Merge pull request #8 from kalmarek/mk/update_readme

Mk/update readme

README.md

@@ -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)_
 

adj_psl2_eigvals.jl

@@ -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)
+function adjacency(ϱ, a, b; prec = 256)
-    order_a = findfirst(i-> isone(a^i), 1:100)
+    order_a = findfirst(i -> isone(a^i), 1:100)
-    order_b = findfirst(i-> isone(b^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)
+    A = AcbMatrix(ϱ(a), prec = prec)
-    B = AcbMatrix(ϱ(b), 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)"
+        help = "the prime p for which to use PSL(2,p)"
-            arg_type = Int
+        arg_type = Int
-            required = true
+        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"
+        help = "set the precision of computations"
-            arg_type = Int
+        arg_type = Int
-            default = 128
+        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)

data/create_json.jl

@@ -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

docs/http_server.py

@@ -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()

scripts/create_json/create_json.jl

@@ -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

scripts/create_json/parse_presentations.jl

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