109 lines
2.5 KiB
Julia
109 lines
2.5 KiB
Julia
|
using Test
|
|||
|
|
|
|||
|
|
using PropertyT
|
|||
|
|
include("../src/SpNs.jl")
|
|||
|
|
using .SpNs
|
|||
|
|
using .SpNs.Roots
|
|||
|
|
|
|||
|
|
@testset "Roots" begin
|
|||
|
|
@test Root((2,1)) isa Root
|
|||
|
|
r = Root((2,1))
|
|||
|
|
@test -r isa Root
|
|||
|
|
@test 2r isa Root
|
|||
|
|
@test length(2r) == 2length(r)
|
|||
|
|
|
|||
|
|
@test r+r isa Root
|
|||
|
|
@test length(r+r) == 2length(r)
|
|||
|
|
@test r-r isa Root;
|
|||
|
|
@test length(r-r) == 0.0
|
|||
|
|
|
|||
|
|
r = Root((1,1));
|
|||
|
|
s = Root((-1,1));
|
|||
|
|
@test string(Root((1,1))) == "[1.0, 1.0]: root of length 1.4142135623730951"
|
|||
|
|
|
|||
|
|
@test isproportional(r, r)
|
|||
|
|
@test isproportional(r, -r)
|
|||
|
|
@test isproportional(r, 2r)
|
|||
|
|
@test isproportional(-r, 2r)
|
|||
|
|
@test isproportional(r+s, -s-r)
|
|||
|
|
|
|||
|
|
@test isorthogonal(r, s)
|
|||
|
|
@test isorthogonal(r, -s)
|
|||
|
|
@test isorthogonal(r, 2s)
|
|||
|
|
@test isorthogonal(-r, 2s)
|
|||
|
|
|
|||
|
|
@test !isorthogonal(r, r+s)
|
|||
|
|
@test !isorthogonal(r, -r)
|
|||
|
|
@test !isorthogonal(r+s, 2s)
|
|||
|
|
@test !isorthogonal(-r, 2s+r)
|
|||
|
|
|
|||
|
|
@test isorthogonal(r+s, -s+r)
|
|||
|
|
|
|||
|
|
N = 3
|
|||
|
|
@test length(Roots.E(N, 1) - Roots.E(N,2)) == sqrt(2)
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
|
|||
|
|
@testset "Symplectic Generators" begin
|
|||
|
|
|
|||
|
|
s = Sp{2}(:a, 1, 2)
|
|||
|
|
@test -s isa Sp
|
|||
|
|
@test inv(s) isa Sp
|
|||
|
|
t = Sp{2}(:b, 1, 2)
|
|||
|
|
@test -t isa Sp
|
|||
|
|
@test inv(t) isa Sp
|
|||
|
|
|
|||
|
|
@test isproportional(s, -s)
|
|||
|
|
@test isproportional(s, -s)
|
|||
|
|
@test isproportional(s, inv(s))
|
|||
|
|
|
|||
|
|
@test isproportional(t, -t)
|
|||
|
|
@test isproportional(t, inv(t))
|
|||
|
|
@test !isproportional(s, t)
|
|||
|
|
@test !isproportional(inv(s), -t)
|
|||
|
|
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
@testset "Symplectic Group" begin
|
|||
|
|
|
|||
|
|
@testset "Symplectic Root System" begin
|
|||
|
|
rs = SpNs.gens_roots(2)
|
|||
|
|
S = [r.matrix for r in rs];
|
|||
|
|
@test all(SpNs.issymplectic.(S))
|
|||
|
|
@test length(S) == 16
|
|||
|
|
|
|||
|
|
rs = SpNs.gens_roots(3)
|
|||
|
|
S = [r.matrix for r in rs];
|
|||
|
|
@test all(SpNs.issymplectic.(S))
|
|||
|
|
@test length(S) == 36
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
@testset "Sp(4,Z)" begin
|
|||
|
|
|
|||
|
|
N = 2
|
|||
|
|
root_system = SpNs.gens_roots(N)
|
|||
|
|
S = [g.matrix for g in root_system]
|
|||
|
|
|
|||
|
|
Δ = PropertyT.Laplacian(S, 2)
|
|||
|
|
RG = parent(Δ)
|
|||
|
|
|
|||
|
|
Δs = SpNs.laplacians(RG, root_system)
|
|||
|
|
|
|||
|
|
@test sum(Δα for (α, Δα) in Δs) == Δ
|
|||
|
|
|
|||
|
|
@testset "Orthogonality & commutation" begin
|
|||
|
|
r = Root([2, 0])
|
|||
|
|
s = Root([0, 2])
|
|||
|
|
|
|||
|
|
a = Δs[r]
|
|||
|
|
b = Δs[s]
|
|||
|
|
@test a*b == b*a
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
Sq = sum( Δα^2 for (α, Δα) in Δs );
|
|||
|
|
Adj = sum( Δα * sum(Δβ for (β, Δβ) in Δs if !isproportional(α, β)) for (α, Δα) in Δs );
|
|||
|
|
|
|||
|
|
@test Sq + Adj == Δ^2
|
|||
|
|
end
|
|||
|
|
end
|