class TestAlternatingGroup(unittest.TestCase):
def setUp(self): pass
def test_alt_5(self):
self.N = 5
self.group = Group()
self.assertEqual(self.group.order(), 1)
self.group.insert(Perm()(0, 1, 2))
self.assertEqual(self.group.order(), 3)
self.group.insert(Perm()(1, 2, 3))
self.assertEqual(self.group.order(), 12)
self.group.insert(Perm()(2, 3, 4))
self.assertEqual(self.group.order(), 60)
self.assertFalse(Perm()(0, 1) in self.group)
self.assertTrue(Perm()(*range(self.N)) in self.group) # N is odd
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def test_alt_n(self):
self.N = 5
self.assertTrue(self.N > 2)
self.group = Group()
order = 1
for i in range(self.N-2):
self.group.insert(Perm()(i, i+1, i+2))
order = order * (i+3)
self.assertEqual(self.group.order(), order)
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def tearDown(self): pass
class TestAlternatingGroup(unittest.TestCase):
def setUp(self):
pass
def test_alt_5(self):
self.N = 5
self.group = Group()
self.assertEqual(self.group.order(), 1)
self.group.insert(Perm()(0, 1, 2))
self.assertEqual(self.group.order(), 3)
self.group.insert(Perm()(1, 2, 3))
self.assertEqual(self.group.order(), 12)
self.group.insert(Perm()(2, 3, 4))
self.assertEqual(self.group.order(), 60)
self.assertFalse(Perm()(0, 1) in self.group)
self.assertTrue(Perm()(*range(self.N)) in self.group) # N is odd
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def test_alt_n(self):
self.N = 5
self.assertTrue(self.N > 2)
self.group = Group()
order = 1
for i in range(self.N - 2):
self.group.insert(Perm()(i, i + 1, i + 2))
order = order * (i + 3)
self.assertEqual(self.group.order(), order)
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def tearDown(self):
pass
class TestSymmetricGroup(unittest.TestCase):
def setUp(self): pass
def test_sym_5(self):
self.N = 5
self.group = Group()
self.assertEqual(self.group.order(), 1)
self.group.insert(Perm()(0, 1))
self.assertEqual(self.group.order(), 2)
self.group.insert(Perm()(1, 2))
self.assertEqual(self.group.order(), 6)
self.group.insert(Perm()(2, 3))
self.assertEqual(self.group.order(), 24)
self.group.insert(Perm()(3, 4))
self.assertEqual(self.group.order(), 120)
self.assertTrue(Perm()(*range(self.N)) in self.group)
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def test_sym_n(self):
self.N = 4
self.group = Group()
order = 1
for i in range(self.N-1):
self.group.insert(Perm()(i, i+1))
order *= (i+2)
self.assertEqual(self.group.order(), order)
self.assertTrue(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 1)
def tearDown(self): pass
class TestCyclicGroup(unittest.TestCase):
def setUp(self):
# The cyclic group from the paper by Knuth.
self.N = 6
self.H = Perm()(0, 1, 2, 4)(3, 5)
self.group = Group()
self.group.insert(self.H)
def test_group(self):
self.assertEqual(self.group.order(), 4)
self.assertFalse(self.group.is_trivial())
self.assertTrue(Perm() in self.group)
self.assertTrue(self.H in self.group)
points = range(self.N)
self.assertFalse(Perm()(*points) in self.group)
self.assertEqual(self.group.orbits(points), [[0, 4, 2, 1], [3, 5]])
self.assertEqual(len(self.group.orbits(points)), 2)
self.assertFalse(self.group.is_transitive(points))
def test_cyclic6(self):
points = range(5)
C6 = Group()
C6.insert(Perm()(0, 1, 2)(3, 4))
self.assertEqual(C6.order(), 6)
self.assertEqual(C6.orbits(points), [[0, 2, 1], [3, 4]])
self.assertEqual(len(C6.orbits(points)), 2)
self.assertFalse(C6.is_transitive(points))
def tearDown(self): pass
class TestCyclicGroup(unittest.TestCase):
def setUp(self):
