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Numerical values for orientation.

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This commit is contained in:
Stefan Witzel 2020-09-03 12:36:58 +02:00
parent 81a239c325
commit b8aa8be0b3
1 changed files with 49 additions and 28 deletions
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77
adj_psl2_eigvals.jl
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@ -1,6 +1,7 @@
using RamanujanGraphs
using LinearAlgebra
using Nemo
using ArgParse
using Logging
using Dates
@ -15,24 +16,6 @@ function SL2p_gens(p)
@assert isone(a^10)
@assert isone(b^10)
a, b
end
elseif p == 41
a, b = let
a = SL₂{p}([19 26; 29 16])
b = SL₂{p}([0 20; 2 6])
@assert isone(a^10)
@assert isone(b^10)
a, b
end
elseif p == 59
a, b = let
a = SL₂{p}([32 12; 20 2])
b = SL₂{p}([14 18; 45 20])
@assert isone(a^10)
@assert isone(b^10)
a, b
end
elseif p == 109
@ -72,9 +55,42 @@ function adjacency(ϱ, CC, a, b)
return sum(A^i for i = 1:4) + sum(B^i for i = 1:4)
end
function parse_our_args()
s = ArgParseSettings()
@add_arg_table! s begin
"-p"
help = "the prime p for which to use PSL(2,p)"
arg_type = Int
required = true
"-a"
help = "generator a (optional)"
"-b"
help = "generator b (optional)"
"--ab"
help = "array of generators a and b (optional)"
end
result = parse_args(s)
for key in ["a", "b", "ab"]
val = get(result, key, "")
if val != nothing
result[key] = eval(Meta.parse(val))
else
delete!(result, key)
end
end
val = get(result, "ab", "")
if val != ""
result["a"] = val[1]
result["b"] = val[2]
end
result
end
parsed_args = parse_our_args()
const p = try
@assert length(ARGS) == 2 && ARGS[1] == "-p"
p = parse(Int, ARGS[2])
p = parsed_args["p"]
RamanujanGraphs.Primes.isprime(p)
p
catch ex
@ -90,6 +106,10 @@ open(joinpath("log", LOGFILE), "w") do io
CC = AcbField(128)
a,b = SL2p_gens(p)
a = SL₂{p}(get(parsed_args, "a", a))
b = SL₂{p}(get(parsed_args, "b", b))
@info "a = " a
@info "b = " b
Borel_cosets = let p = p, (a,b) = (a,b)
SL2p, sizes =
@ -98,8 +118,7 @@ open(joinpath("log", LOGFILE), "w") do io
RamanujanGraphs.CosetDecomposition(SL2p, Borel(SL₂{p}))
end
all_large_ev = []
all_large_evs = []
let α = RamanujanGraphs.generator(RamanujanGraphs.GF{p}(0))
for j = 0:(p-1)÷4
@ -114,9 +133,9 @@ open(joinpath("log", LOGFILE), "w") do io
@time ev = let evs = safe_eigvals(adj)
_count_multiplicites(evs)
end
all_large_evs = vcat(all_large_evs, [Float64(real(x[1])) for x in ev[1:2]])
@info "Principal Series Representation $j" ev[1:2] ev[end]
all_large_ev = vcat(all_large_ev, ev[1:2])
catch ex
@error "Principal Series Representation $j failed" ex
ex isa InterruptException && rethrow(ex)
@ -148,19 +167,21 @@ open(joinpath("log", LOGFILE), "w") do io
@time ev = let evs = safe_eigvals(adj)
_count_multiplicites(evs)
end
all_large_evs = vcat(all_large_evs, [Float64(real(x[1])) for x in ev[1:2]])
@info "Discrete Series Representation $k" ev[1:2] ev[end]
all_large_ev = vcat(all_large_ev, ev[1:2])
catch ex
@error "Discrete Series Representation $k : failed" ex
ex isa InterruptException && rethrow(ex)
end
end
print(all_large_ev)
# all_large_ev = sort(all_large_ev, rev=true)
# lambda = all_large_ev[2]
# print(lambda, " ", (lambda - 3)/5, " ", acos((lambda-3)/5), " ", acos((lambda-3)/5)/pi*180)
end
all_large_evs = sort(all_large_evs, rev=true)
λ = all_large_evs[2]
ε = (λ - 3)/5
α = acos(ε)
α_deg = α/pi*180
@info "Numerically" λ ε α α_deg
end # with_logger
end # open(logfile)