kalmar/GroupRings.jl
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add tests for sum of squares

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kalmarek 2018-11-17 22:46:03 +01:00
parent 558cbc78d8
commit 10f3a97576
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test/runtests.jl
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@ -209,4 +209,91 @@ using GroupRings
end end
end end
@testset "SumOfSquares in group rings" begin
∗ = star
G = FreeGroup(["g", "h", "k", "l"])
S = G.(G.gens)
S = [S; inv.(S)]
ID = G()
RADIUS=3
@time E_R, sizes = Groups.generate_balls(S, ID, radius=2*RADIUS);
@test sizes == [9, 65, 457, 3201, 22409, 156865]
E_rdict = GroupRings.reverse_dict(E_R)
pm = GroupRings.create_pm(E_R, E_rdict, sizes[RADIUS]; twisted=true);
RG = GroupRing(G, E_R, E_rdict, pm)
g = RG.basis[2]
h = RG.basis[3]
k = RG.basis[4]
l = RG.basis[5]
G = (1-RG(g))
@test G^2 == 2 - RG(g) - ∗(RG(g))
G = (1-RG(g))
H = (1-RG(h))
K = (1-RG(k))
L = (1-RG(l))
GH = (1-RG(g*h))
KL = (1-RG(k*l))
X = (2 - ∗(RG(g)) - RG(h))
Y = (2 - ∗(RG(g*h)) - RG(k))
@test -(2 - RG(g*h) - ∗(RG(g*h))) + 2G^2 + 2H^2 == X^2
@test (2 - RG(g*h) - ∗(RG(g*h))) == GH^2
@test -(2 - RG(g*h*k) - ∗(RG(g*h*k))) + 2GH^2 + 2K^2 == Y^2
@test -(2 - 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 -(2 - 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 - (2 - ∗(RG(g)) - RG(h))^2
@test KL^2 == 2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) + 2*GH^2 + 2*KL^2 ==
(2 - ∗(RG(g*h)) - RG(k*l))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2G^2 + 2H^2 - (2 - ∗(RG(g)) - RG(h))^2) +
2(2K^2 + 2L^2 - (2 - ∗(RG(k)) - RG(l))^2) ==
(2 - ∗(RG(g*h)) - RG(k*l))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2G^2 + 2H^2) +
2(2K^2 + 2L^2) ==
(2 - ∗(RG(g*h)) - RG(k*l))^2 +
2(2 - ∗(RG(g)) - RG(h))^2 +
2(2 - ∗(RG(k)) - RG(l))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2 - ∗(RG(g*h*k)) - RG(g*h*k)) + 2L^2 ==
(2 - ∗(RG(g*h*k)) - RG(l))^2
@test 2 - ∗(RG(g*h*k)) - RG(g*h*k) ==
2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2GH^2 + 2K^2 - (2 - ∗(RG(g*h)) - RG(k))^2) + 2L^2 ==
(2 - ∗(RG(g*h*k)) - RG(l))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2(2GH^2 + 2K^2) + 2L^2 ==
(2 - ∗(RG(g*h*k)) - RG(l))^2 +
2(2 - ∗(RG(g*h)) - RG(k))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
8G^2 + 8H^2 + 4K^2 + 2L^2 ==
(2 - ∗(RG(g*h*k)) - RG(l))^2 +
2(2 - ∗(RG(g*h)) - RG(k))^2 +
4(2 - ∗(RG(g)) - RG(h))^2
@test -(2 - ∗(RG(g*h*k*l)) - RG(g*h*k*l)) +
2GH^2 + 2KL^2 == (2 - ∗(RG(g*h)) - RG(k*l))^2
end
end end