cleanup Project.toml and fix imports
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Project.toml
23
Project.toml
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@ -4,23 +4,32 @@ authors = ["Marek Kaluba <kalmar@amu.edu.pl>"]
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version = "0.3.2"
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[deps]
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Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
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Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
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IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
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JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
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SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
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[compat]
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IntervalArithmetic = "^0.16.0"
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JuMP = "^0.20.0"
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SCS = "^0.7.0"
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julia = "^1.3.0"
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COSMO = "0.8"
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Groups = "0.7"
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IntervalArithmetic = "0.20"
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JuMP = "1.3"
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SCS = "1.1.0"
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StaticArrays = "1"
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SymbolicWedderburn = "0.3.1"
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julia = "1.6"
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[extras]
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COSMO = "1e616198-aa4e-51ec-90a2-23f7fbd31d8d"
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Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
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Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
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SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
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Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["Test", "SCS"]
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scripts = ["Dates", "Logging", "Serialization", "SCS", "COSMO"]
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test = ["Test", "SCS", "COSMO"]
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@ -3,14 +3,15 @@ module PropertyT
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using LinearAlgebra
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using SparseArrays
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using Dates
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using IntervalArithmetic
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using JuMP
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using Groups
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using StarAlgebras
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import Groups.GroupsCore
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using SymbolicWedderburn
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import SymbolicWedderburn.StarAlgebras
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import SymbolicWedderburn.PermutationGroups
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include("constraint_matrix.jl")
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include("sos_sdps.jl")
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@ -1,5 +1,5 @@
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import SymbolicWedderburn.action
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StarAlgebras.star(g::GroupElement) = inv(g)
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StarAlgebras.star(g::Groups.GroupElement) = inv(g)
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include("alphabet_permutation.jl")
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@ -1,7 +1,9 @@
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## action induced from permuting letters of an alphabet
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import Groups: Constructions
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struct AlphabetPermutation{GEl,I} <: SymbolicWedderburn.ByPermutations
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perms::Dict{GEl,Perm{I}}
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perms::Dict{GEl,PermutationGroups.Perm{I}}
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end
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function AlphabetPermutation(
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@ -10,14 +12,14 @@ function AlphabetPermutation(
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op,
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)
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return AlphabetPermutation(
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Dict(γ => inv(Perm([A[op(l, γ)] for l in A])) for γ in Γ),
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Dict(γ => inv(PermutationGroups.Perm([A[op(l, γ)] for l in A])) for γ in Γ),
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)
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end
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function AlphabetPermutation(A::Alphabet, W::Constructions.WreathProduct, op)
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return AlphabetPermutation(
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Dict(
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w => inv(Perm([A[op(op(l, w.p), w.n)] for l in A])) for
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w => inv(PermutationGroups.Perm([A[op(op(l, w.p), w.n)] for l in A])) for
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w in W
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),
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)
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@ -25,7 +27,7 @@ end
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function SymbolicWedderburn.action(
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act::AlphabetPermutation,
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γ::GroupElement,
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γ::Groups.GroupElement,
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w::Groups.AbstractWord,
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)
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return w^(act.perms[γ])
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@ -33,7 +35,7 @@ end
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function SymbolicWedderburn.action(
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act::AlphabetPermutation,
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γ::GroupElement,
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γ::Groups.GroupElement,
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g::Groups.AbstractFPGroupElement,
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)
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G = parent(g)
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@ -34,7 +34,7 @@ function _fma_SOS_thr!(
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return result
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end
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function _cnstr_sos!(res::AlgebraElement, Q::AbstractMatrix, cnstrs)
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function _cnstr_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix, cnstrs)
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StarAlgebras.zero!(res)
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Q² = Q' * Q
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for (g, A_g) in cnstrs
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@ -43,7 +43,7 @@ function _cnstr_sos!(res::AlgebraElement, Q::AbstractMatrix, cnstrs)
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return res
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end
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function _augmented_sos!(res::AlgebraElement, Q::AbstractMatrix)
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function _augmented_sos!(res::StarAlgebras.AlgebraElement, Q::AbstractMatrix)
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A = parent(res)
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StarAlgebras.zero!(res)
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Q² = Q' * Q
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@ -64,10 +64,10 @@ function _augmented_sos!(res::AlgebraElement, Q::AbstractMatrix)
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return res
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end
