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kalmarek 2020-06-09 10:52:55 +02:00
parent c2740d58d3
commit 725293a037
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1 changed files with 33 additions and 13 deletions
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46
adj_psl2_eigvals.jl
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@ -18,16 +18,16 @@ const CC = AcbField(256)
SL2p = let SL2p = let
if p == 109 if p == 109
a,b = let a, b = let
a = SL₂{p}([ 0 1; 108 11]) a = SL₂{p}([0 1; 108 11])
b = SL₂{p}([57 2; 52 42]) b = SL₂{p}([57 2; 52 42])
@assert isone(a^10) @assert isone(a^10)
@assert isone(b^10) @assert isone(b^10)
a, b a, b
end end
elseif p == 131 elseif p == 131
a,b = let a, b = let
a = SL₂{p}([-58 -24; -58 46]) a = SL₂{p}([-58 -24; -58 46])
b = SL₂{p}([0 -3; 44 -12]) b = SL₂{p}([0 -3; 44 -12])
@assert isone(a^10) @assert isone(a^10)
@ -37,14 +37,15 @@ SL2p = let
end end
else else
@warn "no special set of generators for prime $p" @warn "no special set of generators for prime $p"
a,b = let a, b = let
a = SL₂{p}(1, 0, 1, 1) a = SL₂{p}(1, 0, 1, 1)
b = SL₂{p}(1, 1, 0, 1) b = SL₂{p}(1, 1, 0, 1)
a, b a, b
end end
end end
E, sizes = RamanujanGraphs.generate_balls([a,b, inv(a), inv(b)], radius=21); E, sizes =
RamanujanGraphs.generate_balls([a, b, inv(a), inv(b)], radius = 21)
@assert sizes[end] == RamanujanGraphs.order(SL₂{p}) @assert sizes[end] == RamanujanGraphs.order(SL₂{p})
E E
end end
@ -115,21 +116,40 @@ let α = RamanujanGraphs.generator(RamanujanGraphs.GF{p}(0)),
end end
end end
#
# using RamanujanGraphs.LightGraphs # using RamanujanGraphs.LightGraphs
# using Arpack # using Arpack
# #
# Γ, eigenvalues = let q = 109 # Γ, eigenvalues = let p = 109,
# a = RamanujanGraphs.PSL₂{q}([ 0 1 # a = PSL₂{p}([ 0 1; 108 11]),
# 108 11]) # b = PSL₂{p}([ 57 2; 52 42])
# b = RamanujanGraphs.PSL₂{q}([57 2
# 52 42])
# #
# S = unique([[a^i for i in 1:4]; [b^i for i in 1:4]]) # S = unique([[a^i for i in 1:4]; [b^i for i in 1:4]])
# #
# @info "Generating set S of $(eltype(S))" S # @info "Generating set S of $(eltype(S))" S
# @time Γ, verts, vlabels, elabels = RamanujanGraphs.cayley_graph((q^3 - q)÷2, S) # @time Γ, verts, vlabels, elabels =
# RamanujanGraphs.cayley_graph(RamanujanGraphs.order(PSL₂{p}), S)
#
# @assert all(LightGraphs.degree(Γ,i) == length(S) for i in vertices(Γ)) # @assert all(LightGraphs.degree(Γ,i) == length(S) for i in vertices(Γ))
# @assert LightGraphs.nv(Γ) == RamanujanGraphs.order(PSL₂{p})
# A = adjacency_matrix(Γ)
# @time eigenvalues, _ = eigs(A, nev=5)
# @show Γ eigenvalues
# Γ, eigenvalues
# end
#
# let p = 131,
# a = PSL₂{p}([-58 -24; -58 46]),
# b = PSL₂{p}([0 -3; 44 -12])
#
# 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(RamanujanGraphs.order(PSL₂{p}), S)
#
# @assert all(LightGraphs.degree(Γ,i) == length(S) for i in vertices(Γ))
# @assert LightGraphs.nv(Γ) == RamanujanGraphs.order(PSL₂{p})
# A = adjacency_matrix(Γ) # A = adjacency_matrix(Γ)
# @time eigenvalues, _ = eigs(A, nev=5) # @time eigenvalues, _ = eigs(A, nev=5)
# @show Γ eigenvalues # @show Γ eigenvalues