kalmar/SmallHyperbolic
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Merge pull request #8 from kalmarek/mk/update_readme

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Mk/update readme
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13
README.md
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@ -5,7 +5,18 @@ The repository contains code for running experiments for
[Marek Kaluba](https://kalmar.faculty.wmi.amu.edu.pl/) and
[Stefan Witzel](https://www.math.uni-bielefeld.de/~switzel/).
There are three disjoint computations covered in this repository.
# Introduction
If you arrived here after reading the article looking for groups and
1. you don't understand any of this, you probably want to visit [this page](https://kalmarek.github.io/SmallHyperbolic/) instead;
2. you want just the machine-readable data, then the `json` file is available [here](https://github.com/kalmarek/SmallHyperbolic/blob/master/data/triangle_groups.json) (the file was generated by calling `julia ./scripts/create_json/create_json.jl`);
3. you want to re-run some of the computations that lead to the results, then continue reading.
# Computations
There are three disjoint computations covered in this repository:
1. certified eigenvalue computations for _PSL₂(p)_,
2. sum of squares computations in an attempt to prove property (T) by estimating spectral gap of the group Laplacian,
3. generation of magma files used to compute e.g. witnesses for non-hyperbolicity, rank of abelianization, etc.
## Eigenvalues computations for _PSL₂(p)_

62
adj_psl2_eigvals.jl
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@ -57,40 +57,41 @@ function SL2p_gens(p::Integer)
end
end
return a,b
return a, b
end
function adjacency(ϱ, a, b; prec=256)
order_a = findfirst(i-> isone(a^i), 1:100)
order_b = findfirst(i-> isone(b^i), 1:100)
function adjacency(ϱ, a, b; prec = 256)
order_a = findfirst(i -> isone(a^i), 1:100)
order_b = findfirst(i -> isone(b^i), 1:100)
@assert !isnothing(order_a) && order_a > 1
@assert !isnothing(order_b) && order_b > 1
k = order_a-1 + order_b-1
k = order_a - 1 + order_b - 1
A = AcbMatrix(ϱ(a), prec=prec)
B = AcbMatrix(ϱ(b), prec=prec)
A = AcbMatrix(ϱ(a), prec = prec)
B = AcbMatrix(ϱ(b), prec = prec)
res = sum(A^i for i = 1:order_a-1) + sum(B^i for i = 1:order_b-1)
return Arblib.scalar_div!(res, res, k)
#return Arblib.scalar_div!(res, res, k)
return res
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
help = "the prime p for which to use PSL(2,p)"
arg_type = Int
required = true
"-a"
help = "generator a (optional)"
help = "generator a (optional)"
"-b"
help = "generator b (optional)"
help = "generator b (optional)"
"--ab"
help = "array of generators a and b (optional)"
help = "array of generators a and b (optional)"
"--precision"
help = "set the precision of computations"
arg_type = Int
default = 128
help = "set the precision of computations"
arg_type = Int
default = 128
end
result = parse_args(s)
@ -113,7 +114,8 @@ end
parsed_args = parse_our_args()
const p = let p = parsed_args["p"]
isprime(p) || @error "You need to provide a prime, ex: `julia adj_psl2_eigvals.jl -p 31`"
isprime(p) ||
@error "You need to provide a prime, ex: `julia adj_psl2_eigvals.jl -p 31`"
p
end
@ -124,14 +126,14 @@ open(LOGFILE, "w") do io
@info "Logging into $LOGFILE"
with_logger(SimpleLogger(io)) do
@info "Arguments:" args=parsed_args
@info "Arguments:" args = parsed_args
a,b = SL2p_gens(p)
a, b = SL2p_gens(p)
a = SL₂{p}(get(parsed_args, "a", a))
b = SL₂{p}(get(parsed_args, "b", b))
@info "Generators" a b
Borel_cosets = let p = p, (a,b) = (a,b)
Borel_cosets = let p = p, (a, b) = (a, b)
SL2p, sizes =
RamanujanGraphs.generate_balls([a, b, inv(a), inv(b)], radius = 21)
@assert sizes[end] == RamanujanGraphs.order(SL₂{p})
@ -143,11 +145,11 @@ open(LOGFILE, "w") do io
for j = 0:(p-1)÷4
h = PrincipalRepr(
α => unit_root((p - 1) ÷ 2, j, prec=PRECISION),
α => unit_root((p - 1) ÷ 2, j, prec = PRECISION),
Borel_cosets,
)
@time adj = adjacency(h, a, b, prec=PRECISION)
@time adj = adjacency(h, a, b, prec = PRECISION)
try
@time evs = let evs = safe_eigvals(adj)
@ -168,20 +170,20 @@ open(LOGFILE, "w") do io
if p % 4 == 1
ub = (p - 1) ÷ 4
ζ = unit_root((p + 1) ÷ 2, 1, prec=PRECISION)
ζ = unit_root((p + 1) ÷ 2, 1, prec = PRECISION)
else # p % 4 == 3
ub = (p + 1) ÷ 4
ζ = unit_root((p + 1), 1, prec=PRECISION)
ζ = unit_root((p + 1), 1, prec = PRECISION)
end
for k = 1:ub
h = DiscreteRepr(
RamanujanGraphs.GF{p}(1) => unit_root(p, prec=PRECISION),
RamanujanGraphs.GF{p}(1) => unit_root(p, prec = PRECISION),
β => ζ^k,
)
@time adj = adjacency(h, a, b, prec=PRECISION)
@time adj = adjacency(h, a, b, prec = PRECISION)
try
@time evs = let evs = safe_eigvals(adj)
@ -196,11 +198,11 @@ open(LOGFILE, "w") do io
end
end
end
all_large_evs = sort(all_large_evs, rev=true)
all_large_evs = sort(all_large_evs, rev = true)
λ = all_large_evs[2]
ε = (λ - 3)/5
ε = (λ - 3) / 5
α = acos(ε)
α_deg = (α/pi)*180
α_deg = (α / pi) * 180
@info "Certified values:" λ ε α α_deg
end # with_logger
end # open(logfile)

