SmallHyperbolic/PSL.jl

using Nemo
using DelimitedFiles

include("src/nemo_utils.jl")


const PRECISION = 256

function parse_eval(arg, expr_str, var)
    ex = Meta.parse(expr_str)
	svar = :($var)
    return @eval begin
        let $svar = $arg
            $ex
        end
    end
end

function load_discrete_repr(i, q = 109; CC = AcbField(PRECISION))
    ζ = root_of_unity(CC, (q - 1) ÷ 2)
    degree = q - 1

    ra = readdlm(
        "data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_a.txt",
        ',',
        String,
    )
    a = matrix(CC, [CC(parse_eval(ζ, s, :Z)) for s in ra[1:degree, 1:degree]])

    rb = readdlm(
        "data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_b.txt",
        ',',
        String,
    )
    b = matrix(CC, [CC(parse_eval(ζ, s, :Z)) for s in rb[1:degree, 1:degree]])

    return a, b
end

function load_principal_repr(i, q = 109; CC = AcbField(PRECISION))
    ζ = root_of_unity(CC, (q - 1) ÷ 2)
    degree = q + 1

    ra = readdlm(
        "data/Principal reps PSL(2, $q)/principal_rep_$(i)_a.txt",
        ',',
        String,
    )
    a = matrix(CC, [CC(parse_eval(ζ, s, :zz)) for s in ra[1:degree, 1:degree]])

    rb = readdlm(
        "data/Principal reps PSL(2, $q)/principal_rep_$(i)_b.txt",
        ',',
        String,
    )
    b = matrix(CC, [CC(parse_eval(ζ, s, :zz)) for s in rb[1:degree, 1:degree]])

    return a, b
end



function safe_eigvals(m::acb_mat)
    CC = base_ring(m)
    X = matrix(CC, rand(CC, size(m)))
    return eigvals(X * m * inv(X))
end

for i in 0:27
	try
		a,b = load_principal_repr(i)
		adjacency = sum([[a^i for i in 1:4]; [b^i for i in 1:4]])
		@time evc = safe_eigvals(adjacency)
		ev = sort(real.(first.(evc)), lt=<, rev=true)
		@info "Principal Series Representation $i" ev[1:2]
	catch ex
		@error "Principal Series Representation $i failed"
		ex isa InterruptException && throw(ex)
	end
end

for i in 1:27
	try
		a,b = load_discrete_repr(i)
		adjacency = sum([[a^i for i in 1:4]; [b^i for i in 1:4]])
		@time evc = safe_eigvals(adjacency)
		ev = sort(real.(first.(evc)), lt=<, rev=true)
		@info "Discrete Series Representation $i" ev[1:2]
	catch ex
		@error "Discrete Series Representation $i : failed"
		ex isa InterruptException && rethrow(ex)
	end
end