SL(3,Z) specific code

SL(3,Z).jl

@@ -0,0 +1,64 @@
+using JuMP
+import SCS: SCSSolver
+import Mosek: MosekSolver
+
+push!(LOAD_PATH, "./")
+
+using GroupAlgebras
+include("property(T).jl")
+
+
+const VERBOSE=true
+
+
+function E(i::Int, j::Int, N::Int=3)
+    @assert i≠j
+    k = eye(N)
+    k[i,j] = 1
+    return k
+end
+
+function SL_3ZZ_generating_set()
+    S = [E(1,2), E(1,3), E(2,3)];
+    S = vcat(S, [x' for x in S]);
+    S = vcat(S, [inv(x) for x in S]);
+    return S
+end
+
+const ID = eye(3)
+
+const S₁ = SL_3ZZ_generating_set()
+
+
+const TOL=10.0^-7
+#solver = SCSSolver(eps=10.0^-TOL, max_iters=ITERATIONS, verbose=true);
+solver = MosekSolver(MSK_DPAR_INTPNT_CO_TOL_REL_GAP=TOL,
+#                      MSK_DPAR_INTPNT_CO_TOL_PFEAS=1e-15,
+#                      MSK_DPAR_INTPNT_CO_TOL_DFEAS=1e-15,
+#                      MSK_IPAR_PRESOLVE_USE=0,
+                  QUIET=!VERBOSE)
+
+# κ, A = solve_for_property_T(S₁, solver, verbose=VERBOSE)
+
+product_matrix = readdlm("SL₃Z.product_matrix", Int)
+L = readdlm("SL₃Z.Δ.coefficients")[:, 1]
+Δ = GroupAlgebraElement(L, product_matrix)
+# @show Δ
+
+A = readdlm("matrix.A.Mosek")
+κ = readdlm("kappa.Mosek")[1]
+
+# @show eigvals(A)
+@assert isapprox(eigvals(A), abs(eigvals(A)), atol=TOL)
+@assert A == Symmetric(A)
+
+
+const A_sqrt = real(sqrtm(A))
+
+SOS_EOI_fp_L₁, Ω_fp_dist = check_solution(κ, A_sqrt, Δ)
+
+κ_rational = rationalize(BigInt, κ;)
+A_sqrt_rational = rationalize(BigInt, A_sqrt)
+Δ_rational = rationalize(BigInt, Δ)
+
+SOS_EOI_rat_L₁, Ω_rat_dist = check_solution(κ_rational, A_sqrt_rational, Δ_rational)