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https://github.com/kalmarek/SmallHyperbolic
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@ -57,40 +57,41 @@ function SL2p_gens(p::Integer)
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end
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end
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return a,b
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return a, b
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end
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function adjacency(ϱ, a, b; prec=256)
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order_a = findfirst(i-> isone(a^i), 1:100)
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order_b = findfirst(i-> isone(b^i), 1:100)
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function adjacency(ϱ, a, b; prec = 256)
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order_a = findfirst(i -> isone(a^i), 1:100)
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order_b = findfirst(i -> isone(b^i), 1:100)
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@assert !isnothing(order_a) && order_a > 1
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@assert !isnothing(order_b) && order_b > 1
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k = order_a-1 + order_b-1
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k = order_a - 1 + order_b - 1
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A = AcbMatrix(ϱ(a), prec=prec)
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B = AcbMatrix(ϱ(b), prec=prec)
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A = AcbMatrix(ϱ(a), prec = prec)
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B = AcbMatrix(ϱ(b), prec = prec)
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res = sum(A^i for i = 1:order_a-1) + sum(B^i for i = 1:order_b-1)
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return Arblib.scalar_div!(res, res, k)
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#return Arblib.scalar_div!(res, res, k)
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return res
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end
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function parse_our_args()
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s = ArgParseSettings()
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@add_arg_table! s begin
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"-p"
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help = "the prime p for which to use PSL(2,p)"
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arg_type = Int
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required = true
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help = "the prime p for which to use PSL(2,p)"
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arg_type = Int
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required = true
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"-a"
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help = "generator a (optional)"
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help = "generator a (optional)"
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"-b"
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help = "generator b (optional)"
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help = "generator b (optional)"
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"--ab"
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help = "array of generators a and b (optional)"
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help = "array of generators a and b (optional)"
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"--precision"
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help = "set the precision of computations"
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arg_type = Int
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default = 128
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help = "set the precision of computations"
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arg_type = Int
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default = 128
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end
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result = parse_args(s)
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@ -113,7 +114,8 @@ end
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parsed_args = parse_our_args()
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const p = let p = parsed_args["p"]
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isprime(p) || @error "You need to provide a prime, ex: `julia adj_psl2_eigvals.jl -p 31`"
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isprime(p) ||
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@error "You need to provide a prime, ex: `julia adj_psl2_eigvals.jl -p 31`"
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p
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end
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@ -124,14 +126,14 @@ open(LOGFILE, "w") do io
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@info "Logging into $LOGFILE"
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with_logger(SimpleLogger(io)) do
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@info "Arguments:" args=parsed_args
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@info "Arguments:" args = parsed_args
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a,b = SL2p_gens(p)
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a, b = SL2p_gens(p)
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a = SL₂{p}(get(parsed_args, "a", a))
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b = SL₂{p}(get(parsed_args, "b", b))
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@info "Generators" a b
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Borel_cosets = let p = p, (a,b) = (a,b)
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Borel_cosets = let p = p, (a, b) = (a, b)
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SL2p, sizes =
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RamanujanGraphs.generate_balls([a, b, inv(a), inv(b)], radius = 21)
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@assert sizes[end] == RamanujanGraphs.order(SL₂{p})
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@ -143,11 +145,11 @@ open(LOGFILE, "w") do io
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for j = 0:(p-1)÷4
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h = PrincipalRepr(
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α => unit_root((p - 1) ÷ 2, j, prec=PRECISION),
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α => unit_root((p - 1) ÷ 2, j, prec = PRECISION),
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Borel_cosets,
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)
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@time adj = adjacency(h, a, b, prec=PRECISION)
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@time adj = adjacency(h, a, b, prec = PRECISION)
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try
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@time evs = let evs = safe_eigvals(adj)