# The cyclic group from the paper by Knuth.
self.N = 6
self.H = Perm()(0, 1, 2, 4)(3, 5)
self.group = Group()
self.group.insert(self.H)
def test_group(self):
self.assertEqual(self.group.order(), 4)
self.assertFalse(self.group.is_trivial())
self.assertTrue(Perm() in self.group)
self.assertTrue(self.H in self.group)
points = range(self.N)
self.assertFalse(Perm()(*points) in self.group)
self.assertEqual(self.group.orbits(points), [[0, 4, 2, 1], [3, 5]])
self.assertEqual(len(self.group.orbits(points)), 2)
self.assertFalse(self.group.is_transitive(points))
def test_cyclic6(self):
points = range(5)
C6 = Group()
C6.insert(Perm()(0, 1, 2)(3, 4))
self.assertEqual(C6.order(), 6)
self.assertEqual(C6.orbits(points), [[0, 2, 1], [3, 4]])
self.assertEqual(len(C6.orbits(points)), 2)
self.assertFalse(C6.is_transitive(points))
def tearDown(self):
pass
def test_cyclic6(self):
points = range(5)
C6 = Group()
C6.insert(Perm()(0, 1, 2)(3, 4))
self.assertEqual(C6.order(), 6)
self.assertEqual(C6.orbits(points), [[0, 2, 1], [3, 4]])
self.assertEqual(len(C6.orbits(points)), 2)
self.assertFalse(C6.is_transitive(points))
def test_cyclic6(self):
points = range(5)
C6 = Group()
C6.insert(Perm()(0, 1, 2)(3, 4))
self.assertEqual(C6.order(), 6)
self.assertEqual(C6.orbits(points), [[0, 2, 1], [3, 4]])
self.assertEqual(len(C6.orbits(points)), 2)
self.assertFalse(C6.is_transitive(points))
class TestCyclicGroup(unittest.TestCase):
def setUp(self):
# The cyclic group from the paper by Knuth.
self.N = 6
self.H = Perm()(0, 1, 2, 4)(3, 5)
self.group = Group()
self.group.insert(self.H)
def test_group(self):
self.assertEqual(self.group.order(), 4)
self.assertFalse(self.group.is_trivial())
self.assertTrue(Perm() in self.group)
self.assertTrue(self.H in self.group)
self.assertFalse(Perm()(*range(self.N)) in self.group)
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertEqual(len(self.group.orbits(range(self.N))), 2)
def tearDown(self): pass
class TestGroupOrbits(unittest.TestCase):
def setUp(self):
pass
def test_orbits1(self):
self.N = 3
self.group = Group()
self.group.insert(Perm()(0, 1))
self.assertEqual(self.group.orbits(range(self.N)), [[0, 1], [2]])
self.assertEqual(self.group.orbits([0, 1]), [[0, 1]])
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertTrue(
self.group.is_transitive(points=range(self.N), strict=False))
def test_orbits2(self):
self.N = 4
self.group = Group()
self.group.insert(Perm()(0, 1))
self.group.insert(Perm()(2, 3))
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertEqual(self.group.orbits(range(self.N)), [[0, 1], [2, 3]])
self.assertEqual(self.group.orbits([0, 1]), [[0, 1]])
self.assertEqual(self.group.orbits([0, 1, 2]), [[0, 1], [2, 3]])
def test_orbits3(self): # grupa cykliczna
self.N = 10
self.group = Group()
self.group.insert(Perm()(*range(self.N)))
self.assertTrue(self.group.is_transitive(points=range(self.N)))
def test_orbits4(self):
self.N = 10
self.group = Group()
self.group.insert(Perm()(0, 1, 2))
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertTrue(
self.group.is_transitive(strict=False, points=range(self.N)))
def tearDown(self):
pass
class TestGroupOrbits(unittest.TestCase):
def setUp(self): pass
def test_orbits1(self):
self.N = 3
self.group = Group()
self.group.insert(Perm()(0,1))
self.assertEqual(self.group.orbits(range(self.N)), [[0, 1],[2]])
self.assertEqual(self.group.orbits([0, 1]), [[0, 1]])
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertTrue(self.group.is_transitive(points=range(self.N), strict=False))
def test_orbits2(self):
self.N = 4
self.group = Group()
self.group.insert(Perm()(0, 1))
self.group.insert(Perm()(2, 3))
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertEqual(self.group.orbits(range(self.N)), [[0, 1],[2, 3]])
self.assertEqual(self.group.orbits([0, 1]), [[0, 1]])
self.assertEqual(self.group.orbits([0, 1, 2]), [[0, 1],[2, 3]])
def test_orbits3(self): # grupa cykliczna
self.N = 10
self.group = Group()
self.group.insert(Perm()(*range(self.N)))
self.assertTrue(self.group.is_transitive(points=range(self.N)))
def test_orbits4(self):
self.N = 10
self.group = Group()
self.group.insert(Perm()(0, 1, 2))
self.assertFalse(self.group.is_transitive(points=range(self.N)))
self.assertTrue(self.group.is_transitive(strict=False, points=range(self.N)))
def tearDown(self): pass