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https://github.com/kalmarek/SmallHyperbolic
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update script to use Arblib
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@ -60,11 +60,18 @@ function SL2p_gens(p::Integer)
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return a,b
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end
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function adjacency(ϱ, CC, a, b)
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A = matrix(CC, ϱ(a))
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B = matrix(CC, ϱ(b))
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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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return sum(A^i for i = 1:4) + sum(B^i for i = 1:4)
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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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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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end
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function parse_our_args()
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@ -111,7 +118,6 @@ const LOGFILE = "SL(2,$p)_eigvals_$(now()).log"
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open(joinpath("log", LOGFILE), "w") do io
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with_logger(SimpleLogger(io)) do
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CC = AcbField(128)
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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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@ -125,24 +131,24 @@ open(joinpath("log", LOGFILE), "w") do io
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RamanujanGraphs.CosetDecomposition(SL2p, Borel(SL₂{p}))
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end
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all_large_evs = []
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all_large_evs = Arb[]
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let α = RamanujanGraphs.generator(RamanujanGraphs.GF{p}(0))
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for j = 0:(p-1)÷4
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h = PrincipalRepr(
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α => root_of_unity(CC, (p - 1) ÷ 2, j),
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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, CC, a, b)
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@time adj = adjacency(h, a, b, prec=PRECISION)
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try
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@time ev = let evs = safe_eigvals(adj)
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_count_multiplicites(evs)
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@time evs = let evs = safe_eigvals(adj)
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count_multiplicites(evs)
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end
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all_large_evs = vcat(all_large_evs, [Float64(real(x[1])) for x in ev[1:2]])
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append!(all_large_evs, [real(first(x)) for x in evs[1:2]])
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@info "Principal Series Representation $j" ev[1:2] ev[end]
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@info "Principal Series Representation $j" evs[1:2] evs[end]
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catch ex
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@error "Principal Series Representation $j failed" ex
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ex isa InterruptException && rethrow(ex)
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@ -155,28 +161,28 @@ open(joinpath("log", 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 = root_of_unity(CC, (p + 1) ÷ 2, 1)
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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 = root_of_unity(CC, (p + 1), 1)
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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) => root_of_unity(CC, p),
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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, CC, a, b)
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@time adj = adjacency(h, a, b, prec=PRECISION)
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try
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@time ev = let evs = safe_eigvals(adj)
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_count_multiplicites(evs)
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@time evs = let evs = safe_eigvals(adj)
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count_multiplicites(evs)
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end
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all_large_evs = vcat(all_large_evs, [Float64(real(x[1])) for x in ev[1:2]])
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append!(all_large_evs, [real(first(x)) for x in evs[1:2]])
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@info "Discrete Series Representation $k" ev[1:2] ev[end]
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@info "Discrete Series Representation $k" evs[1:2] evs[end]
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catch ex
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@error "Discrete Series Representation $k : failed" ex
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ex isa InterruptException && rethrow(ex)
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