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fix indentation to 4 spaces
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@ -34,11 +34,11 @@ function compute_SOS(Q::AbstractArray, pm::Array{Int,2}, l::Int)
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result = @parallel (+) for i in 1:size(Q,2)
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groupring_square(Q[:,i], l, pm)
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end
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end
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println("")
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println("")
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return result
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return result
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end
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function compute_SOS(Q::AbstractArray, RG::GroupRing, l::Int)
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@ -175,21 +175,21 @@ function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})
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append!(all_projs, [Qs[N]*RBN(p, g->BN(g)) for p in SNprojs_nc[N]])
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return all_projs
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end
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end
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##############################################################################
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#
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# General Groups Misc
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#
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##############################################################################
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##############################################################################
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#
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# General Groups Misc
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#
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##############################################################################
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doc"""
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doc"""
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products(X::Vector{GroupElem}, Y::Vector{GroupElem}, op=*)
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> Returns a vector of all possible products (or `op(x,y)`), where $x\in X$ and
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> $y\in Y$ are group elements. You may specify which operation is used when
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> forming 'products' by adding `op` (which is `*` by default).
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"""
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function products{T<:GroupElem}(X::AbstractVector{T}, Y::AbstractVector{T}, op=*)
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> Returns a vector of all possible products (or `op(x,y)`), where $x\in X$ and
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> $y\in Y$ are group elements. You may specify which operation is used when
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> forming 'products' by adding `op` (which is `*` by default).
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"""
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function products{T<:GroupElem}(X::AbstractVector{T}, Y::AbstractVector{T}, op=*)
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result = Vector{T}()
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seen = Set{T}()
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for x in X
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@ -202,18 +202,18 @@ function products{T<:GroupElem}(X::AbstractVector{T}, Y::AbstractVector{T}, op=*
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end
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end
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return result
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end
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end
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doc"""
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doc"""
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generateGroup(gens::Vector{GroupElem}, r=2, Id=parent(first(gens))(), op=*)
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> Produces all elements of a group generated by elements in `gens` in ball of
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> radius `r` (word-length metric induced by `gens`).
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> If `r(=2)` is specified the procedure will terminate after generating ball
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> of radius `r` in the word-length metric induced by `gens`.
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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{T<:GroupElem}(gens::Vector{T}, r=2, Id::T=parent(first(gens))(), op=*)
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> Produces all elements of a group generated by elements in `gens` in ball of
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> radius `r` (word-length metric induced by `gens`).
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> If `r(=2)` is specified the procedure will terminate after generating ball
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> of radius `r` in the word-length metric induced by `gens`.
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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{T<:GroupElem}(gens::Vector{T}, r=2, Id::T=parent(first(gens))(), op=*)
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n = 0
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R = 1
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elts = gens
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@ -225,4 +225,4 @@ function generateGroup{T<:GroupElem}(gens::Vector{T}, r=2, Id::T=parent(first(ge
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elts = products(elts, gens, op)
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end
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return elts
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end
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end
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@ -68,9 +68,7 @@ function time_string(elapsedtime, bytes, gctime, allocs)
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return str
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end
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function exists(fname::String)
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return isfile(fname) || islink(fname)
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end
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exists(fname::String) = isfile(fname) || islink(fname)
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function pmΔfilenames(prefix::String)
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isdir(prefix) || mkdir(prefix)
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@ -168,7 +166,6 @@ function λandP(name::String, SDP_problem::JuMP.Model, varλ, varP, warmstart=fa
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throw(ErrorException("Solver did not produce a valid solution!: λ = $λ"))
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end
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return λ, P
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end
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function fillfrominternal!(m::JuMP.Model, traits)
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@ -318,7 +315,6 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
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SDP_problem, λ, P = create_SDP_problem(Δ, sdp_constraints, upper_bound=upper_bound)
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JuMP.setsolver(SDP_problem, solver)
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λ, P = λandP(name, SDP_problem, λ, P)
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end
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@ -334,7 +330,6 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
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isapprox(eigvals(P), abs(eigvals(P)), atol=tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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# @assert P == Symmetric(P)
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@logtime LOGGER Q = real(sqrtm(Symmetric(P)))
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sgap = distance_to_positive_cone(Δ, λ, Q, 2*radius, LOGGER)
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