143 lines
3.1 KiB
Julia
143 lines
3.1 KiB
Julia
using JLD
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using JuMP
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import Primes: isprime
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import SCS: SCSSolver
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import Mosek: MosekSolver
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using Mods
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using Groups
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function SL_generatingset(n::Int)
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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S = [E(i,j,N=n) for (i,j) in indexing];
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S = vcat(S, [convert(Array{Int,2},x') for x in S]);
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S = vcat(S, [convert(Array{Int,2},inv(x)) for x in S]);
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return unique(S)
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end
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function E(i::Int, j::Int; val=1, N::Int=3, mod=Inf)
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@assert i≠j
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m = eye(Int, N)
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m[i,j] = val
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if mod == Inf
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return m
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else
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return [Mod(x,mod) for x in m]
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end
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end
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function cofactor(i,j,M)
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z1 = ones(Bool,size(M,1))
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z1[i] = false
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z2 = ones(Bool,size(M,2))
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z2[j] = false
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return M[z1,z2]
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end
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import Base.LinAlg.det
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function det(M::Array{Mod,2})
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if size(M,1) ≠ size(M,2)
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d = Mod(0,M[1,1].mod)
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elseif size(M,1) == 2
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d = M[1,1]*M[2,2] - M[1,2]*M[2,1]
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else
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d = zero(eltype(M))
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for i in 1:size(M,1)
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d += (-1)^(i+1)*M[i,1]*det(cofactor(i,1,M))
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end
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end
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# @show (M, d)
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return d
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end
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function adjugate(M)
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K = similar(M)
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for i in 1:size(M,1), j in 1:size(M,2)
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K[j,i] = (-1)^(i+j)*det(cofactor(i,j,M))
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end
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return K
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end
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import Base: inv, one, zero, *
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one(::Type{Mod}) = 1
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zero(::Type{Mod}) = 0
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zero(x::Mod) = Mod(x.mod)
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function inv(M::Array{Mod,2})
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d = det(M)
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d ≠ 0*d || thow(ArgumentError("Matrix is not invertible!"))
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return inv(det(M))*adjugate(M)
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return adjugate(M)
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end
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function SL_generatingset(n::Int, p::Int)
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(p > 1 && n > 1) || throw(ArgumentError("Both n and p should be integers!"))
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isprime(p) || throw(ArgumentError("p should be a prime number!"))
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indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
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S = [E(i,j, N=n, mod=p) for (i,j) in indexing]
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S = vcat(S, [inv(s) for s in S])
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S = vcat(S, [permutedims(x, [2,1]) for x in S]);
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return unique(S)
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end
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function products{T}(U::AbstractVector{T}, V::AbstractVector{T})
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result = Vector{T}()
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for u in U
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for v in V
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push!(result, u*v)
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end
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end
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return unique(result)
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end
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function ΔandSDPconstraints(identity, S)
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B₁ = vcat([identity], S)
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B₂ = products(B₁, B₁);
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B₃ = products(B₁, B₂);
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B₄ = products(B₁, B₃);
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@assert B₄[1:length(B₂)] == B₂
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product_matrix = create_product_matrix(B₄,length(B₂));
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sdp_constraints = constraints_from_pm(product_matrix, length(B₄))
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L_coeff = splaplacian_coeff(S, B₂, length(B₄));
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Δ = GroupAlgebraElement(L_coeff, product_matrix)
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return Δ, sdp_constraints
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end
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@everywhere push!(LOAD_PATH, "./")
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using GroupAlgebras
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include("property(T).jl")
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const N = 3
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const name = "SL$(N)Z"
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const ID = eye(Int, N)
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S() = SL_generatingset(N)
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const upper_bound=0.27
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# const p = 7
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# const upper_bound=0.738 # (N,p) = (3,7)
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# const name = "SL($N,$p)"
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# const ID = [Mod(x,p) for x in eye(Int,N)]
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# S() = SL_generatingset(N, p)
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BLAS.set_num_threads(4)
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@time check_property_T(name, ID, S; verbose=true, tol=1e-10, upper_bound=upper_bound)
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