Add SL_orbit.jl

SL_orbit.jl

@@ -0,0 +1,145 @@
+include("Orb_AutFN.jl")
+
+###############################################################################
+#
+#  Action of WreathProductElems on Nemo.MatElem
+#
+###############################################################################
+
+function matrix_emb(MM::Nemo.MatSpace, g::WreathProducts.WreathProductElem)
+    parent(g).P.n == MM.cols == MM.rows || throw("No natural embedding of $(parent(g)) in ")
+    powers = [(elt == parent(elt)() ? 0: 1) for elt in g.n.elts]
+    elt = diagm([(-1)^(elt == parent(elt)() ? 0: 1) for elt in g.n.elts])
+    return MM(elt)*MM(Nemo.matrix_repr(g.p)')
+end
+
+function (g::WreathProducts.WreathProductElem)(A::Nemo.MatElem)
+    G = matrix_emb(parent(A), g)
+    inv_G = matrix_emb(parent(A), inv(g))
+    return G*A*inv_G
+end
+
+###############################################################################
+#
+#  Generating set
+#
+###############################################################################
+
+function E(i::Int, j::Int, M::Nemo.MatSpace)
+    @assert i≠j
+    m = one(M)
+    m[i,j] = m[1,1]
+    return m
+end
+
+function SLsize(n,p)
+    result = BigInt(1)
+    for k in 0:n-1
+        result *= p^n - p^k
+    end
+    return div(result, p-1)
+end
+
+function SL_generatingset(n::Int)
+    indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
+    G = Nemo.MatrixSpace(Nemo.ZZ, n, n)
+    S = [E(i,j,G) for (i,j) in indexing];
+    S = vcat(S, [transpose(x) for x in S]);
+    return G, unique(S)
+end
+
+function SL_generatingset(n::Int, p::Int)
+    p == 0 && return SL_generatingset(n)
+    (p > 1 && n > 1) || throw("Both n and p should be positive integers!")
+    @info("Size(SL($n,$p)) = $(SLsize(n,p))")
+    F = Nemo.ResidueRing(Nemo.ZZ, p)
+    G = Nemo.MatrixSpace(F, n, n)
+    indexing = [(i,j) for i in 1:n for j in 1:n if i≠j]
+    S = [E(i, j, G) for (i,j) in indexing]
+    S = vcat(S, [transpose(x) for x in S])
+    return G, unique(S)
+end
+
+###############################################################################
+#
+#  Parsing command line
+#
+###############################################################################
+
+function parse_commandline()
+    settings = ArgParseSettings()
+
+    @add_arg_table settings begin
+        "--tol"
+            help = "set numerical tolerance for the SDP solver (default: 1e-5)"
+            arg_type = Float64
+            default = 1e-5
+        "--iterations"
+            help = "set maximal number of iterations for the SDP solver (default: 20000)"
+            arg_type = Int
+            default = 20000
+        "--upper-bound"
+            help = "Set an upper bound for the spectral gap (default: Inf)"
+            arg_type = Float64
+            default = Inf
+        "--cpus"
+            help = "Set number of cpus used by solver (default: auto)"
+            arg_type = Int
+            required = false
+        "-N"
+            help = "Consider automorphisms of free group on N generators (default: N=2)"
+            arg_type = Int
+            default = 2
+        "-p"
+            help = "Matrices over filed of p-elements (default: p=0 => over ZZ)"
+            arg_type = Int
+            default = 0
+        "--radius"
+            help = "Find the decomposition over B_r(e,S)"
+            arg_type = Int
+            default = 2
+    end
+
+    return parse_args(settings)
+end
+
+###############################################################################
+#
+#  main
+#
+###############################################################################
+
+function main()
+   parsed_args = parse_commandline()
+
+   N = parsed_args["N"]
+   p = parsed_args["p"]
+
+   if p == 0
+      dirname = "SL$(N)Z"
+   else
+      dirname = "SL$(N)_$p"
+   end
+
+   radius = parsed_args["radius"]
+   dirname = "$(dirname)_r=$radius"
+
+   isdir(dirname) || mkdir(dirname)
+   logger = PropertyT.setup_logging(dirname)
+
+   G, S = SL_generatingset(N, p)
+   info(logger, G)
+   info(logger, "Symmetric generating set of size $(length(S))")
+   info(logger, S)
+   AutS = WreathProduct(Nemo.FiniteField(2,1, "a")[1], PermutationGroup(N))
+
+   tol = parsed_args["tol"]
+   iterations = parsed_args["iterations"]
+   upper_bound = parsed_args["upper-bound"]
+
+   solver = SCS.SCSSolver(eps=tol, max_iters=iterations, verbose=true, linearsolver=SCS.Indirect)
+
+   orbit_check_propertyT(logger, dirname, G, S, AutS, solver, upper_bound)
+end
+
+main()