def test_pow(self):
# test if pow behaves as expected with conjugates
for g, h in itertools.product(self.perms, self.perms):
for n in range(10):
self.assertEqual(h * g**n * h.inverse(),
(h * g * h.inverse())**n)
for g in self.perms:
# check if iterative calculation agrees
prod = self.operm
for n in range(10):
self.assertTrue((g**n).is_permutation())
self.assertEqual(g**n, prod)
self.assertEqual(g**(-n), prod.inverse())
prod *= g
# check if cyclic subgroup generated by g is abelian :)
for a in range(-10, 10):
for b in range(-10, 10):
self.assertEqual(g**a * g**b, g**(a + b))
self.assertEqual(g**-1, g.inverse())
# check if the order divides the LCM of cycle lengths
order = reduce(mul,
map(len, g.disjoint_cycle_decomposition_unstable()),
1)
self.assertEqual(g**order, self.operm)
self.assertEqual(
Perm.from_cycle(range(10))**9,
Perm.from_cycle(range(10)).inverse())
def test_comp(self):
for g in self.perms:
self.assertEqual(g * g.inverse(), self.operm)
for g, h in itertools.product(self.perms, self.perms):
self.assertTrue((g * h).is_permutation())
# conjugates should preserve cycle type
conj = h * g * h.inverse()
self.assertCountEqual(
list(map(len, g.disjoint_cycle_decomposition_unstable())),
list(map(len, conj.disjoint_cycle_decomposition_unstable())))
# associativity of composition
for g, h, k in itertools.product(*[self.perms] * 3):
self.assertEqual((g * h) * k, g * (h * k))
self.assertEqual(
Perm.from_cycle([4, 5, 6]) * self.perm6,
Perm({
1: 2,
2: 1,
4: 6,
5: 4,
6: 5
}))
self.assertEqual(
Perm.from_cycle([1, 2]) * Perm.from_cycle([2, 3]),
Perm.from_cycle([1, 2, 3]))
self.assertEqual(self.perm3c**3, self.operm)
def setUp(self):
self.perm6 = Perm({1: 2, 2: 1, 3: 3, 4: 5, 5: 6, 6: 4})
self.operm = Perm({})
self.permoc = Perm.from_cycle([])
self.perm1c = Perm.from_cycle([1])
self.perm2c = Perm.from_cycle([1, 2])
self.perm3c = Perm.from_cycle([1, 2, 3])
# huge list of hopefully lots of different kinds of permutation covering
# lots of edge cases
self.reg_perms = [
self.permoc, self.perm1c, self.perm2c, self.perm3c,
*(Perm.from_cycle(range(j, j + i)) for i in range(4, 9)
for j in range(9 - i)),
*(Perm.from_cycle(range(j, j + i)[::-1]) for i in range(2, 9)
for j in range(9 - i)), self.operm, self.perm6
]
# add some more random permutations to hopefully catch more edge cases,
# but keep them in a separate list so I can also access a deterministic
# list of permutations that I can guarantee properties of
self.perms = [
*self.reg_perms, *(Perm.random(range(i)) for i in range(4, 20))
]
for _ in range(10):
a, b = sample(self.perms, 2)
self.perms.append(a * b)
def test_repr(self):
for g in self.perms:
repr(g)
self.assertEqual(repr(Perm(OrderedDict(((1, 2), (2, 1))))),
"Perm(OrderedDict([(1, 2), (2, 1)]))")
self.assertEqual(repr(Perm()),
"Perm({})")
def test_autoperm_decipher(self):
sigma = Perm.from_cycle("ABCD")
tau = Perm.from_cycle("AB") * Perm.from_cycle("CD")
self.assertEqual(list(autoperm_decipher.func("BADCCB", sigma, tau)),
list("ABCDAB"))
self.assertEqual(list(autoperm_decipher.func("BADCC", sigma, tau)),
list("ABCDA"))
