mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-12-25 02:15:29 +01:00
102 lines
3.5 KiB
Julia
102 lines
3.5 KiB
Julia
@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)
|
|
|
|
function ssgs(A::AutGroup, i, j)
|
|
rmuls = [Groups.transvection_R(i,j), Groups.transvection_R(j,i)]
|
|
lmuls = [Groups.transvection_L(i,j), Groups.transvection_L(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 [SymmetricGroup(N), WreathProduct(SymmetricGroup(2), SymmetricGroup(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 SymmetricGroup(N))
|
|
|
|
@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(SymmetricGroup(2), SymmetricGroup(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 [SymmetricGroup(N), WreathProduct(SymmetricGroup(2), SymmetricGroup(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 SymmetricGroup(N))
|
|
|
|
@test all(g(Δij) == PropertyT.spLaplacian(RG, ssgs(M, g.p[i], g.p[j])) for g in WreathProduct(SymmetricGroup(2), SymmetricGroup(N)))
|
|
end
|
|
end
|
|
|
|
end
|