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