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tidy ValidatedNumerics and move functions
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@ -1,7 +1,10 @@
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using ProgressMeter
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using ValidatedNumerics
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import Base: rationalize
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using ValidatedNumerics
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setrounding(Interval, :narrow)
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setdisplay(:standard)
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function EOI{T<:Number}(Δ::GroupAlgebraElement{T}, κ::T)
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return Δ*Δ - κ*Δ
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end
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@ -41,6 +44,22 @@ function correct_to_augmentation_ideal{T<:Rational}(sqrt_matrix::Array{T,2})
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return sqrt_corrected
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end
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import ValidatedNumerics.±
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function (±){T<:Number}(X::AbstractArray{T}, tol::Real)
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r{T}(x::T) = (x == zero(T)? @biginterval(0) : x ± tol)
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return r.(X)
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end
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(±)(X::GroupAlgebraElement, tol::Real) = GroupAlgebraElement(X.coefficients ± tol, X.product_matrix)
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function Base.rationalize{T<:Integer, S<:Real}(::Type{T},
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X::AbstractArray{S}; tol::Real=eps(eltype(X)))
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r(x) = rationalize(T, x, tol=tol)
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return r.(X)
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end
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ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
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function check_solution{T<:Number}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlgebraElement{T}; verbose=true, augmented=false)
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result = compute_SOS(sqrt_matrix, Δ)
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if augmented
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@ -67,21 +86,10 @@ function check_solution{T<:Number}(κ::T, sqrt_matrix::Array{T,2}, Δ::GroupAlge
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return distance_to_cone
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end
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import ValidatedNumerics.±
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function (±)(X::AbstractArray, tol::Real)
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r{T}(x::T) = ( x==zero(T) ? @interval(x) : x ± tol)
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return r.(X)
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end
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(±)(X::GroupAlgebraElement, tol::Real) = GroupAlgebraElement(X.coefficients ± tol, X.product_matrix)
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function Base.rationalize{T<:Integer, S<:Real}(::Type{T},
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X::AbstractArray{S}; tol::Real=eps(eltype(X)))
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r(x) = rationalize(T, x, tol=tol)
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return r.(X)
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end
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ℚ(x, tol::Real) = rationalize(BigInt, x, tol=tol)
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function ℚ_distance_to_positive_cone(Δ::GroupAlgebraElement, κ, A;
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tol=1e-7, verbose=true, rational=false)
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