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function compute_sos(A::StarAlgebra, Q::AbstractMatrix; augmented::Bool)
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function compute_sos(A::StarAlgebras.StarAlgebra, Q::AbstractMatrix; augmented::Bool)
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if augmented
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z = zeros(eltype(Q), length(basis(A)))
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res = AlgebraElement(z, A)
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res = StarAlgebras.AlgebraElement(z, A)
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return _augmented_sos!(res, Q)
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cnstrs = constraints(basis(A), A.mstructure; augmented=true)
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return _cnstr_sos!(res, Q, cnstrs)
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@ -77,11 +77,11 @@ function compute_sos(A::StarAlgebra, Q::AbstractMatrix; augmented::Bool)
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_fma_SOS_thr!(z, A.mstructure, Q)
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return AlgebraElement(z, A)
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return StarAlgebras.AlgebraElement(z, A)
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end
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end
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function sufficient_λ(residual::AlgebraElement, λ; halfradius)
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function sufficient_λ(residual::StarAlgebras.AlgebraElement, λ; halfradius)
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L1_norm = norm(residual, 1)
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suff_λ = λ - 2.0^(2ceil(log2(halfradius))) * L1_norm
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@ -97,7 +97,7 @@ function sufficient_λ(residual::AlgebraElement, λ; halfradius)
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info_strs = [
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"Numerical metrics of the obtained SOS:",
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"ɛ(elt - λu - ∑ξᵢ*ξᵢ) $eq_sign $(aug(residual))",
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"ɛ(elt - λu - ∑ξᵢ*ξᵢ) $eq_sign $(StarAlgebras.aug(residual))",
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"‖elt - λu - ∑ξᵢ*ξᵢ‖₁ $eq_sign $(L1_norm)",
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" λ $eq_sign $suff_λ",
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]
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@ -107,10 +107,10 @@ function sufficient_λ(residual::AlgebraElement, λ; halfradius)
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end
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function sufficient_λ(
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elt::AlgebraElement,
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order_unit::AlgebraElement,
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elt::StarAlgebras.AlgebraElement,
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order_unit::StarAlgebras.AlgebraElement,
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λ,
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sos::AlgebraElement;
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sos::StarAlgebras.AlgebraElement;
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halfradius
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)
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@ -121,15 +121,15 @@ function sufficient_λ(
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end
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function certify_solution(
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elt::AlgebraElement,
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orderunit::AlgebraElement,
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elt::StarAlgebras.AlgebraElement,
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orderunit::StarAlgebras.AlgebraElement,
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λ,
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Q::AbstractMatrix{<:AbstractFloat};
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halfradius,
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augmented=iszero(aug(elt)) && iszero(aug(orderunit))
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augmented=iszero(StarAlgebras.aug(elt)) && iszero(StarAlgebras.aug(orderunit))
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)
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should_we_augment = !augmented && aug(elt) == aug(orderunit) == 0
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should_we_augment = !augmented && StarAlgebras.aug(elt) == StarAlgebras.aug(orderunit) == 0
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Q = should_we_augment ? augment_columns!(Q) : Q
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@time sos = compute_sos(parent(elt), Q, augmented=augmented)
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@ -46,7 +46,7 @@ function _groupby(keys::AbstractVector{K}, vals::AbstractVector{V}) where {K,V}
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return d
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end
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function laplacians(RG::StarAlgebra, S, grading)
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function laplacians(RG::StarAlgebras.StarAlgebra, S, grading)
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d = _groupby(grading, S)
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Δs = Dict(α => RG(length(Sα)) - sum(RG(s) for s in Sα) for (α, Sα) in d)
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return Δs
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@ -61,7 +61,7 @@ function Adj(rootsystem::AbstractDict, subtype::Symbol)
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+,
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(
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Δα * Δβ for (α, Δα) in rootsystem for (β, Δβ) in rootsystem if
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PropertyT_new.Roots.classify_sub_root_system(
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Roots.classify_sub_root_system(
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roots,
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first(α),
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first(β),
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@ -5,8 +5,8 @@ Formulate the dual to the sum of squares decomposition problem for `X - λ·u`.
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See also [sos_problem_primal](@ref).
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"""
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function sos_problem_dual(
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elt::AlgebraElement,
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order_unit::AlgebraElement=zero(elt);
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elt::StarAlgebras.AlgebraElement,
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order_unit::StarAlgebras.AlgebraElement=zero(elt);
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lower_bound=-Inf
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)
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@assert parent(elt) == parent(order_unit)
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@ -70,7 +70,7 @@ function constraints(
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a, b = basis[i], basis[j]
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push!(cnstrs[basis[one(a)]], k)
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push!(cnstrs[basis[star(a)]], -k)
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push!(cnstrs[basis[StarAlgebras.star(a)]], -k)
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push!(cnstrs[basis[b]], -k)
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end
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end
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@ -80,7 +80,7 @@ function constraints(
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)
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end
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function constraints(A::StarAlgebra; augmented::Bool, twisted::Bool)
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function constraints(A::StarAlgebras.StarAlgebra; augmented::Bool, twisted::Bool)
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mstructure = if StarAlgebras._istwisted(A.mstructure) == twisted
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A.mstructure
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else
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@ -108,10 +108,10 @@ be added to the model. This may improve the accuracy of the solution if
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The default `u = zero(X)` formulates a simple feasibility problem.