self.assertEqual(list(autoperm_decipher.func("", sigma, tau)), [])
self.assertEqual(list(autoperm_decipher.func("B", sigma, tau)), ["A"])
def test_table_format(self):
for g in self.perms:
g.table_format()
self.assertEqual(Perm().table_format(), "Id\n")
self.assertEqual(
Perm(OrderedDict(((1, 2), (2, 1)))).table_format(), "1 2\n2 1")
self.assertEqual(
Perm(OrderedDict(((100, 2), (2, 100)))).table_format(),
"100 2\n 2 100")
def test_substitution(self):
self.assertEqual("".join(substitution.func("", Perm())), "")
self.assertEqual(
"".join(substitution.func("ABC", Perm.from_cycle("AB"))), "BAC")
self.assertEqual(
"".join(substitution.func("ABCBD", Perm.from_cycle("AB"))),
"BACAD")
self.assertEqual(
"".join(substitution.func("ABCBD", Perm.from_cycle("CD"))),
"ABDBC")
def test_str(self):
for g in self.perms:
str(g)
self.assertEqual(str(Perm()), "Id"),
self.assertEqual(str(self.perm2c), "(1 2)")
self.assertEqual(str(self.perm3c), "(1 2 3)")
self.assertEqual(str(self.perm6), "(1 2)(4 5 6)")
def test_eq(self):
for g in self.perms:
self.assertEqual(g, g)
self.assertEqual(g, Perm(g.mapping))
self.assertEqual(g, Perm(g.mapping.copy()))
self.assertNotEqual(g, Perm({**g.mapping, -1: -2}))
self.assertEqual(self.perm6, Perm({1: 2, 2: 1, 4: 5, 5: 6, 6: 4}))
self.assertEqual(Perm({1: 2, 2: 1}), Perm({2: 1, 1: 2}))
self.assertEqual(Perm({1: 2, 2: 1, 3: 3}), Perm({2: 1, 1: 2, 4: 4}))
self.assertEqual(self.permoc, self.perm1c)
self.assertEqual(self.permoc, self.operm)
self.assertEqual(self.perm1c, self.operm)
self.assertEqual(self.operm, Perm({1: 1}))
self.assertEqual(self.operm, Perm({None: None}))
for g, h in itertools.combinations(
[p for p in self.reg_perms if len(p.mapping) > 2], 2):
self.assertNotEqual(g, h)
def test_disjoint_cycle_decomposition(self):
self.assertEqual(Perm().disjoint_cycle_decomposition_stable(), [])
self.assertEqual(self.perm6.disjoint_cycle_decomposition_stable(),
[[1, 2], [4, 5, 6]])
self.assertEqual(self.perm3c.disjoint_cycle_decomposition_stable(),
[[1, 2, 3]])
# reconstruct permutations as a cycle composition
for g in self.perms:
self.assertEqual(
reduce(
mul,
map(Perm.from_cycle,
g.disjoint_cycle_decomposition_unstable()), Perm()), g)
self.assertEqual(
reduce(
mul,
map(Perm.from_cycle,
g.disjoint_cycle_decomposition_stable()), Perm()), g)
def test_table_format(self):
for g in self.perms:
g.table_format()
self.assertEqual(Perm().table_format(),
"Id\n")
self.assertEqual(Perm({1: 1}).table_format(), "1\n1")
self.assertEqual(Perm({1: 100}).table_format(), " 1\n100")
self.assertEqual(Perm({100: 1}).table_format(), "100\n 1")
self.assertEqual(Perm({1: 2, 2: 1}).table_format(), "1 2\n2 1")
self.assertEqual(Perm({2: 1, 1: 2}).table_format(), "1 2\n2 1")
self.assertEqual(Perm({100: 2, 2: 100}).table_format(),
" 2 100\n100 2")
self.assertEqual(Perm({-2: 1, 1: -2}).table_format(),
"-2 1\n 1 -2")
self.assertEqual(Perm({-2: 1, 1: -2}).table_format(key=abs),
" 1 -2\n-2 1")
self.assertEqual(Perm({100: 2, 2: 100}).table_format(lambda x: -x),
"100 2\n 2 100")
def test_inverse(self):
for g in self.perms:
self.assertEqual(g.inverse().inverse(), g)
for g in self.operm, self.permoc, self.perm1c, self.perm2c:
self.assertEqual(g.inverse(), g)
self.assertTrue(g.inverse().is_permutation())
# standard inverse formula works
for g, h in itertools.product(self.perms, self.perms):
self.assertEqual((g * h).inverse(), h.inverse() * g.inverse())
self.assertEqual(Perm.from_cycle([3, 2, 1]).inverse(), self.perm3c)
def test_random(self):
# check valid permutations are given
for i in range(100):
self.assertTrue(Perm.random(range(i)).is_permutation)
def test_from_cycle(self):
self.assertEqual(self.permoc, self.operm)
self.assertEqual(self.perm1c, self.operm)
self.assertEqual(self.perm2c, Perm({1: 2, 2: 1}))
self.assertEqual(self.perm3c, Perm({1: 2, 2: 3, 3: 1}))
self.assertEqual(Perm.from_cycle([1] * 2), Perm())
self.assertEqual(Perm.from_cycle([1] * 3), Perm())
self.assertEqual(Perm.from_cycle([1] * 4), Perm())
self.assertEqual(Perm.from_cycle([2, 3, 1]), self.perm3c)
self.assertEqual(Perm.from_cycle([3, 2, 1]), Perm({1: 3, 2: 1, 3: 2}))
for i in range(20):
for j in range(1, 5):
self.assertEqual(Perm.from_cycle(list(range(i)) * j),
Perm.from_cycle(range(i)))
self.assertTrue(
Perm.from_cycle(list(range(i)) * j).is_permutation())
def test_is_permutation(self):
for g in self.perms:
self.assertTrue(g.is_permutation())
self.assertFalse(Perm({1: 2, 2: 2}).is_permutation())
self.assertFalse(Perm({1: 2, 2: 3}).is_permutation())
def test_permutation_from_key(self):
self.assertEqual(Perm(), permutation_from_key(""))
self.assertEqual(Perm(), permutation_from_key("a"))
self.assertEqual(Perm(), permutation_from_key("A"))
self.assertEqual(Perm(), permutation_from_key("?a?"))
self.assertEqual(Perm(), permutation_from_key("!!"))
for ind, l in enumerate(string.ascii_uppercase):
self.assertEqual(
Perm.from_cycle(string.ascii_uppercase)**ind,
permutation_from_key(l))
self.assertEqual(
Perm(
dict(zip(string.ascii_uppercase,
"LINUSTORVADEFGHJKMPQWXYZBC"))),
permutation_from_key("linustorvalds"))
self.assertEqual(
Perm(
dict(zip(string.ascii_uppercase,
"LINUSTORVADEFGHJKMPQWXYZBC"))),
permutation_from_key("linuStOrvALds"))
self.assertEqual(
Perm(
dict(zip(string.ascii_uppercase,
"LINUSTORVADEFGHJKMPQWXYZBC"))),
permutation_from_key(" lin\nuStO&&(*rvA)*)(*Lds"))
self.assertEqual(
Perm(
dict(zip(string.ascii_uppercase,
"RICHADSTLMNOPQUVWXYZBEFGJK"))),
permutation_from_key("richardstallman"))
self.assertEqual(
Perm(
dict(zip(string.ascii_uppercase,
"ZEBRACDFGHIJKLMNOPQSTUVWXY"))),
permutation_from_key("zebra"))
for _ in range(100):
key = "".join(
random.choices(string.ascii_uppercase, k=random.randrange(30)))
self.assertTrue(permutation_from_key(key).is_permutation())
class TestPerm(unittest.TestCase):
def setUp(self):
self.perm6 = Perm({1: 2, 2: 1, 3: 3, 4: 5, 5: 6, 6: 4})
self.operm = Perm({})
self.permoc = Perm.from_cycle([])
self.perm1c = Perm.from_cycle([1])
self.perm2c = Perm.from_cycle([1, 2])
self.perm3c = Perm.from_cycle([1, 2, 3])
# huge list of hopefully lots of different kinds of permutation covering
# lots of edge cases
self.reg_perms = [
