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