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"""
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function sos_problem_primal(
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elt::AlgebraElement,
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order_unit::AlgebraElement=zero(elt);
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elt::StarAlgebras.AlgebraElement,
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order_unit::StarAlgebras.AlgebraElement=zero(elt);
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upper_bound=Inf,
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augmented::Bool=iszero(aug(elt)) && iszero(aug(order_unit))
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augmented::Bool=iszero(StarAlgebras.aug(elt)) && iszero(StarAlgebras.aug(order_unit))
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)
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@assert parent(elt) === parent(order_unit)
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@ -168,22 +168,25 @@ function isorth_projection(ds::SymbolicWedderburn.DirectSummand)
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end
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sos_problem_primal(
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elt::AlgebraElement,
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elt::StarAlgebras.AlgebraElement,
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wedderburn::WedderburnDecomposition;
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kwargs...
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) = sos_problem_primal(elt, zero(elt), wedderburn; kwargs...)
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function sos_problem_primal(
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elt::AlgebraElement,
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orderunit::AlgebraElement,
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elt::StarAlgebras.AlgebraElement,
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orderunit::StarAlgebras.AlgebraElement,
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wedderburn::WedderburnDecomposition;
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upper_bound=Inf,
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augmented=iszero(aug(elt)) && iszero(aug(orderunit))
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augmented=iszero(StarAlgebras.aug(elt)) && iszero(StarAlgebras.aug(orderunit)),
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check_orthogonality=true
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)
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@assert parent(elt) === parent(orderunit)
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if any(!isorth_projection, direct_summands(wedderburn))
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error("Wedderburn decomposition contains a non-orthogonal projection")
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if check_orthogonality
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if any(!isorth_projection, direct_summands(wedderburn))
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error("Wedderburn decomposition contains a non-orthogonal projection")
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end
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end
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feasibility_problem = iszero(orderunit)
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@ -215,8 +218,8 @@ function sos_problem_primal(
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tmps = SymbolicWedderburn._tmps(wedderburn)
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end
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X = convert(Vector{T}, coeffs(elt))
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U = convert(Vector{T}, coeffs(orderunit))
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X = convert(Vector{T}, StarAlgebras.coeffs(elt))
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U = convert(Vector{T}, StarAlgebras.coeffs(orderunit))
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# defining constraints based on the multiplicative structure
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cnstrs = constraints(parent(elt), augmented=augmented, twisted=true)
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@ -278,7 +281,7 @@ function reconstruct!(
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if eltype(res) <: AbstractFloat
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SymbolicWedderburn.zerotol!(tmp2, atol=1e-12)
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end
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tmp2 .*= degree(ds)
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tmp2 .*= SymbolicWedderburn.degree(ds)
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@assert size(tmp2) == size(res)
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@ -291,7 +294,7 @@ function reconstruct!(
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end
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end
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end
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res ./= order(Int, G)
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res ./= Groups.order(Int, G)
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return res
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end
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@ -1,4 +1,4 @@
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import PermutationGroups.AbstractPerm
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import SymbolicWedderburn.PermutationGroups.AbstractPerm
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# move to Groups
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Base.keys(a::Alphabet) = keys(1:length(a))
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@ -15,7 +15,7 @@ isadjacent(σ::AbstractPerm, τ::AbstractPerm, i=1, j=2) =
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(j^σ == i^τ && i^σ ≠ j^τ) # second σ equal to first τ
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function _ncycle(start, length, n=start + length - 1)
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p = Perm(Int8(n))
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p = PermutationGroups.Perm(Int8(n))
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@assert n ≥ start + length - 1
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for k in start:start+length-2
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p[k] = k + 1
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@ -24,7 +24,7 @@ function _ncycle(start, length, n=start + length - 1)
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return p
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end
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alternating_group(n::Integer) = PermGroup([_ncycle(i, 3) for i in 1:n-2])
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alternating_group(n::Integer) = PermutationGroups.PermGroup([_ncycle(i, 3) for i in 1:n-2])
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function small_gens(G::MatrixGroups.SpecialLinearGroup)
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A = alphabet(G)
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@ -46,13 +46,13 @@ function small_gens(G::Groups.AutomorphismGroup{<:FreeGroup})
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return union!(S, inv.(S))
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end
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function small_laplacian(RG::StarAlgebra)
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function small_laplacian(RG::StarAlgebras.StarAlgebra)
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G = StarAlgebras.object(RG)
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S₂ = small_gens(G)
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return length(S₂) * one(RG) - sum(RG(s) for s in S₂)
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end
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function SqAdjOp(A::StarAlgebra, n::Integer, Δ₂=small_laplacian(A))
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function SqAdjOp(A::StarAlgebras.StarAlgebra, n::Integer, Δ₂=small_laplacian(A))
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@assert parent(Δ₂) === A
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alt_n = alternating_group(n)
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