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define and use one(::Group)
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@ -17,6 +17,8 @@ import AbstractAlgebra: Group, NCRing, perm
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import MathProgBase.SolverInterface.AbstractMathProgSolver
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AbstractAlgebra.one(G::Group) = G()
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include("laplacians.jl")
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include("RGprojections.jl")
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include("orbitdata.jl")
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@ -70,7 +70,7 @@ end
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function central_projection(RG::GroupRing, chi::AbstractCharacter, T::Type=Rational{Int})
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result = RG(zeros(T, length(RG.basis)))
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dim = chi(RG.group())
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dim = chi(one(RG.group))
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ord = Int(order(RG.group))
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for g in RG.basis
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@ -187,8 +187,8 @@ function rankOne_projections(RBn::GroupRing{G}, T::Type=Rational{Int}) where {G<
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r = collect(1:N)
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for i in 1:N-1
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first_emb = g->Bn(Generic.emb!(Bn.P(), g, view(r, 1:i)))
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last_emb = g->Bn(Generic.emb!(Bn.P(), g, view(r, (i+1):N)))
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first_emb = g->Bn(Generic.emb!(one(Bn.P), g, view(r, 1:i)))
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last_emb = g->Bn(Generic.emb!(one(Bn.P), g, view(r, (i+1):N)))
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Sk_first = (RBn(first_emb, p) for p in Sn_rankOnePr[i])
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Sk_last = (RBn(last_emb, p) for p in Sn_rankOnePr[N-i])
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@ -238,7 +238,7 @@ end
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> The identity element `Id` and binary operation function `op` can be supplied
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> to e.g. take advantage of additive group structure.
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"""
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function generateGroup(gens::Vector{T}, r=2, Id::T=parent(first(gens))(), op=*) where {T<:GroupElem}
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function generateGroup(gens::Vector{T}, r=2, Id::T=one(parent(first(gens))), op=*) where {T<:GroupElem}
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n = 0
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R = 1
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elts = gens
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@ -4,36 +4,26 @@
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#
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###############################################################################
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function spLaplacian(RG::GroupRing, S::AbstractVector{El}, T::Type=Float64) where El
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function spLaplacian(RG::GroupRing, S::AbstractVector, T::Type=Float64)
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result = RG(T)
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id = (El <: AbstractAlgebra.NCRingElem ? one(RG.group) : RG.group())
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result[id] = T(length(S))
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result[one(RG.group)] = T(length(S))
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for s in S
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result[s] -= one(T)
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end
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return result
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end
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function Laplacian(S::AbstractVector{REl}, halfradius) where REl<:AbstractAlgebra.NCRingElem
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R = parent(first(S))
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return Laplacian(S, one(R), halfradius)
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end
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function Laplacian(S::AbstractVector{E}, halfradius) where E<:AbstractAlgebra.GroupElem
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function Laplacian(S::AbstractVector{REl}, halfradius) where REl<:Union{NCRingElem, GroupElem}
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G = parent(first(S))
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return Laplacian(S, G(), halfradius)
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end
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function Laplacian(S, Id, halfradius)
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@info "Generating metric ball of radius" radius=2halfradius
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@time E_R, sizes = Groups.generate_balls(S, Id, radius=2halfradius)
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@time E_R, sizes = Groups.generate_balls(S, one(G), radius=2halfradius)
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@info "Generated balls:" sizes
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@info "Creating product matrix..."
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rdict = GroupRings.reverse_dict(E_R)
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@time pm = GroupRings.create_pm(E_R, rdict, sizes[halfradius]; twisted=true)
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RG = GroupRing(parent(Id), E_R, rdict, pm)
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RG = GroupRing(G, E_R, rdict, pm)
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Δ = spLaplacian(RG, S)
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return Δ
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end
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@ -28,7 +28,7 @@ function OrbitData(RG::GroupRing, autS::Group, verbose=true)
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@time Uπs = [orthSVD(matrix_repr(p, mreps)) for p in autS_mps]
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multiplicities = size.(Uπs,2)
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dimensions = [Int(p[autS()]*Int(order(autS))) for p in autS_mps]
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dimensions = [Int(p[one(autS)]*Int(order(autS))) for p in autS_mps]
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if verbose
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info_strs = ["",
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lpad("multiplicities", 14) * " =" * join(lpad.(multiplicities, 4), ""),
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@ -273,8 +273,8 @@ end
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function AutFG_emb(A::AutGroup, g::WreathProductElem)
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isa(A.objectGroup, FreeGroup) || throw("Not an Aut(Fₙ)")
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parent(g).P.n == length(A.objectGroup.gens) || throw("No natural embedding of $(parent(g)) into $A")
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elt = A()
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Id = parent(g.n.elts[1])()
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elt = one(A)
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Id = one(parent(g.n.elts[1]))
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flips = Groups.AutSymbol[Groups.flip_autsymbol(i) for i in 1:length(g.p.d) if g.n.elts[i] != Id]
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Groups.r_multiply!(elt, flips, reduced=false)
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Groups.r_multiply!(elt, [Groups.perm_autsymbol(g.p)])
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