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add eigenvalues computations

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kalmarek 2020-05-26 00:10:24 +02:00
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adj_psl2_eigvals.jl Normal file
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using RamanujanGraphs
using LinearAlgebra
using Nemo
include("src/nemo_utils.jl")
const p = try
@assert length(ARGS) == 2 && ARGS[1] == "-p"
p = parse(Int, ARGS[2])
RamanujanGraphs.Primes.isprime(p)
@assert p % 4 == 1
catch ex
@error "You need to provide a prime `-p` which is congruent to 1 mod 4."
rethrow(ex)
end
const CC = AcbField(256)
SL2p = let
if p == 109
a,b = let
a = SL₂{p}([ 0 1; 108 11])
b = SL₂{p}([57 2; 52 42])
@assert isone(a^10)
@assert isone(b^10)
a, b
end
elseif p == 131
a,b = let
a = SL₂{p}([-58 -24; -58 46])
b = SL₂{p}([0 -3; 44 -12])
@assert isone(a^10)
@assert isone(b^10)
a, b
end
else
@warn "no special set of generators for prime $p"
a,b = let
a = SL₂{p}(1, 0, 1, 1)
b = SL₂{p}(1, 1, 0, 1)
a, b
end
end
E, sizes = RamanujanGraphs.generate_balls([a,b, inv(a), inv(b)], radius=21);
@assert sizes[end] == RamanujanGraphs.order(SL₂{p})
E
end
let Borel_cosets = Bcosets = RamanujanGraphs.CosetDecomposition(SL2p, Borel(SL₂{p})),
α = RamanujanGraphs.generator(RamanujanGraphs.GF{p}(0))
for j in 0:(p-1)÷4
try
h = PrincipalRepr(
α => root_of_unity(CC, (p-1)÷2, j),
Borel_cosets)
@time adjacency = let
A = matrix(CC, h(SL2p[2]))
B = matrix(CC, h(SL2p[3]))
sum(A^i for i in 1:4) + sum(B^i for i in 1:4)
end
@time ev = let evs = safe_eigvals(adjacency)
_count_multiplicites(evs)
end
if length(ev) == 1
@info "Principal Series Representation $j" ev[1]
else
@info "Principal Series Representation $j" ev[1:2] ev[end]
end
catch ex
@error "Principal Series Representation $j failed" ex
ex isa InterruptException && rethrow(ex)
end
end
end
let α = RamanujanGraphs.generator(RamanujanGraphs.GF{p}(0)),
β = RamanujanGraphs.generator_min(QuadraticExt(α))
for j = 1:(p-1)÷4
try
h = DiscreteRepr(
RamanujanGraphs.GF{p}(1) => root_of_unity(CC, p),
β => root_of_unity(CC, (p+1)÷2, j*(p-1)÷4))
@time adjacency = let
A = matrix(CC, h(SL2p[2]))
B = matrix(CC, h(SL2p[3]))
sum(A^i for i in 1:4) + sum(B^i for i in 1:4)
end
@time ev = let evs = safe_eigvals(adjacency)
_count_multiplicites(evs)
end
@info "Discrete Series Representation $j" ev[1:2] ev[end]
catch ex
@error "Discrete Series Representation $j : failed" ex
ex isa InterruptException && rethrow(ex)
end
end
end
# using RamanujanGraphs.LightGraphs
# using Arpack
#
# Γ, eigenvalues = let q = 109
# a = RamanujanGraphs.PSL₂{q}([ 0 1
# 108 11])
# b = RamanujanGraphs.PSL₂{q}([57 2
# 52 42])
#
# S = unique([[a^i for i in 1:4]; [b^i for i in 1:4]])
#
# @info "Generating set S of $(eltype(S))" S
# @time Γ, verts, vlabels, elabels = RamanujanGraphs.cayley_graph((q^3 - q)÷2, S)
# @assert all(LightGraphs.degree(Γ,i) == length(S) for i in vertices(Γ))
# A = adjacency_matrix(Γ)
# @time eigenvalues, _ = eigs(A, nev=5)
# @show Γ eigenvalues
# Γ, eigenvalues
# end