PropertyT.jl/test/quick_tests.jl

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@testset "Quick tests" begin
@testset "SL(2,F₇)" begin
N = 2
p = 7
halfradius = 3
G = MatrixGroups.SpecialLinearGroup{N}(SymbolicWedderburn.Characters.FiniteFields.GF{p})
RG, S, sizes = PropertyT.group_algebra(G, halfradius=3, twisted=true)
Δ = let RG = RG, S = S
RG(length(S)) - sum(RG(s) for s in S)
end
elt = Δ^2
unit = Δ
ub = 0.58578# Inf# 1.5
@testset "standard formulation" begin
status, certified, λ_cert = check_positivity(
elt,
unit,
upper_bound=ub,
halfradius=2,
optimizer=cosmo_optimizer(
eps=1e-7,
max_iters=5_000,
accel=50,
alpha=1.95,
)
)
@test status == JuMP.OPTIMAL
@test certified
@test λ_cert > 5857 // 10000
m = PropertyT.sos_problem_dual(elt, unit)
PropertyT.solve(m, cosmo_optimizer(
eps=1e-7,
max_iters=10_000,
accel=50,
alpha=1.95,
))
@test JuMP.termination_status(m) in (JuMP.ALMOST_OPTIMAL, JuMP.OPTIMAL)
@test JuMP.objective_value(m) λ_cert atol = 1e-2
end
@testset "Wedderburn decomposition" begin
P = PermGroup(perm"(1,2)", Perm(circshift(1:N, -1)))
Σ = PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
act = PropertyT.action_by_conjugation(G, Σ)
wd = WedderburnDecomposition(
Float64,
Σ,
act,
basis(RG),
StarAlgebras.Basis{UInt16}(@view basis(RG)[1:sizes[halfradius]]),
)
status, certified, λ_cert = check_positivity(
elt,
unit,
wd,
upper_bound=ub,
halfradius=2,
optimizer=cosmo_optimizer(
eps=1e-7,
max_iters=10_000,
accel=50,
alpha=1.9,
),
)
@test status == JuMP.OPTIMAL
@test certified
@test λ_cert > 5857 // 10000
end
end
end