rework AutFN.jl (most functionality is in Groups module)

AutFN.jl

@@ -1,7 +1,10 @@
 using ArgParse
 
+using Nemo
+Nemo.setpermstyle(:cycles)
+
 using Groups
-using GroupAlgebras
+using GroupRings
 using PropertyT
 
 import SCS.SCSSolver
@@ -16,155 +19,6 @@ Moreover, due to work of Potapchik and Rapinchuk [1] every real representation o
 We need a different approach: Here we actually compute in Aut(𝔽₄)
 =#
 
-import Combinatorics.nthperm
-SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
-
-function generating_set_of_AutF(N::Int)
-
-    indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
-    σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
-    ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
-    λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
-    ɛs = [flip_AutSymbol(i) for i in 1:N];
-
-    S = vcat(ϱs,λs)
-    S = vcat(S..., σs..., ɛs)
-    S = vcat(S..., [inv(g) for g in S])
-    return Vector{AutWord}(unique(S)), one(AutWord)
-end
-
-function generating_set_of_OutF(N::Int)
-    indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
-    ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
-    λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
-    ɛs = [flip_AutSymbol(i) for i in 1:N];
-
-    S = ϱs
-    push!(S, λs..., ɛs...)
-    push!(S,[inv(g) for g in S]...)
-
-    return Vector{AutWord}(unique(S)), one(AutWord)
-end
-
-function generating_set_of_SOutF(N::Int)
-    indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
-    ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
-    λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
-
-    S = ϱs
-    push!(S, λs...)
-    push!(S,[inv(g) for g in S]...)
-
-    return Vector{AutWord}(unique(S)), one(AutWord)
-end
-
-
-function generating_set_of_Sym(N::Int)
-    σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
-
-    S = σs
-    push!(S, [inv(s) for s in S]...)
-    return Vector{AutWord}(unique(S)), one(AutWord)
-end
-
-
-function products(S1::Vector{AutWord}, S2::Vector{AutWord})
-    result = Vector{AutWord}()
-    seen = Set{Vector{FGWord}}()
-    n = length(S1)
-    for (i,x) in enumerate(S1)
-        for y in S2
-            z::AutWord = x*y
-            v::Vector{FGWord} = z(domain)
-            if !in(v, seen)
-                push!(seen, v)
-                push!(result, z)
-            end
-        end
-    end
-    return result
-end
-
-function products_images(S1::Vector{AutWord}, S2::Vector{AutWord})
-    result = Vector{Vector{FGWord}}()
-    seen = Set{Vector{FGWord}}()
-    n = length(S1)
-    for (i,x) in enumerate(S1)
-        z = x(domain)
-        for y in S2
-            v = y(z)
-            if !in(v, seen)
-                push!(seen, v)
-                push!(result, v)
-            end
-        end
-    end
-    return result
-end
-
-function hashed_product{T}(image::T, B, images_dict::Dict{T, Int})
-    n = size(B,1)
-    column = zeros(Int,n)
-    Threads.@threads for j in 1:n
-        w = (B[j])(image)
-        k = images_dict[w]
-        k ≠ 0 || throw(ArgumentError(
-            "($i,$j): $(x^-1)*$y don't seem to be supported on basis!"))
-        column[j] = k
-    end
-    return column
-end
-
-function create_product_matrix(images, basis::Vector{AutWord})
-    n = length(basis)
-    product_matrix = zeros(Int, (n, n));
-    print("Creating hashtable of images...")
-    @time images_dict = Dict{Vector{FGWord}, Int}(x => i
-        for (i,x) in enumerate(images))
-
-    for i in 1:n
-        z = (inv(basis[i]))(domain)
-        product_matrix[i,:] = hashed_product(z, basis, images_dict)
-    end
-    return product_matrix
-end
-
-function generate_balls{T}(S::Vector{T}, Id::T; radius=4)
-    sizes = Vector{Int}()
-    S = vcat([Id], S)
-    B = [Id]
-    for i in 1:radius
-        B = products(B, S);
-        push!(sizes, length(B))
-    end
-    return B, sizes
-end
-
-
-function ΔandSDPconstraints(Id::AutWord, S::Vector{AutWord}, r::Int=2)
-    B, sizes = generate_balls(S, Id, radius=2*r)
-    basis = B[1:sizes[r]]
-    B_images = unique([f(domain) for f in B])
-
-    println("Generated balls of sizes $sizes")
-
-    println("Creating product matrix...")
-    @time pm = create_product_matrix(B_images, basis)
-    println("Creating sdp_constratints...")
-    @time sdp_constraints = PropertyT.constraints_from_pm(pm)
-
-    L_coeff = PropertyT.splaplacian_coeff(S, basis, length(B_images))
-    Δ = PropertyT.GroupAlgebraElement(L_coeff, Array{Int,2}(pm))
-
-    return Δ, sdp_constraints
-end
-
-const symbols =  [FGSymbol("x₁",1), FGSymbol("x₂",1), FGSymbol("x₃",1), FGSymbol("x₄",1), FGSymbol("x₅",1), FGSymbol("x₆",1)]
-
-const TOL=1e-8
-const N = 4
-const domain = Vector{FGWord}(symbols[1:N])
-
 function cpuinfo_physicalcores()
     maxcore = -1
     for line in eachline("/proc/cpuinfo")
@@ -199,7 +53,7 @@ function parse_commandline()
         "-N"
             help = "Consider automorphisms of free group on N generators (default: N=3)"
             arg_type = Int
-            default = 3
+            default = 2
     end
 
     return parse_args(s)
@@ -214,27 +68,41 @@ end
 # S() = generating_set_of_AutF(N)
 
 function main()
+
     parsed_args = parse_commandline()
 
-    tol = parsed_args["tol"]
-    iterations = parsed_args["iterations"]
-
-    solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
-
-    N = parsed_args["N"]
-    upper_bound = parsed_args["upper-bound"]
-
-    name = "SOutF$N"
-    name = name*"-$(string(upper_bound))"
-    S() = generating_set_of_SOutF(N)
-
     if parsed_args["cpus"] ≠ nothing
         if parsed_args["cpus"] > cpuinfo_physicalcores()
             warn("Number of specified cores exceeds the physical core cound. Performance will suffer.")
         end
         Blas.set_num_threads(parsed_args["cpus"])
     end
-    @time PropertyT.check_property_T(name, S, solver, upper_bound, tol, 2)
+
+    tol = parsed_args["tol"]
+    iterations = parsed_args["iterations"]
+
+   #  solver = SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
+    solver = SCSSolver(eps=tol, max_iters=iterations, linearsolver=SCS.Direct)
+
+    N = parsed_args["N"]
+    upper_bound = parsed_args["upper-bound"]
+
+    name = "SOutF$N"
+    name = name*"-$(string(upper_bound))"
+
+    logger = PropertyT.setup_logging(name)
+
+    info(logger, "Group:       $name")
+    info(logger, "Iterations:  $iterations")
+    info(logger, "Precision:   $tol")
+    info(logger, "Upper bound: $upper_bound")
+
+    AutFN = AutGroup(FreeGroup(N), special=true, outer=true)
+    S = generators(AutFN);
+    S = unique([S; [inv(s) for s in S]])
+    Id = AutFN()
+
+    @time PropertyT.check_property_T(name, S, Id, solver, upper_bound, tol, 2)
     return 0
 end