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