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@ -168,20 +170,20 @@ open(LOGFILE, "w") do io
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if p % 4 == 1
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ub = (p - 1) ÷ 4
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ζ = unit_root((p + 1) ÷ 2, 1, prec=PRECISION)
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ζ = unit_root((p + 1) ÷ 2, 1, prec = PRECISION)
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else # p % 4 == 3
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ub = (p + 1) ÷ 4
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ζ = unit_root((p + 1), 1, prec=PRECISION)
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ζ = unit_root((p + 1), 1, prec = PRECISION)
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end
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for k = 1:ub
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h = DiscreteRepr(
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RamanujanGraphs.GF{p}(1) => unit_root(p, prec=PRECISION),
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RamanujanGraphs.GF{p}(1) => unit_root(p, prec = PRECISION),
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β => ζ^k,
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)
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@time adj = adjacency(h, a, b, prec=PRECISION)
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@time adj = adjacency(h, a, b, prec = PRECISION)
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try
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@time evs = let evs = safe_eigvals(adj)
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@ -196,11 +198,11 @@ open(LOGFILE, "w") do io
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end
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end
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end
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all_large_evs = sort(all_large_evs, rev=true)
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all_large_evs = sort(all_large_evs, rev = true)
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λ = all_large_evs[2]
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ε = (λ - 3)/5
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ε = (λ - 3) / 5
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α = acos(ε)
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α_deg = (α/pi)*180
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α_deg = (α / pi) * 180
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@info "Certified values:" λ ε α α_deg
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end # with_logger
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end # open(logfile)
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@ -10,35 +10,33 @@ const DATA_DIR = joinpath(@__DIR__, "..", "..", "data")
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function _files_with_extension(dir::AbstractString, ext::AbstractString)
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return [
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joinpath(dir, f) for f in readdir(dir) if
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isfile(joinpath(dir, f)) && endswith(f, '.'*ext)
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joinpath(dir, f) for
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f in readdir(dir) if isfile(joinpath(dir, f)) && endswith(f, '.' * ext)
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]
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end
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all_grps_presentations =
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let tables = _files_with_extension(DATA_DIR, "txt")
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mapreduce(parse_grouppresentations_abstract, union, tables) |> Dict
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end
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all_grps_presentations = let tables = _files_with_extension(DATA_DIR, "txt")
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mapreduce(parse_grouppresentations_abstract, union, tables) |> Dict
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end
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grps =
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let csvs = _files_with_extension(DATA_DIR, "csv")
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grps = let csvs = _files_with_extension(DATA_DIR, "csv")
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trGrps = mapreduce(union, csvs) do file
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m = match(r".*_(\d)_(\d)_(\d).csv", basename(file))
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@assert !isnothing(m)
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type = parse.(Int, tuple(m[1], m[2], m[3]))
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trGrps = mapreduce(union, csvs) do file
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m = match(r".*_(\d)_(\d)_(\d).csv", basename(file))
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@assert !isnothing(m)
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type = parse.(Int, tuple(m[1], m[2], m[3]))
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data = readdlm(file, '&')
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labels = Symbol.(replace.(strip.(data[1, :]), ' ' => '_', '-' => '_'))
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groups = data[2:end, :]
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grps = map(enumerate(eachrow(groups))) do (i, props)
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nt = (; (Symbol(l) => v for (l, v) in zip(labels, props))...)
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@debug i, grp_name(nt)
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P = all_grps_presentations[grp_name(nt)]
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grp = TriangleGrp(type, P.generators, P.relations, nt)
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end
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data = readdlm(file, '&')
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labels = Symbol.(replace.(strip.(data[1, :]), ' ' => '_', '-' => '_'))
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groups = data[2:end, :]
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grps = map(enumerate(eachrow(groups))) do (i, props)
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nt = (; (Symbol(l) => v for (l, v) in zip(labels, props))...)
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# @debug i, grp_name(nt)
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P = all_grps_presentations[grp_name(nt)]
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grp = TriangleGrp(type, P.generators, P.relations, nt)
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end
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end
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end
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open(joinpath(DATA_DIR, "triangle_groups.json"), "w") do io
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f(args...) = show_json(args...; indent = 4)
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