94 lines
2.7 KiB
Julia
94 lines
2.7 KiB
Julia
using AbstractAlgebra, Nemo, Groups, SCS
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using JLD
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using PropertyT
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using Test
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indexing(n) = [(i,j) for i in 1:n for j in (i+1):n]
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function Groups.gens(M::MatSpace)
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@assert M.cols == M.rows
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N = M.cols
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E(i,j) = begin g = M(1); g[i,j] = 1; g end
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S = [E(i,j) for (i,j) in indexing(N)]
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S = [S; transpose.(S)]
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S = [S; inv.(S)]
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return S
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end
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solver(iters; accel=1) =
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SCSSolver(max_iters=iters, acceleration_lookback=accel, eps=1e-10)
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@testset "1703.09680 Examples" begin
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@testset "SL(2,Z)" begin
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rm("SL(2,Z)", recursive=true, force=true)
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N = 2
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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sett = PropertyT.Settings("SL($N,Z)", G, S, solver(20000, accel=20); upper_bound=0.1)
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@test PropertyT.check_property_T(sett) == false
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end
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@testset "SL(3,Z)" begin
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rm("SL(3,Z)", recursive=true, force=true)
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N = 3
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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sett = PropertyT.Settings("SL($N,Z)", G, S, solver(1000, accel=20); upper_bound=0.1)
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@test PropertyT.check_property_T(sett) == true
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end
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@testset "SAut(F₂)" begin
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rm("SAut(F2)", recursive=true, force=true)
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N = 2
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G = SAut(FreeGroup(N))
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S = Groups.gens(G)
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S = [S; inv.(S)]
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sett = PropertyT.Settings("SAut(F$N)", G, S, solver(20000);
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upper_bound=0.15, warmstart=false)
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@test PropertyT.check_property_T(sett) == false
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end
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end
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@testset "17.12.07167 Examples" begin
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@testset "oSL(3,Z)" begin
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rm("oSL(3,Z)", recursive=true, force=true)
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N = 3
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G = MatrixSpace(Nemo.ZZ, N,N)
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S = Groups.gens(G)
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(2000, accel=20);
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upper_bound=0.27, warmstart=false)
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@test PropertyT.check_property_T(sett) == false
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#second run just checks the solution
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@test PropertyT.check_property_T(sett) == false
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sett = PropertyT.Settings("SL($N,Z)", G, S, autS, solver(2000, accel=10);
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upper_bound=0.27, warmstart=true)
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@test PropertyT.check_property_T(sett) == true
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end
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@testset "SAut(F₂)" begin
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rm("oSAut(F3)", recursive=true, force=true)
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N = 3
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G = SAut(FreeGroup(N))
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S = Groups.gens(G)
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S = [S; inv.(S)]
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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sett = PropertyT.Settings("SAut(F$N)", G, S, autS, solver(10000);
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upper_bound=0.15, warmstart=false)
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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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