def test_tuple_normalize_4(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
app_group = DuplicateGroup(
ProductGroup([
TrivialGroup(1, action=1),
SymmetricGroupTranspositions(4, action=1),
]),
times=4,
)
full_group = PermutationGroupFromGens(
list(app_group) + list(arch_group))
assert full_group.tuple_normalize([
2,
2,
8,
2,
2,
2,
2,
2,
2,
25,
25,
24,
25,
24,
25,
2,
2,
24,
2,
2,
]) == [
0,
0,
0,
0,
8,
0,
0,
0,
25,
0,
25,
24,
24,
25,
25,
0,
0,
0,
0,
24,
]
def test_tuple_normalize(self):
s4xs8 = ProductGroup(
[SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4)])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
assert arch_group.tuple_normalize(
[1, 10, 1, 9, 7, 1, 1, 1, 22, 25,
24]) == [0, 8, 0, 9, 1, 0, 0, 0, 20, 25, 24]
def test_tuple_orbit_2(self):
s4xs8 = ProductGroup(
[SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4)])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
assert (len(
list(arch_group.tuple_orbit([1, 10, 1, 9, 7, 1, 1, 1, 22, 25,
24]))) == 672)
def test_tuple_normalize_2(self):
s4xs8 = ProductGroup(
[SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4)])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
assert arch_group.tuple_normalize(
[
0,
8,
0,
0,
0,
0,
0,
0,
0,
25,
25,
24,
25,
24,
25,
0,
0,
24,
0,
0,
],
verbose=True,
) == [
0,
8,
0,
0,
0,
0,
0,
0,
0,
25,
25,
24,
25,
24,
25,
0,
0,
24,
0,
0,
]
def test_tuple_normalize_3(self):
app_group = DuplicateGroup(
ProductGroup([
TrivialGroup(1, action=1),
SymmetricGroupTranspositions(4, action=1),
]),
times=4,
)
assert app_group.tuple_normalize([
0,
8,
0,
0,
0,
0,
0,
0,
0,
25,
25,
24,
25,
24,
25,
0,
0,
24,
0,
0,
]) == [
0,
0,
0,
0,
8,
0,
0,
0,
25,
0,
25,
24,
25,
25,
24,
0,
0,
24,
0,
0,
]
def test_generators(self):
s4xs8 = ProductGroup(
[SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4)])
s4xs8_double = DuplicateGroup(s4xs8)
assert s4xs8_double.generators() == [
[[12, 13], [0, 1]],
[[12, 14], [0, 2]],
[[12, 15], [0, 3]],
[[12, 16], [0, 4]],
[[12, 17], [0, 5]],
[[12, 18], [0, 6]],
[[12, 19], [0, 7]],
[[13, 14], [1, 2]],
[[13, 15], [1, 3]],
[[13, 16], [1, 4]],
[[13, 17], [1, 5]],
[[13, 18], [1, 6]],
[[13, 19], [1, 7]],
[[14, 15], [2, 3]],
[[14, 16], [2, 4]],
[[14, 17], [2, 5]],
[[14, 18], [2, 6]],
[[14, 19], [2, 7]],
[[15, 16], [3, 4]],
[[15, 17], [3, 5]],
[[15, 18], [3, 6]],
[[15, 19], [3, 7]],
[[16, 17], [4, 5]],
[[16, 18], [4, 6]],
[[16, 19], [4, 7]],
[[17, 18], [5, 6]],
[[17, 19], [5, 7]],
[[18, 19], [6, 7]],
[[20, 21], [8, 9]],
[[20, 22], [8, 10]],
[[20, 23], [8, 11]],
[[21, 22], [9, 10]],
[[21, 23], [9, 11]],
[[22, 23], [10, 11]],
]
def test_ProductGroup(self):
s4xs8 = ProductGroup(
[SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4)])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
# fmt: off
assert (arch_group == [
[
1, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 12, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
2, 1, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 13, 12, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
3, 1, 2, 0, 4, 5, 6, 7, 8, 9, 10, 11, 15, 13, 14, 12, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
4, 1, 2, 3, 0, 5, 6, 7, 8, 9, 10, 11, 16, 13, 14, 15, 12, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
