Merge a596fd78f5
into a10132e441
This commit is contained in:
commit
1fcca1bfde
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@ -1,8 +1,8 @@
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# This file is machine-generated - editing it directly is not advised
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julia_version = "1.10.0"
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julia_version = "1.10.1"
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manifest_format = "2.0"
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project_hash = "b435980f07b6de69a5d6ab1d537b9adb4a603bdd"
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project_hash = "7b0e0c798d016406da5e7a51aaec57e29f93bbb7"
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[[deps.AMD]]
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deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse_jll"]
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@ -99,7 +99,7 @@ weakdeps = ["Dates", "LinearAlgebra"]
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[[deps.CompilerSupportLibraries_jll]]
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deps = ["Artifacts", "Libdl"]
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uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
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version = "1.0.5+1"
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version = "1.1.0+0"
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[[deps.Conda]]
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deps = ["Downloads", "JSON", "VersionParsing"]
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@ -418,7 +418,7 @@ version = "0.3.24+0"
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[[deps.OpenBLAS_jll]]
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deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
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uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
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version = "0.3.23+2"
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version = "0.3.23+4"
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[[deps.OpenLibm_jll]]
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deps = ["Artifacts", "Libdl"]
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@ -0,0 +1,162 @@
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using LinearAlgebra
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BLAS.set_num_threads(4)
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ENV["OMP_NUM_THREADS"] = 4
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include(joinpath(@__DIR__, "../test/optimizers.jl"))
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using SCS_MKL_jll
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using Groups
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import Groups.MatrixGroups
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using PropertyT
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import PropertyT.SW as SW
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using PropertyT.PG
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using PropertyT.SA
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include(joinpath(@__DIR__, "argparse.jl"))
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const N = parsed_args["N"]
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const HALFRADIUS = parsed_args["halfradius"]
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const UPPER_BOUND = parsed_args["upper_bound"]
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# fixes/hacks
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import Groups.KnuthBendix
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KnuthBendix.ordering(o::KnuthBendix.WordOrdering) = o
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function KnuthBendix.rewrite!(
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u::KnuthBendix.AbstractWord,
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w::KnuthBendix.AbstractWord,
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o::KnuthBendix.WordOrdering,
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)
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return KnuthBendix.rewrite!(u, w, KnuthBendix.alphabet(o))
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end
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struct Letter{T} <: Groups.GSymbol # letter of an Alphabet
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elt::T
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end
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Base.show(io::IO, tt::Letter) = show(io, tt.elt)
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Base.inv(tt::Letter) = Letter(inv(tt.elt))
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Base.:(==)(tt::Letter, ss::Letter) = tt.elt == ss.elt
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Base.hash(tt::Letter, h::UInt) = hash(tt.elt, hash(Letter, h))
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Base.Base.@propagate_inbounds function Groups.evaluate!(
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v::Tuple{Vararg{T,N}},
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tt::Letter,
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tmp = one(first(v)),
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) where {T,N}
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return Groups.evaluate!(v, tt.elt, tmp)
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end
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function PropertyT._conj(tt::Letter, g)
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G = parent(tt.elt)
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A = alphabet(G)
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w = [A[PropertyT._conj(A[l], g)] for l in word(tt.elt)]
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return Letter(G(w))
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end
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G = let G = SpecialAutomorphismGroup(FreeGroup(N + 1))
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A = alphabet(G)
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lambdas = [Groups.λ(1, i) for i in 2:N+1]
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append!(lambdas, [Groups.λ(i, 1) for i in 2:N+1])
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rhos = [Groups.ϱ(1, i) for i in 2:N+1]
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append!(rhos, [Groups.ϱ(i, 1) for i in 2:N+1])
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_alph = eltype(G)[]
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for i in 2:N+1
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for j in 2:N+1
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i == j && continue
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g = G([A[Groups.ϱ(1, i)], A[Groups.ϱ(j, 1)]])
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h = G([A[Groups.λ(1, i)], A[Groups.λ(j, 1)]])
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push!(_alph, g, h)
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end
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end
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alph = Letter.(_alph)
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AutomorphismGroup(
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FreeGroup(N + 1),
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alph,
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KnuthBendix.LenLex(Groups.Alphabet(alph)),
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Groups.domain(one(G)),
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)
