAlgebra.Field) = elem_type(F)[gen(F)] gens(F::AbstractAlgebra.Field) = elem_type(F)[gen(F)]
order(G::AddGrp{<:AbstractAlgebra.GFField}) = order(G.obj) order(G::AddGrp{<:AbstractAlgebra.GFField}) = order(G.obj)
elements(G::AddGrp{F}) where F <: AbstractAlgebra.GFField = (G((i-1)*G.obj(1)) for i in 1:order(G))
order(G::MltGrp{<:AbstractAlgebra.GFField}) = order(G.obj) - 1 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))
function iterate(G::AddGrp, s=0) function iterate(G::AddGrp, s=0)
if s >= order(G) if s >= order(G)
@ -283,38 +283,28 @@ end
# #
############################################################################### ###############################################################################
struct DirectPowerIter{GrEl<:AbstractAlgebra.GroupElem} order(G::DirectPowerGroup{N}) where N = order(G.group)^N
N::Int length(G::DirectPowerGroup) = order(G)
elts::Vector{GrEl}
totalorder::Int function iterate(G::DirectPowerGroup{N}) where N
orderG::Int elts = collect(G.group)
indices = CartesianIndices(ntuple(i -> order(G.group), N))
idx, s = iterate(indices)
g = DirectPowerGroupElem(ntuple(i -> elts[idx[i]], N))
return g, (elts, indices, s)
end end
function DirectPowerIter(G::Gr, N::Integer) where {Gr<:AbstractAlgebra.Group} function iterate(G::DirectPowerGroup{N}, state) where N
return DirectPowerIter{elem_type(G)}(N, collect(G), order(G)^N, order(G)) elts, indices, s = state
end res = iterate(indices, s)
if res == nothing
length(DPIter::DirectPowerIter) = DPIter.totalorder
function iterate(DPIter::DirectPowerIter, state=0)
if state >= DPIter.totalorder
return nothing return nothing
else
idx, s = res
end end
idx = Tuple(CartesianIndices(ntuple(i -> DPIter.orderG, DPIter.N))[state+1]) g = DirectPowerGroupElem(ntuple(i -> elts[idx[i]], N))
return DirectPowerGroupElem([DPIter.elts[i] for i in idx]), state+1 return g, (elts, indices, s)
end end
eltype(::Type{DirectPowerIter{GrEl}}) where {GrEl} = DirectPowerGroupElem{GrEl} eltype(::Type{DirectPowerGroup{N, G}}) where {N, G} = DirectPowerGroupElem{N, elem_type(G)}
@doc doc"""
elements(G::DirectPowerGroup)
> Returns `generator` that produces all elements of group `G` (provided that
> `G.group` implements the `elements` method).
"""
elements(G::DirectPowerGroup) = DirectPowerIter(G.group, G.n)
@doc doc"""
order(G::DirectPowerGroup)
> Returns the order (number of elements) in the group.
"""
order(G::DirectPowerGroup) = order(G.group)^G.n

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@ -87,7 +87,7 @@ end
@doc doc""" @doc doc"""
(G::WreathProduct)(n::DirectPowerGroupElem) (G::WreathProduct)(n::DirectPowerGroupElem)
> Returns the image of `n` in `G` via embedding `n -> (n,())`. This is the > Returns the image of `n` in `G` via embedding `n -> (n,())`. This is the
> embedding that makes sequence `1 -> N -> G -> P -> 1` exact. > embedding that makes the sequence `1 -> N -> G -> P -> 1` exact.
""" """
(G::WreathProduct)(n::DirectPowerGroupElem) = G(n, G.P()) (G::WreathProduct)(n::DirectPowerGroupElem) = G(n, G.P())
@ -180,10 +180,32 @@ end
matrix_repr(g::WreathProductElem) = Any[matrix_repr(g.p) g.n] matrix_repr(g::WreathProductElem) = Any[matrix_repr(g.p) g.n]
function elements(G::WreathProduct) function iterate(G::WreathProduct)
Nelts = collect(elements(G.N)) n, state_N = iterate(G.N)
Pelts = collect(G.P) p, state_P = iterate(G.P)
return (WreathProductElem(n, p, false) for n in Nelts, p in Pelts) return G(n,p), (state_N, p, state_P)
end end
function iterate(G::WreathProduct, state)
state_N, p, state_P = state
res = iterate(G.N, state_N)
if res == nothing
resP = iterate(G.P, state_P)
if resP == nothing
return nothing
else
n, state_N = iterate(G.N)
p, state_P = resP
end
else
n, state_N = res
end
return G(n,p), (state_N, p, state_P)
end
eltype(::Type{WreathProduct{N,G,I}}) where {N,G,I} = WreathProductElem{N, elem_type(G), I}
order(G::WreathProduct) = order(G.P)*order(G.N) order(G::WreathProduct) = order(G.P)*order(G.N)
length(G::WreathProduct) = order(G)