5, 1, 2, 3, 4, 0, 6, 7, 8, 9, 10, 11, 17, 13, 14, 15, 16, 12,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
6, 1, 2, 3, 4, 5, 0, 7, 8, 9, 10, 11, 18, 13, 14, 15, 16, 17,
12, 19, 20, 21, 22, 23, 24, 25, 26
],
[
7, 1, 2, 3, 4, 5, 6, 0, 8, 9, 10, 11, 19, 13, 14, 15, 16, 17,
18, 12, 20, 21, 22, 23, 24, 25, 26
],
[
0, 2, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 13, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 3, 2, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 14, 13, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 4, 2, 3, 1, 5, 6, 7, 8, 9, 10, 11, 12, 16, 14, 15, 13, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 5, 2, 3, 4, 1, 6, 7, 8, 9, 10, 11, 12, 17, 14, 15, 16, 13,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 6, 2, 3, 4, 5, 1, 7, 8, 9, 10, 11, 12, 18, 14, 15, 16, 17,
13, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 7, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 19, 14, 15, 16, 17,
18, 13, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 4, 3, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 15, 14, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 5, 3, 4, 2, 6, 7, 8, 9, 10, 11, 12, 13, 17, 15, 16, 14,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 6, 3, 4, 5, 2, 7, 8, 9, 10, 11, 12, 13, 18, 15, 16, 17,
14, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 7, 3, 4, 5, 6, 2, 8, 9, 10, 11, 12, 13, 19, 15, 16, 17,
18, 14, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 4, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 15, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 5, 4, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 16, 15,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 6, 4, 5, 3, 7, 8, 9, 10, 11, 12, 13, 14, 18, 16, 17,
15, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 7, 4, 5, 6, 3, 8, 9, 10, 11, 12, 13, 14, 19, 16, 17,
18, 15, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 5, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16,
18, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 6, 5, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 17,
16, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 7, 5, 6, 4, 8, 9, 10, 11, 12, 13, 14, 15, 19, 17,
18, 16, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18,
17, 19, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 7, 6, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19,
18, 17, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
19, 18, 20, 21, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 21, 20, 22, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 10, 9, 8, 11, 12, 13, 14, 15, 16, 17,
18, 19, 22, 21, 20, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 11, 9, 10, 8, 12, 13, 14, 15, 16, 17,
18, 19, 23, 21, 22, 20, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 22, 21, 23, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 10, 9, 12, 13, 14, 15, 16, 17,
18, 19, 20, 23, 22, 21, 24, 25, 26
],
[
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 23, 22, 24, 25, 26
]
])
def test_tuple_normalize_7(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
assert arch_group.tuple_normalize(
[
11,
6,
10,
7,
10,
10,
5,
8,
10,
8,
11,
2,
24,
24,
18,
24,
10,