self.permoc, self.perm1c, self.perm2c, self.perm3c,
*(Perm.from_cycle(range(j, j + i)) for i in range(4, 9)
for j in range(9 - i)),
*(Perm.from_cycle(range(j, j + i)[::-1]) for i in range(2, 9)
for j in range(9 - i)), self.operm, self.perm6
]
# add some more random permutations to hopefully catch more edge cases,
# but keep them in a separate list so I can also access a deterministic
# list of permutations that I can guarantee properties of
self.perms = [
*self.reg_perms, *(Perm.random(range(i)) for i in range(4, 20))
]
for _ in range(10):
a, b = sample(self.perms, 2)
self.perms.append(a * b)
def test_is_permutation(self):
for g in self.perms:
self.assertTrue(g.is_permutation())
self.assertFalse(Perm({1: 2, 2: 2}).is_permutation())
self.assertFalse(Perm({1: 2, 2: 3}).is_permutation())
def test_eq(self):
for g in self.perms:
self.assertEqual(g, g)
self.assertEqual(g, Perm(g.mapping))
self.assertEqual(g, Perm(g.mapping.copy()))
self.assertNotEqual(g, Perm({**g.mapping, -1: -2}))
self.assertEqual(self.perm6, Perm({1: 2, 2: 1, 4: 5, 5: 6, 6: 4}))
self.assertEqual(Perm({1: 2, 2: 1}), Perm({2: 1, 1: 2}))
self.assertEqual(Perm({1: 2, 2: 1, 3: 3}), Perm({2: 1, 1: 2, 4: 4}))
self.assertEqual(self.permoc, self.perm1c)
self.assertEqual(self.permoc, self.operm)
self.assertEqual(self.perm1c, self.operm)
self.assertEqual(self.operm, Perm({1: 1}))
self.assertEqual(self.operm, Perm({None: None}))
for g, h in itertools.combinations(
[p for p in self.reg_perms if len(p.mapping) > 2], 2):
self.assertNotEqual(g, h)
def test_from_cycle(self):
self.assertEqual(self.permoc, self.operm)
self.assertEqual(self.perm1c, self.operm)
self.assertEqual(self.perm2c, Perm({1: 2, 2: 1}))
self.assertEqual(self.perm3c, Perm({1: 2, 2: 3, 3: 1}))
self.assertEqual(Perm.from_cycle([1] * 2), Perm())
self.assertEqual(Perm.from_cycle([1] * 3), Perm())
self.assertEqual(Perm.from_cycle([1] * 4), Perm())
self.assertEqual(Perm.from_cycle([2, 3, 1]), self.perm3c)
self.assertEqual(Perm.from_cycle([3, 2, 1]), Perm({1: 3, 2: 1, 3: 2}))
for i in range(20):
for j in range(1, 5):
self.assertEqual(Perm.from_cycle(list(range(i)) * j),
Perm.from_cycle(range(i)))
self.assertTrue(
Perm.from_cycle(list(range(i)) * j).is_permutation())
def test_random(self):
# check valid permutations are given
for i in range(100):
self.assertTrue(Perm.random(range(i)).is_permutation)
def test_disjoint_cycle_decomposition(self):
self.assertEqual(Perm().disjoint_cycle_decomposition_stable(), [])
self.assertEqual(self.perm6.disjoint_cycle_decomposition_stable(),
[[1, 2], [4, 5, 6]])
self.assertEqual(self.perm3c.disjoint_cycle_decomposition_stable(),
[[1, 2, 3]])
# reconstruct permutations as a cycle composition
for g in self.perms:
self.assertEqual(
reduce(
mul,
map(Perm.from_cycle,
g.disjoint_cycle_decomposition_unstable()), Perm()), g)
self.assertEqual(
reduce(
mul,
map(Perm.from_cycle,
g.disjoint_cycle_decomposition_stable()), Perm()), g)
def test_inverse(self):
for g in self.perms:
self.assertEqual(g.inverse().inverse(), g)
for g in self.operm, self.permoc, self.perm1c, self.perm2c:
self.assertEqual(g.inverse(), g)
self.assertTrue(g.inverse().is_permutation())
# standard inverse formula works
for g, h in itertools.product(self.perms, self.perms):
self.assertEqual((g * h).inverse(), h.inverse() * g.inverse())
self.assertEqual(Perm.from_cycle([3, 2, 1]).inverse(), self.perm3c)
def test_comp(self):
for g in self.perms:
self.assertEqual(g * g.inverse(), self.operm)
for g, h in itertools.product(self.perms, self.perms):
self.assertTrue((g * h).is_permutation())
# conjugates should preserve cycle type
conj = h * g * h.inverse()
self.assertCountEqual(
list(map(len, g.disjoint_cycle_decomposition_unstable())),
list(map(len, conj.disjoint_cycle_decomposition_unstable())))
# associativity of composition
for g, h, k in itertools.product(*[self.perms] * 3):
self.assertEqual((g * h) * k, g * (h * k))
self.assertEqual(
Perm.from_cycle([4, 5, 6]) * self.perm6,
Perm({
1: 2,
2: 1,
4: 6,
5: 4,
6: 5
}))
self.assertEqual(
Perm.from_cycle([1, 2]) * Perm.from_cycle([2, 3]),
Perm.from_cycle([1, 2, 3]))
self.assertEqual(self.perm3c**3, self.operm)
def test_pow(self):
# test if pow behaves as expected with conjugates
for g, h in itertools.product(self.perms, self.perms):
for n in range(10):
self.assertEqual(h * g**n * h.inverse(),
(h * g * h.inverse())**n)
for g in self.perms:
# check if iterative calculation agrees
prod = self.operm
for n in range(10):
self.assertTrue((g**n).is_permutation())
self.assertEqual(g**n, prod)
self.assertEqual(g**(-n), prod.inverse())
prod *= g
# check if cyclic subgroup generated by g is abelian :)
for a in range(-10, 10):
for b in range(-10, 10):
self.assertEqual(g**a * g**b, g**(a + b))
self.assertEqual(g**-1, g.inverse())
# check if the order divides the LCM of cycle lengths
order = reduce(mul,
map(len, g.disjoint_cycle_decomposition_unstable()),
1)
self.assertEqual(g**order, self.operm)
self.assertEqual(
Perm.from_cycle(range(10))**9,
Perm.from_cycle(range(10)).inverse())
def test_lookup(self):
for g in self.perms:
self.assertIsNone(g[None])
self.assertEqual(g["xyz"], "xyz")
self.assertEqual(g[-1], -1)
for item in g.mapping:
self.assertEqual(g.mapping[item], g[item])
def test_str(self):
for g in self.perms:
str(g)
self.assertEqual(str(Perm()), "Id"),
self.assertEqual(str(self.perm2c), "(1 2)")
self.assertEqual(str(self.perm3c), "(1 2 3)")
self.assertEqual(str(self.perm6), "(1 2)(4 5 6)")
# The following tests are for string representations. They therefore use
# OrderedDicts, so that this program is compatible with as much of Python 3
# as possible, seeing as dictionary order preservation was only added to the
# spec in 3.7.
def test_repr(self):
for g in self.perms:
repr(g)
self.assertEqual(repr(Perm(OrderedDict(((1, 2), (2, 1))))),
"Perm(OrderedDict([(1, 2), (2, 1)]))")
self.assertEqual(repr(Perm()), "Perm({})")
def test_table_format(self):
for g in self.perms:
g.table_format()
self.assertEqual(Perm().table_format(), "Id\n")
self.assertEqual(
Perm(OrderedDict(((1, 2), (2, 1)))).table_format(), "1 2\n2 1")
self.assertEqual(
Perm(OrderedDict(((100, 2), (2, 100)))).table_format(),
"100 2\n 2 100")
