mirror of
https://github.com/kalmarek/PropertyT.jl.git
synced 2024-08-15 01:40:39 +02:00
211 lines
6.2 KiB
Julia
211 lines
6.2 KiB
Julia
function test_action(basis, group, act)
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action = SymbolicWedderburn.action
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return @testset "action definition" begin
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@test all(basis) do b
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e = one(group)
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action(act, e, b) == b
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end
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a = let a = rand(basis)
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while isone(a)
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a = rand(basis)
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end
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@assert !isone(a)
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a
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end
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g, h = let g_h = rand(group, 2)
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while any(isone, g_h)
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g_h = rand(group, 2)
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end
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@assert all(!isone, g_h)
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g_h
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end
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action = SymbolicWedderburn.action
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@test action(act, g, a) in basis
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@test action(act, h, a) in basis
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@test action(act, h, action(act, g, a)) == action(act, g * h, a)
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@test all([(g, h) for g in group for h in group]) do (g, h)
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x = action(act, h, action(act, g, a))
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y = action(act, g * h, a)
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x == y
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end
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if act isa SymbolicWedderburn.ByPermutations
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@test all(basis) do b
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action(act, g, b) ∈ basis && action(act, h, b) ∈ basis
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end
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end
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end
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end
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## Testing
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@testset "Actions on SL(3,ℤ)" begin
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n = 3
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SL = MatrixGroups.SpecialLinearGroup{n}(Int8)
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RSL, S, sizes = PropertyT.group_algebra(SL, halfradius=2, twisted=true)
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@testset "Permutation action" begin
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Γ = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
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ΓpA = PropertyT.action_by_conjugation(SL, Γ)
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test_action(basis(RSL), Γ, ΓpA)
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@testset "mps is successful" begin
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charsΓ =
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SymbolicWedderburn.Character{
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Rational{Int},
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}.(SymbolicWedderburn.irreducible_characters(Γ))
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RΓ = SymbolicWedderburn._group_algebra(Γ)
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@time mps, simple =
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SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
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@test all(simple)
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end
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@testset "Wedderburn decomposition" begin
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wd = SymbolicWedderburn.WedderburnDecomposition(
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Rational{Int},
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Γ,
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ΓpA,
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basis(RSL),
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StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]])
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)
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@test length(invariant_vectors(wd)) == 918
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@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [40, 23, 18]
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@test all(issimple, direct_summands(wd))
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end
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end
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@testset "Wreath action" begin
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Γ = let P = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
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PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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end
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ΓpA = PropertyT.action_by_conjugation(SL, Γ)
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test_action(basis(RSL), Γ, ΓpA)
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@testset "mps is successful" begin
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charsΓ =
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SymbolicWedderburn.Character{
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Rational{Int},
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}.(SymbolicWedderburn.irreducible_characters(Γ))
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RΓ = SymbolicWedderburn._group_algebra(Γ)
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@time mps, simple =
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SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
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@test all(simple)
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end
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@testset "Wedderburn decomposition" begin
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wd = SymbolicWedderburn.WedderburnDecomposition(
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Rational{Int},
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Γ,
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ΓpA,
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basis(RSL),
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StarAlgebras.Basis{UInt16}(@view basis(RSL)[1:sizes[2]])
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)
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@test length(invariant_vectors(wd)) == 247
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@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [14, 9, 6, 14, 12]
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@test all(issimple, direct_summands(wd))
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end
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end
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end
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@testset "Actions on SAut(F4)" begin
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n = 4
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SAutFn = SpecialAutomorphismGroup(FreeGroup(n))
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RSAutFn, S, sizes = PropertyT.group_algebra(SAutFn, halfradius=1, twisted=true)
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@testset "Permutation action" begin
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Γ = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
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ΓpA = PropertyT.action_by_conjugation(SAutFn, Γ)
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test_action(basis(RSAutFn), Γ, ΓpA)
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@testset "mps is successful" begin
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charsΓ =
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SymbolicWedderburn.Character{
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Rational{Int},
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}.(SymbolicWedderburn.irreducible_characters(Γ))
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RΓ = SymbolicWedderburn._group_algebra(Γ)
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@time mps, simple =
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SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
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@test all(simple)
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end
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@testset "Wedderburn decomposition" begin
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wd = SymbolicWedderburn.WedderburnDecomposition(
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Rational{Int},
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Γ,
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ΓpA,
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basis(RSAutFn),
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StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]])
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)
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@test length(invariant_vectors(wd)) == 93
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@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [4, 8, 5, 4]
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@test all(issimple, direct_summands(wd))
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end
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end
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@testset "Wreath action" begin
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Γ = let P = PermGroup(perm"(1,2)", Perm(circshift(1:n, -1)))
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PropertyT.Constructions.WreathProduct(PermGroup(perm"(1,2)"), P)
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end
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ΓpA = PropertyT.action_by_conjugation(SAutFn, Γ)
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test_action(basis(RSAutFn), Γ, ΓpA)
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@testset "mps is successful" begin
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charsΓ =
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SymbolicWedderburn.Character{
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Rational{Int},
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}.(SymbolicWedderburn.irreducible_characters(Γ))
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RΓ = SymbolicWedderburn._group_algebra(Γ)
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@time mps, simple =
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SymbolicWedderburn.minimal_projection_system(charsΓ, RΓ)
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@test all(simple)
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end
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@testset "Wedderburn decomposition" begin
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wd = SymbolicWedderburn.WedderburnDecomposition(
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Rational{Int},
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Γ,
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ΓpA,
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basis(RSAutFn),
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StarAlgebras.Basis{UInt16}(@view basis(RSAutFn)[1:sizes[1]])
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)
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@test length(invariant_vectors(wd)) == 18
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@test SymbolicWedderburn.size.(direct_summands(wd), 1) == [1, 1, 2, 2, 1, 2, 2, 1]
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@test all(issimple, direct_summands(wd))
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end
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end
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end
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