22,
24,
22,
22,
24,
20,
10,
20,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
9,
2,
10,
9,
10,
8,
3,
24,
24,
12,
24,
9,
21,
24,
21,
21,
24,
22,
9,
22,
24,
24,
]
def test_tuple_normalize_6(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
mjpeg_gens_func = lambda l: [(i, j) for i in l
for j in l[l.index(i):]]
mjpeg_procs_gens = mjpeg_gens_func(
[6, 8, 10, 1]) + mjpeg_gens_func([5, 7, 9, 11])
mjpeg_chans_gens = (mjpeg_gens_func([16, 17, 18, 19]) +
mjpeg_gens_func([20, 22, 24, 26]) +
mjpeg_gens_func([21, 23, 25, 14]))
mjpeg_group = PermutationGroupFromGens(
list(
map(
lambda trans: Permutation.fromLists(
[list(trans)], action=1, n=27),
(mjpeg_chans_gens + mjpeg_procs_gens),
)))
mjpeg_full_group = PermutationGroupFromGens(
list(arch_group) + list(mjpeg_group))
assert mjpeg_full_group.tuple_normalize(
[
11,
6,
10,
7,
10,
10,
5,
8,
10,
8,
11,
2,
24,
24,
18,
24,
10,
22,
24,
22,
22,
24,
20,
10,
20,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
2,
3,
9,
8,
10,
9,
10,
24,
24,
9,
24,
9,
21,
21,
24,
21,
12,
22,
24,
22,
24,
24,
]
def test_tuple_normalize_5(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
mandelbrot_group = DuplicateGroup(
SymmetricGroupTranspositions(16, action=1),
times=3,
trivials=[16, 17],
)
mandelbrot_full_group = PermutationGroupFromGens(
list(arch_group) + list(mandelbrot_group))
assert mandelbrot_full_group.tuple_normalize([
6,
6,
1,
2,
7,
6,
9,
10,
6,
11,
9,
0,
1,
0,
4,
3,
5,
0,
18,
24,
25,
14,
24,
24,
25,
24,
24,
24,
25,
12,
13,
25,
25,
15,
25,
24,
25,
25,
24,
12,
25,
25,
25,
24,
12,
0,
24,
0,
24,
12,
]) == [
0,
0,
0,
0,
1,
1,
2,
3,
4,
5,
5,
6,
8,
8,
9,
10,
7,
5,
12,
24,
24,
24,
13,
25,
14,
15,
25,
17,
25,
24,
25,
25,
24,
24,
25,
17,
24,
25,
24,
25,
25,
17,
24,
5,
5,
24,
17,
25,
24,
25,
]
def test_duplicate_group(self):
app_group = DuplicateGroup(
ProductGroup([
TrivialGroup(1, action=1),
SymmetricGroupTranspositions(4, action=1),
]),
times=4,
)
# fmt: off
assert (app_group == [[
0, 2, 1, 3, 4, 5, 7, 6, 8, 9, 10, 12, 11, 13, 14, 15, 17, 16, 18,
19
],
[
0, 3, 2, 1, 4, 5, 8, 7, 6, 9, 10, 13, 12, 11,
14, 15, 18, 17, 16, 19
],
[
0, 4, 2, 3, 1, 5, 9, 7, 8, 6, 10, 14, 12, 13,
11, 15, 19, 17, 18, 16
],
[
0, 1, 3, 2, 4, 5, 6, 8, 7, 9, 10, 11, 13, 12,
14, 15, 16, 18, 17, 19
],
[
0, 1, 4, 3, 2, 5, 6, 9, 8, 7, 10, 11, 14, 13,
12, 15, 16, 19, 18, 17
],
[
0, 1, 2, 4, 3, 5, 6, 7, 9, 8, 10, 11, 12, 14,
13, 15, 16, 17, 19, 18
]])
# fmt: on
def test_tuple_normalize_3(self):
app_group = DuplicateGroup(
ProductGroup([
TrivialGroup(1, action=1),
SymmetricGroupTranspositions(4, action=1),
]),
times=4,
)
assert app_group.tuple_normalize([
0,
8,
0,
0,
0,
0,
0,
0,
0,
25,
25,
24,
25,
24,
25,
0,
0,
24,
0,
0,
]) == [
0,
0,
0,
0,
8,
0,
0,
0,
25,
0,
25,
24,
25,
25,
24,
0,
0,
24,
0,
0,
]
def test_tuple_normalize_4(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
app_group = DuplicateGroup(
ProductGroup([
TrivialGroup(1, action=1),
SymmetricGroupTranspositions(4, action=1),
]),
times=4,
)
full_group = PermutationGroupFromGens(
list(app_group) + list(arch_group))
assert full_group.tuple_normalize([
2,
2,
8,
2,
2,
2,
2,
2,
2,
25,
25,
24,
25,
24,
25,
2,
2,
24,
2,
2,
]) == [
0,
0,
0,
0,
8,
0,
0,
0,
25,
0,
25,
24,
24,
25,
25,
0,
0,
0,
0,
24,
]
