mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-11-26 00:55:27 +01:00
add sqadjop.jl and unit tests
This commit is contained in:
parent
b9dc701f17
commit
6c906b05cb
@ -22,6 +22,9 @@ include("RGprojections.jl")
|
||||
include("orbitdata.jl")
|
||||
include("sos_sdps.jl")
|
||||
include("checksolution.jl")
|
||||
include("sqadjop.jl")
|
||||
|
||||
include("1712.07167.jl")
|
||||
|
||||
|
||||
end # module Property(T)
|
||||
|
||||
125
src/sqadjop.jl
Normal file
125
src/sqadjop.jl
Normal file
@ -0,0 +1,125 @@
|
||||
indexing(n) = [(i,j) for i in 1:n for j in 1:n if i≠j]
|
||||
|
||||
function generating_set(G::AutGroup{N}, n=N) where N
|
||||
|
||||
rmuls = [Groups.rmul_autsymbol(i,j) for (i,j) in indexing(n)]
|
||||
lmuls = [Groups.lmul_autsymbol(i,j) for (i,j) in indexing(n)]
|
||||
gen_set = G.([rmuls; lmuls])
|
||||
|
||||
return [gen_set; inv.(gen_set)]
|
||||
end
|
||||
|
||||
function E(M::MatSpace, i::Integer, j::Integer, val=1)
|
||||
@assert i ≠ j
|
||||
@assert 1 ≤ i ≤ nrows(M)
|
||||
@assert 1 ≤ j ≤ ncols(M)
|
||||
m = one(M)
|
||||
m[i,j] = val
|
||||
return m
|
||||
end
|
||||
|
||||
function generating_set(M::MatSpace, n=nrows(M))
|
||||
@assert nrows(M) == ncols(M)
|
||||
|
||||
elts = [E(M, i,j) for (i,j) in indexing(n)]
|
||||
return elem_type(M)[elts; inv.(elts)]
|
||||
end
|
||||
|
||||
isopposite(σ::perm, τ::perm, i=1, j=2) =
|
||||
σ[i] ≠ τ[i] && σ[i] ≠ τ[j] &&
|
||||
σ[j] ≠ τ[i] && σ[j] ≠ τ[j]
|
||||
|
||||
isadjacent(σ::perm, τ::perm, i=1, j=2) =
|
||||
(σ[i] == τ[i] && σ[j] ≠ τ[j]) || # first equal, second differ
|
||||
(σ[j] == τ[j] && σ[i] ≠ τ[i]) || # sedond equal, first differ
|
||||
(σ[i] == τ[j] && σ[j] ≠ τ[i]) || # first σ equal to second τ
|
||||
(σ[j] == τ[i] && σ[i] ≠ τ[j]) # second σ equal to first τ
|
||||
|
||||
Base.div(X::GroupRingElem, x::Number) = parent(X)(X.coeffs.÷x)
|
||||
|
||||
function Sq(RG::GroupRing, N::Integer)
|
||||
S₂ = generating_set(RG.group, 2)
|
||||
ℤ = Int64
|
||||
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
|
||||
|
||||
Alt_N = [g for g in PermutationGroup(N) if parity(g) == 0]
|
||||
|
||||
sq = RG()
|
||||
for σ in Alt_N
|
||||
GroupRings.addeq!(sq, *(σ(Δ₂), σ(Δ₂), false))
|
||||
end
|
||||
return sq÷factorial(N-2)
|
||||
end
|
||||
|
||||
function Adj(RG::GroupRing, N::Integer)
|
||||
S₂ = generating_set(RG.group, 2)
|
||||
ℤ = Int64
|
||||
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
|
||||
|
||||
Alt_N = [g for g in PermutationGroup(N) if parity(g) == 0]
|
||||
Δ₂s = Dict(σ=>σ(Δ₂) for σ in Alt_N)
|
||||
adj = RG()
|
||||
|
||||
for σ in Alt_N
|
||||
for τ in Alt_N
|
||||
if isadjacent(σ, τ)
|
||||
GroupRings.addeq!(adj, *(Δ₂s[σ], Δ₂s[τ], false))
|
||||
end
|
||||
end
|
||||
end
|
||||
return adj÷factorial(N-2)^2
|
||||
end
|
||||
|
||||
function Op(RG::GroupRing, N::Integer)
|
||||
if N < 4
|
||||
return RG()
|
||||
end
|
||||
S₂ = generating_set(RG.group, 2)
|
||||
ℤ = Int64
|
||||
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
|
||||
|
||||
Alt_N = [g for g in PermutationGroup(N) if parity(g) == 0]
|
||||
Δ₂s = Dict(σ=>σ(Δ₂) for σ in Alt_N)
|
||||
op = RG()
|
||||
|
||||
for σ in Alt_N
|
||||
for τ in Alt_N
|
||||
if isopposite(σ, τ)
|
||||
GroupRings.addeq!(op, *(Δ₂s[σ], Δ₂s[τ], false))
|
||||
end
|
||||
end
|
||||
end
|
||||
return op÷factorial(N-2)^2
|
||||
end
|
||||
|
||||
for Elt in [:Sq, :Adj, :Op]
|
||||
@eval begin
|
||||
$Elt(RG::GroupRing{AutGroup{N}}) where N = $Elt(RG, N)
|
||||
$Elt(RG::GroupRing{<:MatSpace}) = $Elt(RG, nrows(RG.group))
|
||||
end
|
||||
end
|
||||
|
||||
function SqAdjOp(RG::GroupRing, N::Integer)
|
||||
S₂ = generating_set(RG.group, 2)
|
||||
ℤ = Int64
|
||||
Δ₂ = length(S₂)*one(RG, ℤ) - RG(S₂, ℤ);
|
||||
|
||||
Alt_N = [σ for σ in PermutationGroup(N) if parity(σ) == 0]
|
||||
sq, adj, op = RG(), RG(), RG()
|
||||
|
||||
Δ₂s = Dict(σ=>σ(Δ₂) for σ in Alt_N)
|
||||
|
||||
for σ in Alt_N
|
||||
GroupRings.addeq!(sq, *(Δ₂s[σ], Δ₂s[σ], false))
|
||||
for τ in Alt_N
|
||||
if isopposite(σ, τ)
|
||||
GroupRings.addeq!(op, *(Δ₂s[σ], Δ₂s[τ], false))
|
||||
elseif isadjacent(σ, τ)
|
||||
GroupRings.addeq!(adj, *(Δ₂s[σ], Δ₂s[τ], false))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
k = factorial(N-2)
|
||||
return sq÷k, adj÷k^2, op÷k^2
|
||||
end
|
||||
93
test/1812.03456.jl
Normal file
93
test/1812.03456.jl
Normal file
@ -0,0 +1,93 @@
|
||||
@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
|
||||
|
||||
@ -23,3 +23,4 @@ solver(iters; accel=1) =
|
||||
include("1703.09680.jl")
|
||||
include("1712.07167.jl")
|
||||
include("SOS_correctness.jl")
|
||||
include("1812.03456.jl")
|
||||
|
||||
Loading…
Reference in New Issue
Block a user