45
data/create_json.jl
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@ -1,45 +0,0 @@
using Pkg
Pkg.activate(@__DIR__)
using DelimitedFiles
using JSON
include(joinpath(@__DIR__, "parse_presentations.jl"))
include(joinpath(@__DIR__, "smallhyperbolicgrp.jl"))
all_grps_presentations =
let tables = [
joinpath(@__DIR__, f) for f in readdir(@__DIR__) if
isfile(joinpath(@__DIR__, f)) && endswith(f, ".txt")
]
mapreduce(parse_grouppresentations_abstract, union, tables) |> Dict
end
tr_grps =
let csvs = [
joinpath(@__DIR__, f) for f in readdir(@__DIR__) if
isfile(joinpath(@__DIR__, f)) && endswith(f, ".csv")
]
trGrps = mapreduce(union, csvs) do file
m = match(r".*_(\d)_(\d)_(\d).csv", basename(file))
@assert !isnothing(m)
type = parse.(Int, tuple(m[1], m[2], m[3]))
data = readdlm(file, '&')
labels = Symbol.(replace.(strip.(data[1, :]), ' ' => '_', '-' => '_'))
groups = data[2:end, :]
grps = map(enumerate(eachrow(groups))) do (i, props)
nt = (; (Symbol(l) => v for (l, v) in zip(labels, props))...)
@debug i, grp_name(nt)
P = all_grps_presentations[grp_name(nt)]
grp = TriangleGrp(type, P.generators, P.relations, nt)
end
end
end
open(joinpath(@__DIR__, "triangle_groups.json"), "w") do io
f(args...) = show_json(args...; indent = 4)
s = sprint(f, TriangleGrpSerialization(), tr_grps)
# JSON.print(io, , 4)
print(io, s)
end

16
docs/http_server.py
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@ -1,16 +0,0 @@
#!/usr/bin/env python3
# encoding: utf-8
"""Use instead of `python3 -m http.server` when you need CORS"""
from http.server import HTTPServer, SimpleHTTPRequestHandler
class CORSRequestHandler(SimpleHTTPRequestHandler):
def end_headers(self):
self.send_header('Access-Control-Allow-Origin', '*')
self.send_header('Access-Control-Allow-Methods', 'GET')
self.send_header('Cache-Control', 'no-store, no-cache, must-revalidate')
return super(CORSRequestHandler, self).end_headers()
httpd = HTTPServer(('localhost', 8003), CORSRequestHandler)
httpd.serve_forever()

0
data/Manifest.toml → scripts/create_json/Manifest.toml
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0
data/Project.toml → scripts/create_json/Project.toml
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46
scripts/create_json/create_json.jl Normal file
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@ -0,0 +1,46 @@
using Pkg
Pkg.activate(@__DIR__)
using DelimitedFiles
using JSON
include(joinpath(@__DIR__, "parse_presentations.jl"))
include(joinpath(@__DIR__, "smallhyperbolicgrp.jl"))
const DATA_DIR = joinpath(@__DIR__, "..", "..", "data")
function _files_with_extension(dir::AbstractString, ext::AbstractString)
return [
joinpath(dir, f) for
f in readdir(dir) if isfile(joinpath(dir, f)) && endswith(f, '.' * ext)
]
end
all_grps_presentations = let tables = _files_with_extension(DATA_DIR, "txt")
mapreduce(parse_grouppresentations_abstract, union, tables) |> Dict
end
grps = let csvs = _files_with_extension(DATA_DIR, "csv")
trGrps = mapreduce(union, csvs) do file
m = match(r".*_(\d)_(\d)_(\d).csv", basename(file))
@assert !isnothing(m)
type = parse.(Int, tuple(m[1], m[2], m[3]))
data = readdlm(file, '&')
labels = Symbol.(replace.(strip.(data[1, :]), ' ' => '_', '-' => '_'))
groups = data[2:end, :]
grps = map(enumerate(eachrow(groups))) do (i, props)
nt = (; (Symbol(l) => v for (l, v) in zip(labels, props))...)
# @debug i, grp_name(nt)
P = all_grps_presentations[grp_name(nt)]
grp = TriangleGrp(type, P.generators, P.relations, nt)
end
end
end
open(joinpath(DATA_DIR, "triangle_groups.json"), "w") do io
f(args...) = show_json(args...; indent = 4)
s = sprint(f, TriangleGrpSerialization(), grps)
# JSON.print(io, , 4)
print(io, s)
end

2
data/parse_presentations.jl → scripts/create_json/parse_presentations.jl
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@ -1,4 +1,4 @@
include("../src/groupparse.jl")
include(joinpath(@__DIR__, "..", "..", "src", "groupparse.jl"))
function parse_grouppresentations_abstract(filename::AbstractString)
lines = strip.(readlines(filename))

0
data/smallhyperbolicgrp.jl → scripts/create_json/smallhyperbolicgrp.jl
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