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Allow generation of SL(n,p) (matrices over Z/p)
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SL3Z.jl
77
SL3Z.jl
@ -1,25 +1,82 @@
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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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using ProgressMeter
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function SL₃ℤ_generatingset()
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function SL_generatingset(n::Int)
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function E(i::Int, j::Int, N::Int=3)
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@assert i≠j
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k = eye(N)
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k[i,j] = 1
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return k
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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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S = [E(1,2), E(1,3), E(2,3)];
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S = vcat(S, [x' for x in S]);
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S = vcat(S, [inv(x) for x in S]);
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return S
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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 prepare_Δ_sdp_constraints(identity, S)
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