105 lines
3.2 KiB
Julia
105 lines
3.2 KiB
Julia
@testset "1712.07167 Examples" begin
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@testset "SL(3,Z)" begin
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N = 3
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))
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NAME = "SL($N,Z)_orbit"
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rm(NAME, recursive=true, force=true)
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sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000, accel=20);
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upper_bound=0.27, force_compute=false)
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@info sett
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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# second run just checks the solution due to force_compute=false above
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@test λ == PropertyT.spectral_gap(sett)
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(4000, accel=20);
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upper_bound=0.27, force_compute=true)
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@info sett
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λ = PropertyT.spectral_gap(sett)
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@test λ > 0.269999
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@test PropertyT.interpret_results(sett, λ) == true
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# this should be very fast due to warmstarting:
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@test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
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@test PropertyT.check_property_T(sett) == true
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##########
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# Symmetrizing by SymmetricGroup(3):
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sett = PropertyT.Settings(NAME, G, S, SymmetricGroup(N), with_SCS(4000, accel=20, warm_start=false);
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upper_bound=0.27, force_compute=true)
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@info sett
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λ = PropertyT.spectral_gap(sett)
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@test λ > 0.269999
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@test PropertyT.interpret_results(sett, λ) == true
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end
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@testset "SL(4,Z)" begin
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N = 4
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G = MatrixAlgebra(zz, N)
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S = PropertyT.generating_set(G)
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autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))
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NAME = "SL($N,Z)_orbit"
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rm(NAME, recursive=true, force=true)
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sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000, accel=20);
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upper_bound=1.3, force_compute=false)
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@info sett
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λ = PropertyT.spectral_gap(sett)
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@test λ < 0.0
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@test PropertyT.interpret_results(sett, λ) == false
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# second run just checks the solution due to force_compute=false above
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@test λ == PropertyT.spectral_gap(sett)
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(7000, accel=20, warm_start=true);
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upper_bound=1.3, force_compute=true)
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@info sett
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@time λ = PropertyT.spectral_gap(sett)
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@test λ > 1.2999
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@test PropertyT.interpret_results(sett, λ) == true
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# this should be very fast due to warmstarting:
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@time @test λ ≈ PropertyT.spectral_gap(sett) atol=1e-5
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@time @test PropertyT.check_property_T(sett) == true
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end
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@testset "SAut(F₃)" begin
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N = 3
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G = SAut(FreeGroup(N))
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S = PropertyT.generating_set(G)
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autS = WreathProduct(SymmetricGroup(2), SymmetricGroup(N))
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NAME = "SAut(F$N)_orbit"
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rm(NAME, recursive=true, force=true)
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sett = PropertyT.Settings(NAME, G, S, autS, with_SCS(1000);
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upper_bound=0.15)
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@info sett
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@test PropertyT.check_property_T(sett) == false
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end
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end
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