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add tests for actions

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kalmarek 2019-07-05 18:57:39 +02:00
parent 2ef8de7d42
commit e9bb6f13dd
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3 changed files with 117 additions and 0 deletions

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@ -32,6 +32,18 @@
# this should be very fast due to warmstarting:
@test λ PropertyT.spectral_gap(sett) atol=1e-5
@test PropertyT.check_property_T(sett) == true
##########
# Symmetrizing by PermGroup(3):
sett = PropertyT.Settings("SL($N,Z)", G, S, PermGroup(N), with_SCS(4000, accel=20);
upper_bound=0.27, warmstart=true)
PropertyT.print_summary(sett)
λ = PropertyT.spectral_gap(sett)
@test λ > 0.269999
@test PropertyT.interpret_results(sett, λ) == true
end
@testset "oSL(4,Z)" begin

104
test/actions.jl Normal file
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@ -0,0 +1,104 @@
@testset "actions on Group[Rings]" begin
Eij = PropertyT.EltaryMat
ssgs(M::MatAlgebra, i, j) = (S = [Eij(M, i, j), Eij(M, j, i)];
S = unique([S; inv.(S)]); S)
rmul = Groups.rmul_autsymbol
lmul = Groups.lmul_autsymbol
function ssgs(A::AutGroup, i, j)
rmuls = [rmul(i,j), rmul(j,i)]
lmuls = [lmul(i,j), lmul(j,i)]
gen_set = A.([rmuls; lmuls])
return unique([gen_set; inv.(gen_set)])
end
@testset "actions on SL(3,Z) and its group ring" begin
N = 3
halfradius = 2
M = MatrixAlgebra(zz, N)
S = PropertyT.generating_set(M)
E_R, sizes = Groups.generate_balls(S, one(M), radius=2halfradius);
rdict = GroupRings.reverse_dict(E_R)
pm = GroupRings.create_pm(E_R, rdict, sizes[halfradius]; twisted=false);
RG = GroupRing(M, E_R, rdict, pm)
@testset "correctness of actions" begin
Δ = length(S)*RG(1) - sum(RG(s) for s in S)
@test Δ == PropertyT.spLaplacian(RG, S)
elt = S[5]
x = RG(1) - RG(elt)
elt2 = E_R[rand(sizes[1]:sizes[2])]
y = 2RG(elt2) - RG(elt)
for G in [PermGroup(N), WreathProduct(PermGroup(2), PermGroup(N))]
@test all(g(one(M)) == one(M) for g in G)
@test all(rdict[g(m)] <= sizes[1] for g in G for m in S)
@test all(g(m)*g(n) == g(m*n) for g in G for m in S for n in S)
@test all(g(Δ) == Δ for g in G)
@test all(g(x) == RG(1) - RG(g(elt)) for g in G)
@test all(2RG(g(elt2)) - RG(g(elt)) == g(y) for g in G)
end
end
@testset "small Laplacians" begin
for (i,j) in PropertyT.indexing(N)
Sij = ssgs(M, i,j)
Δij= PropertyT.spLaplacian(RG, Sij)
@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in PermGroup(N))
@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(PermGroup(2), PermGroup(N)))
end
end
end
@testset "actions on SAut(F_3) and its group ring" begin
N = 3
halfradius = 2
M = SAut(FreeGroup(N))
S = PropertyT.generating_set(M)
E_R, sizes = Groups.generate_balls(S, one(M), radius=2halfradius);
rdict = GroupRings.reverse_dict(E_R)
pm = GroupRings.create_pm(E_R, rdict, sizes[halfradius]; twisted=false);
RG = GroupRing(M, E_R, rdict, pm)
@testset "correctness of actions" begin
Δ = length(S)*RG(1) - sum(RG(s) for s in S)
@test Δ == PropertyT.spLaplacian(RG, S)
elt = S[5]
x = RG(1) - RG(elt)
elt2 = E_R[rand(sizes[1]:sizes[2])]
y = 2RG(elt2) - RG(elt)
for G in [PermGroup(N), WreathProduct(PermGroup(2), PermGroup(N))]
@test all(g(one(M)) == one(M) for g in G)
@test all(rdict[g(m)] <= sizes[1] for g in G for m in S)
@test all(g(m)*g(n) == g(m*n) for g in G for m in S for n in S)
@test all(g(Δ) == Δ for g in G)
@test all(g(x) == RG(1) - RG(g(elt)) for g in G)
@test all(2RG(g(elt2)) - RG(g(elt)) == g(y) for g in G)
end
end
for (i,j) in PropertyT.indexing(N)
Sij = ssgs(M, i,j)
Δij= PropertyT.spLaplacian(RG, Sij)
@test all(p(Δij) == PropertyT.spLaplacian(RG, ssgs(M, p[i], p[j])) for p in PermGroup(N))
@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(PermGroup(2), PermGroup(N)))
end
end
end

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@ -12,6 +12,7 @@ with_SCS(iters; accel=1, eps=1e-10) =
acceleration_lookback=accel, eps=eps, warm_start=true)
include("1703.09680.jl")
include("actions.jl")
include("1712.07167.jl")
include("SOS_correctness.jl")
include("1812.03456.jl")