def test_tuple_normalize_5(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
mandelbrot_group = DuplicateGroup(
SymmetricGroupTranspositions(16, action=1),
times=3,
trivials=[16, 17],
)
mandelbrot_full_group = PermutationGroupFromGens(
list(arch_group) + list(mandelbrot_group))
assert mandelbrot_full_group.tuple_normalize([
6,
6,
1,
2,
7,
6,
9,
10,
6,
11,
9,
0,
1,
0,
4,
3,
5,
0,
18,
24,
25,
14,
24,
24,
25,
24,
24,
24,
25,
12,
13,
25,
25,
15,
25,
24,
25,
25,
24,
12,
25,
25,
25,
24,
12,
0,
24,
0,
24,
12,
]) == [
0,
0,
0,
0,
1,
1,
2,
3,
4,
5,
5,
6,
8,
8,
9,
10,
7,
5,
12,
24,
24,
24,
13,
25,
14,
15,
25,
17,
25,
24,
25,
25,
24,
24,
25,
17,
24,
25,
24,
25,
25,
17,
24,
5,
5,
24,
17,
25,
24,
25,
]
def test_tuple_normalize_6(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
mjpeg_gens_func = lambda l: [(i, j) for i in l
for j in l[l.index(i):]]
mjpeg_procs_gens = mjpeg_gens_func(
[6, 8, 10, 1]) + mjpeg_gens_func([5, 7, 9, 11])
mjpeg_chans_gens = (mjpeg_gens_func([16, 17, 18, 19]) +
mjpeg_gens_func([20, 22, 24, 26]) +
mjpeg_gens_func([21, 23, 25, 14]))
mjpeg_group = PermutationGroupFromGens(
list(
map(
lambda trans: Permutation.fromLists(
[list(trans)], action=1, n=27),
(mjpeg_chans_gens + mjpeg_procs_gens),
)))
mjpeg_full_group = PermutationGroupFromGens(
list(arch_group) + list(mjpeg_group))
assert mjpeg_full_group.tuple_normalize(
[
11,
6,
10,
7,
10,
10,
5,
8,
10,
8,
11,
2,
24,
24,
18,
24,
10,
22,
24,
22,
22,
24,
20,
10,
20,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
2,
3,
9,
8,
10,
9,
10,
24,
24,
9,
24,
9,
21,
21,
24,
21,
12,
22,
24,
22,
24,
24,
]
def test_tuple_normalize_7(self):
s4xs8 = ProductGroup([
SymmetricGroupTranspositions(8),
SymmetricGroupTranspositions(4),
])
s4xs8_double = DuplicateGroup(s4xs8)
arch_group = ProductGroup([s4xs8_double, TrivialGroup(3)])
assert arch_group.tuple_normalize(
[
11,
6,
10,
7,
10,
10,
5,
8,
10,
8,
11,
2,
24,
24,
18,
24,
10,
22,
24,
22,
22,
24,
20,
10,
20,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
9,
2,
10,
9,
10,
8,
3,
24,
24,
12,
24,
9,
21,
24,
21,
21,
24,
22,
9,
22,
24,
24,
]
def test_tuple_normalize_8(self):
mjpeg_gens_func = lambda l: [(i, j) for i in l
for j in l[l.index(i):]]
mjpeg_procs_gens = mjpeg_gens_func(
[6, 8, 10, 1]) + mjpeg_gens_func([5, 7, 9, 11])
mjpeg_chans_gens = (mjpeg_gens_func([16, 17, 18, 19]) +
mjpeg_gens_func([20, 22, 24, 26]) +
mjpeg_gens_func([21, 23, 25, 14]))
mjpeg_group = PermutationGroupFromGens(
list(
map(
lambda trans: Permutation.fromLists(
[list(trans)], action=1, n=27),
(mjpeg_chans_gens + mjpeg_procs_gens),
)))
assert mjpeg_group.tuple_normalize(
[
8,
0,
9,
1,
9,
9,
2,
10,
9,
10,
8,
3,
24,
24,
12,
24,
9,
21,
24,
21,
21,
24,
22,
9,
22,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
3,
2,
9,
8,
10,
9,
10,
24,
24,
9,
24,
9,
21,
21,
24,
21,
12,
22,
24,
22,
24,
24,
]
assert mjpeg_group.tuple_normalize(
[
8,
0,
9,
1,
9,
9,
2,
10,
9,
10,
8,
3,
24,
24,
12,
24,
9,
21,
24,
21,
21,
24,
22,
9,
22,
24,
24,
],
verbose=True,
) == [
8,
0,
9,
1,
9,
3,
2,
9,
8,
10,
9,
10,
24,
24,
9,
24,
9,
21,
21,
24,
21,
12,
22,
24,
22,
24,
24,
]
def test_DuplicateGroup(self):
assert (DuplicateGroup(
SymmetricGroupTranspositions(2, action=1),
times=7,
trivials=[6, 7],
) == [[1, 0, 3, 2, 5, 4, 6, 7, 9, 8, 11, 10, 13, 12, 15, 14]])