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PropertyT.jl/test/1812.03456.jl

94 lines
2.8 KiB
Julia

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