-
Notifications
You must be signed in to change notification settings - Fork 112
/
FiniteFormOrthogonalGroup.jl
144 lines (117 loc) · 4.17 KB
/
FiniteFormOrthogonalGroup.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
@testset "odd" begin
R = residue_ring(ZZ, ZZ(3))[1]
F = GF(3)
G = zero_matrix(R, 0, 0)
@test Oscar._orthogonal_grp_gens_odd(G, 3) == []
G = diagonal_matrix([R(1)])
@test Oscar._orthogonal_grp_gens_odd(G, 3) == [R[-1;]]
Oscar._gens(G,2, 3)
G = diagonal_matrix([R(1), R(1)])
L = Oscar._orthogonal_grp_gens_odd(G, 3)
L = [change_base_ring(F, lift(g)) for g in L]
@test order(matrix_group(L)) == 8
Oscar._gens(G,2, 3)
G = diagonal_matrix([R(1),R(2)])
L = Oscar._orthogonal_grp_gens_odd(G, 3)
L = [change_base_ring(F, lift(g)) for g in L]
@test order(matrix_group(L)) == 4
Oscar._gens(G,2, 3)
R = residue_ring(ZZ, 3^5)[1]
F = GF(3)
G = diagonal_matrix([R(x) for x in [3*1, 3*1]])
L = [change_base_ring(F, lift(g)) for g in Oscar._gens_mod_p(G, 3)]
@test order(matrix_group(L))==8
# Oscar._gens(G,2, 3)
G = diagonal_matrix([R(x) for x in [1, 3, 3, 9, 2*27]])
L = [change_base_ring(F,lift(g)) for g in Oscar._gens_mod_p(G, 3)]
@test order(matrix_group(L))==1259712
#Oscar._gens(G,2, 3)
R = residue_ring(ZZ, ZZ(3)^5)[1] #det(::zzModMatrix) is broken and cannot be used here
G = diagonal_matrix([R(x) for x in [2*27, 9, 3, 3, 1 ]])
Oscar._gens(G,2, 3)
end
@testset "_gens_mod_2" begin
R = residue_ring(ZZ, ZZ(2)^10)[1]
F = GF(2)
U = matrix(R, 2, 2, [0, 1, 1, 0])
V = matrix(R, 2, 2, [2, 1, 1, 2])
W0 = matrix(R, 2, 2, [1, 0, 0, 3])
W1 = matrix(R, 2, 2, [1, 0, 0, 1])
w1 = matrix(R, 1, 1, [1])
w3 = matrix(R, 1, 1, [3])
w5 = matrix(R, 1, 1, [5])
w7 = matrix(R, 1, 1, [7])
@test length(Oscar._orthogonal_gens_bilinear(zero_matrix(R,0,0))) == 0
L = [[U], [V], [V, w1, w1], [U, w1, w3], [w1, w7], [U, V], [V, w3],
[U, w1, w5]]
GG = [diagonal_matrix(G) for G in L]
GG = [Oscar._orthogonal_gens_bilinear(G) for G in GG]
GG = [matrix_group([change_base_ring(F, lift(g)) for g in G]) for G in GG]
GG = [order(G) for G in GG]
@test GG == [6, 6, 48, 48, 2, 720, 6, 48]
GG = [diagonal_matrix(G) for G in [[U,V], [U, W0],[V,W0],[U,U,W0],[U,V,W0], [W1]]]
GG = [Oscar._orthogonal_grp_quadratic(G) for G in GG]
GG = [matrix_group([change_base_ring(F, lift(g)) for g in G]) for G in GG]
GG = [order(G) for G in GG]
@test GG == [120, 8, 24, 1152,1920,2]
_ker_gens = Oscar._ker_gens
W0 = matrix(R, 2, 2, [0, 1, 1, 1])
W1 = matrix(R, 1, 1, [1])
W2 = matrix(R, 2, 2, [2, 1, 1, 1])
G = diagonal_matrix([V*4, U*2, U])
gen1 = _ker_gens(G, 2, 4, [0, 0, 0])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1)==8
G = diagonal_matrix([V*4, W1*2, W2])
gen1 = _ker_gens(G, 2, 3, [0, 1, 1])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1)==4
G = diagonal_matrix([V*4, U*2, W1])
gen1 = _ker_gens(G, 2, 4, [0, 0, 1])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
length(gen1)
@test length(gen1) == 2
G = diagonal_matrix([V*4, W2*2, U])
gen1 = _ker_gens(G, 2, 4, [0, 1, 0])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1) == 6
G = diagonal_matrix([W1*4, U*2, U])
gen1 = _ker_gens(G, 1, 3, [1,0,0])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1)==6
G = diagonal_matrix([W1*4, U*2, W0])
gen1 = _ker_gens(G, 1, 3, [1,0,1])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1)==5
G = diagonal_matrix([W0*4, W0*2, U])
gen1 = _ker_gens(G, 2, 4, [1,1,0])
gen1 = [Hecke.hensel_qf(G, g, 1, 2, 2) for g in gen1]
@test length(gen1)==6
G = diagonal_matrix([W1*4, U*2, W2*2, W1])
gen1 = _ker_gens(G, 2, 6, [1,1,1])
@test length(gen1)==0
L =[[2*U,2*V, w1], [2*U, w1,w7], [2*V,w5], [4*U,2*U,V,w5],
[8*U,V,w1,w3], [4*U,2*U,w1,w1],
[8*w1,4*V,2*U,2*w1,2*w5,U,V],
#[8*U,4*V,2*U,2*w1,2*w5,U,V],
[8*V,4*w1,2*U,2*w1,2*w5,U,V],
[8*V,4*V,4*w7,2*U,2*w1,2*w5,w1]
]
M = [diagonal_matrix(G) for G in L]
GG = [Oscar._gens_mod_2(G) for G in M]
GG = [matrix_group([change_base_ring(F, lift(g)) for g in G]) for G in GG]
GG = [order(G) for G in GG]
@test GG == [720,
24,
6,
1179648,
12288,
24576,
1781208836997120,
#7295831396340203520,
890604418498560,
57982058496]
for G in M
Oscar._gens(G, 8,2)
end
end