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end
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# @info "Running Δ² - λ·Δ sum of squares decomposition for " G
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@info "computing group algebra structure"
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RG, S, sizes = @time PropertyT.group_algebra(G, halfradius = HALFRADIUS)
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@info "computing WedderburnDecomposition"
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wd = let RG = RG, N = N
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G = StarAlgebras.object(RG)
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P = PermGroup(perm"(2,3)", Perm([1; 1 .+ circshift(1:N, -1)]))
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Σ = Groups.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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act = PropertyT.action_by_conjugation(G, P)
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wdfl = @time SW.WedderburnDecomposition(
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Float64,
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P,
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act,
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basis(RG),
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StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[HALFRADIUS]]),
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)
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end
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@info wd
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Δ = RG(length(S)) - sum(RG(s) for s in S)
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elt = Δ^2;
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unit = Δ;
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warm = nothing
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@info "defining optimization problem"
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@time model, varP = PropertyT.sos_problem_primal(
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elt,
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unit,
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wd;
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upper_bound = UPPER_BOUND,
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augmented = true,
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show_progress = true,
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)
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let status = JuMP.OPTIMIZE_NOT_CALLED, warm = warm, eps = 1e-10
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certified, λ = false, 0.0
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while status ≠ JuMP.OPTIMAL
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@time status, warm = PropertyT.solve(
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model,
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scs_optimizer(;
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linear_solver = SCS.MKLDirectSolver,
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eps = eps,
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max_iters = N * 10_000,
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accel = 50,
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alpha = 1.95,
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),
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warm,
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)
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@info "reconstructing the solution"
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Q = @time let wd = wd, Ps = [JuMP.value.(P) for P in varP], eps = 1e-10
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PropertyT.__droptol!.(Ps, 100eps)
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Qs = real.(sqrt.(Ps))
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PropertyT.__droptol!.(Qs, eps)
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PropertyT.reconstruct(Qs, wd)
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end
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@info "certifying the solution"
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certified, λ = PropertyT.certify_solution(
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elt,
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unit,
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JuMP.objective_value(model),
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Q;
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halfradius = HALFRADIUS,
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augmented = true,
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)
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end
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if certified && λ > 0
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Κ(λ, S) = round(sqrt(2λ / length(S)), Base.RoundDown; digits = 5)
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@info "Certified result: $G has property (T):" N λ Κ(λ, S)
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else
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@info "Could NOT certify the result:" certified λ
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end
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end
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@ -3,6 +3,7 @@ ArgParse = "c7e460c6-2fb9-53a9-8c5b-16f535851c63"
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COSMO = "1e616198-aa4e-51ec-90a2-23f7fbd31d8d"
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Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
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IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
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JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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PermutationGroups = "8bc5a954-2dfc-11e9-10e6-cd969bffa420"
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PropertyT = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
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@ -177,16 +177,17 @@ function _constraints(
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)
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cnstrs = [signed(eltype(mstr))[] for _ in 1:num_constraints]
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LI = LinearIndices(size(mstr))
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star_of = [mstr.basis[SA.star(mstr.basis[i])] for i in 1:size(mstr, 1)]
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for ci in CartesianIndices(size(mstr))
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k = LI[ci]
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i, j = Tuple(ci)
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a_star_b = mstr[-i, j]
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a_star_b = mstr[star_of[i], j]
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push!(cnstrs[a_star_b], k)
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if augmented
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# (1-a)'(1-b) = 1 - a' - b + a'b
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push!(cnstrs[id], k)
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a_star, b = mstr[-i, id], j
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a_star, b = mstr[star_of[i], id], j
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push!(cnstrs[a_star], -k)
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push!(cnstrs[b], -k)
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end
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