94 lines
2.8 KiB
Julia
94 lines
2.8 KiB
Julia
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@testset "Sq, Adj, Op" begin
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function isconstant_on_orbit(v, orb)
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isempty(orb) && return true
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k = v[first(orb)]
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return all(v[o] == k for o in orb)
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end
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@testset "unit tests" begin
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for N in [3,4]
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M = MatrixSpace(Nemo.ZZ, N,N)
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A = SAut(FreeGroup(N))
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@test length(PropertyT.generating_set(M)) == 2N*(N-1)
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S = PropertyT.generating_set(M)
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@test all(inv(s) ∈ S for s in S)
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@test length(PropertyT.generating_set(A)) == 4N*(N-1)
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S = PropertyT.generating_set(A)
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@test all(inv(s) ∈ S for s in S)
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end
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N = 4
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M = MatrixSpace(Nemo.ZZ, N,N)
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S = PropertyT.generating_set(M)
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@test PropertyT.E(M, 1, 2) isa MatElem
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e12 = PropertyT.E(M, 1, 2)
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@test e12[1,2] == 1
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@test inv(e12)[1,2] == -1
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@test e12 ∈ S
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@test PropertyT.isopposite(perm"(1,2,3)(4)", perm"(1,4,2)")
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@test PropertyT.isadjacent(perm"(1,2,3)", perm"(1,2)(3)")
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@test !PropertyT.isopposite(perm"(1,2,3)", perm"(1,2)(3)")
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@test !PropertyT.isadjacent(perm"(1,4)", perm"(2,3)(4)")
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@test isconstant_on_orbit([1,1,1,2,2], [2,3])
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@test !isconstant_on_orbit([1,1,1,2,2], [2,3,4])
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end
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@testset "Sq, Adj, Op" begin
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N = 4
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M = MatrixSpace(Nemo.ZZ, N,N)
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S = PropertyT.generating_set(M)
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Δ = PropertyT.Laplacian(S, 2)
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RG = parent(Δ)
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autS = WreathProduct(PermGroup(2), PermGroup(N))
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orbits = PropertyT.orbit_decomposition(autS, RG.basis)
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@test PropertyT.Sq(RG) isa GroupRingElem
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sq = PropertyT.Sq(RG)
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@test all(isconstant_on_orbit(sq, orb) for orb in orbits)
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@test PropertyT.Adj(RG) isa GroupRingElem
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adj = PropertyT.Adj(RG)
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@test all(isconstant_on_orbit(adj, orb) for orb in orbits)
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@test PropertyT.Op(RG) isa GroupRingElem
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op = PropertyT.Op(RG)
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@test all(isconstant_on_orbit(op, orb) for orb in orbits)
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sq, adj, op = PropertyT.SqAdjOp(RG, N)
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@test sq == PropertyT.Sq(RG)
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@test adj == PropertyT.Adj(RG)
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@test op == PropertyT.Op(RG)
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e = one(M)
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g = PropertyT.E(M, 1,2)
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h = PropertyT.E(M, 1,3)
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k = PropertyT.E(M, 3,4)
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edges = N*(N-1)÷2
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@test sq[e] == 20*edges
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@test sq[g] == sq[h] == -8
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@test sq[g^2] == sq[h^2] == 1
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@test sq[g*h] == sq[h*g] == 0
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# @test adj[e] == ...
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@test adj[g] == adj[h] # == ...
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@test adj[g^2] == adj[h^2] == 0
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@test adj[g*h] == adj[h*g] # == ...
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# @test op[e] == ...
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@test op[g] == op[h] # == ...
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@test op[g^2] == op[h^2] == 0
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@test op[g*h] == op[h*g] == 0
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@test op[g*k] == op[k*g] # == ...
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@test op[h*k] == op[k*h] == 0
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end
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end
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