mirror of
https://github.com/kalmarek/SmallHyperbolic
synced 2024-09-01 13:25:35 +02:00
103 lines
2.5 KiB
Julia
103 lines
2.5 KiB
Julia
using Nemo
|
|
using DelimitedFiles
|
|
using LinearAlgebra
|
|
|
|
include("src/nemo_utils.jl")
|
|
|
|
const PRECISION = 256
|
|
|
|
function parse_eval(expr_str, value, var_name)
|
|
ex = Meta.parse(expr_str)
|
|
svar = :($var_name)
|
|
return @eval begin
|
|
let $svar = $value
|
|
$ex
|
|
end
|
|
end
|
|
end
|
|
|
|
function read_eval(fname, var_name, value)
|
|
a = readdlm(fname, ',', String)
|
|
a .= replace.(a, '/' => "//")
|
|
return parse_eval.(a, value, var_name)
|
|
end
|
|
|
|
function load_discrete_repr(i, q = 109; CC = AcbField(PRECISION))
|
|
ζ = root_of_unity(CC, (q + 1) ÷ 2)
|
|
degree = q - 1
|
|
|
|
ra = read_eval(
|
|
"data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_a.txt",
|
|
:Z,
|
|
ζ,
|
|
)
|
|
a = matrix(CC, [CC(s) for s in ra[1:degree, 1:degree]])
|
|
|
|
rb = read_eval(
|
|
"data/Discrete reps PSL(2, $q)/discrete_rep_$(i)_b.txt",
|
|
:Z,
|
|
ζ,
|
|
)
|
|
b = matrix(CC, [CC(s) for s in rb[1:degree, 1:degree]])
|
|
@assert contains(det(a), 1)
|
|
@assert contains(det(b), 1)
|
|
|
|
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 = read_eval(
|
|
"data/Principal reps PSL(2, $q)/principal_rep_$(i)_a.txt",
|
|
:zz,
|
|
ζ,
|
|
)
|
|
a = matrix(CC, [CC(z) for z in ra[1:degree, 1:degree]])
|
|
|
|
rb = read_eval(
|
|
"data/Principal reps PSL(2, $q)/principal_rep_$(i)_b.txt",
|
|
:zz,
|
|
ζ,
|
|
)
|
|
b = matrix(CC, [CC(z) for z in rb[1:degree, 1:degree]])
|
|
@assert contains(det(a), 1)
|
|
@assert contains(det(b), 1)
|
|
|
|
return a, b
|
|
end
|
|
|
|
if !isinteractive()
|
|
|
|
for i = 0:27
|
|
try
|
|
a, b = load_principal_repr(i)
|
|
adjacency = sum(a^i for i = 1:4) + sum(b^i for i = 1:4)
|
|
@time ev = let evs = safe_eigvals(adjacency)
|
|
_count_multiplicites(evs)
|
|
end
|
|
|
|
@info "Principal Series Representation $i" ev[1:2] ev[end]
|
|
catch ex
|
|
@error "Principal Series Representation $i failed" ex
|
|
ex isa InterruptException && throw(ex)
|
|
end
|
|
end
|
|
|
|
for i = 1:27
|
|
try
|
|
a, b = load_discrete_repr(i)
|
|
adjacency = sum(a^i for i = 1:4) + sum(b^i for i = 1:4)
|
|
@time ev = let evs = safe_eigvals(adjacency)
|
|
_count_multiplicites(evs)
|
|
end
|
|
|
|
@info "Discrete Series Representation $i" ev[1:2] ev[end]
|
|
catch ex
|
|
@error "Discrete Series Representation $i : failed" ex
|
|
ex isa InterruptException && rethrow(ex)
|
|
end
|
|
end
|
|
end
|