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GroupRings.jl
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add SOS tests in FreeGroup & test MTables

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Marek Kaluba 2021-06-19 01:03:26 +02:00
parent 6fac166a04
commit 625e521a54
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2 changed files with 118 additions and 0 deletions
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1
test/runtests.jl
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@ -13,6 +13,7 @@ using GroupRings.New
include("constructors.jl")
include("cachedmtables.jl")
include("arithmetic.jl")
include("sum_of_squares.jl")
end
@testset "GroupRings" begin

117
test/sum_of_squares.jl Normal file
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@ -0,0 +1,117 @@
using Groups
@testset "FreeGroup algebra" begin
New.star(g::Groups.New.GroupElement) = inv(g)
F = Groups.New.FreeGroup(4)
S = [gens(F); inv.(gens(F))]
ID = one(F)
RADIUS=3
@time E_R, sizes = Groups.wlmetric_ball(S, ID, radius=2*RADIUS);
@test sizes == [9, 65, 457, 3201, 22409, 156865]
b = New.Basis{UInt32}(E_R)
@testset "MTables" begin
mstr = New.MTable{false}(b, table_size=(sizes[RADIUS], sizes[RADIUS]))
@test mstr isa New.MTable{UInt32, false}
@test all(mstr[i,i]≠1 for i in 2:size(mstr, 1))
@test all(mstr[1,i]==i for i in 1:size(mstr, 2))
@test all(mstr[i,1]==i for i in 1:size(mstr, 1))
tmstr = New.MTable{true}(b, table_size=(sizes[RADIUS], sizes[RADIUS]))
@test tmstr isa New.MTable{UInt32, true}
@test all(tmstr[i,i]==1 for i in 1:size(tmstr, 1))
@test all(tmstr[1,i]==i for i in 1:size(tmstr, 2))
@test all(tmstr[i,1]≠ i for i in 2:size(tmstr, 1))
end
tmstr = New.MTable{true}(b, table_size=(sizes[RADIUS], sizes[RADIUS]))
RG = New.StarAlgebra(F, b, tmstr)
g, h, k, l = S[1:4]
length(b)
G = (one(RG)-RG(g))
G
@test G^2 == New.mul!(zero(G), G, G) == 2one(RG) - RG(g) - New.star(RG(g))
@test New.star(G*G) == G*G
@testset "Sums of hermitian squares" begin
∗ = New.star
𝕀 = one(RG)
G = (𝕀 - RG(g))
H = (𝕀 - RG(h))
K = (𝕀 - RG(k))
L = (𝕀 - RG(l))
GH = (𝕀 - RG(g*h))
KL = (𝕀 - RG(k*l))
X = (2𝕀 - ∗(RG(g)) - RG(h))
Y = (2𝕀 - ∗(RG(g*h)) - RG(k))
@test -(2𝕀 - RG(g*h) - ∗(RG(g*h))) + 2G^2 + 2H^2 == X^2
@test (2𝕀 - RG(g*h) - ∗(RG(g*h))) == GH^2
@test -(2𝕀 - RG(g*h*k) - ∗(RG(g*h*k))) + 2GH^2 + 2K^2 == Y^2
@test -(2𝕀 - RG(g*h*k) - ∗(RG(g*h*k))) +
2(GH^2 - 2G^2 - 2H^2) +
4G^2 + 4H^2 + 2K^2 ==
Y^2
@test GH^2 - 2G^2 - 2H^2 == - X^2
@test -(2𝕀 - RG(g*h*k) - ∗(RG(g*h*k))) + 4G^2 + 4H^2 + 2K^2 == 2X^2 + Y^2
@test GH^2 == 2G^2 + 2H^2 - (2𝕀 - ∗(RG(g)) - RG(h))^2
@test KL^2 == 2K^2 + 2L^2 - (2𝕀 - ∗(RG(k)) - RG(l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2*GH^2 + 2*KL^2 ==
(2𝕀 - ∗(RG(g*h)) - RG(k*l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2G^2 + 2H^2 - (2𝕀 - ∗(RG(g)) - RG(h))^2) +
2(2K^2 + 2L^2 - (2𝕀 - ∗(RG(k)) - RG(l))^2) ==
(2𝕀 - ∗(RG(g*h)) - RG(k*l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2G^2 + 2H^2) +
2(2K^2 + 2L^2) ==
(2𝕀 - ∗(RG(g*h)) - RG(k*l))^2 +
2(2𝕀 - ∗(RG(g)) - RG(h))^2 +
2(2𝕀 - ∗(RG(k)) - RG(l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2𝕀 - ∗(RG(g*h*k)) - RG(g*h*k)) + 2L^2 ==
(2𝕀 - ∗(RG(g*h*k)) - RG(l))^2
@test 2𝕀 - ∗(RG(g*h*k)) - RG(g*h*k) ==
2GH^2 + 2K^2 - (2𝕀 - ∗(RG(g*h)) - RG(k))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2GH^2 + 2K^2 - (2𝕀 - ∗(RG(g*h)) - RG(k))^2) + 2L^2 ==
(2𝕀 - ∗(RG(g*h*k)) - RG(l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2GH^2 + 2K^2) + 2L^2 ==
(2𝕀 - ∗(RG(g*h*k)) - RG(l))^2 +
2(2𝕀 - ∗(RG(g*h)) - RG(k))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
8G^2 + 8H^2 + 4K^2 + 2L^2 ==
(2𝕀 - ∗(RG(g*h*k)) - RG(l))^2 + 2(2𝕀 - ∗(RG(g*h)) - RG(k))^2 + 4(2𝕀 - ∗(RG(g)) - RG(h))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2GH^2 + 2KL^2 == (2𝕀 - ∗(RG(g*h)) - RG(k*l))^2
@test -(2𝕀 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2(2G^2 + 2H^2) + 2(2K^2 + 2L^2) ==
(2𝕀 - ∗(RG(g*h)) - RG(k*l))^2 + 2(2𝕀 - ∗(RG(k)) - RG(l))^2 + 2(2𝕀 - ∗(RG(g)) - RG(h))^2
end
end