class TestSubgroup(unittest.TestCase):
def setUp(self):
self.N = 4
# Tworze grupe symetryczna.
self.group1 = Group()
self.group1.insert(Perm()(0, 1))
self.group1.insert(Perm()(*range(self.N)))
def test_subgroup_search(self):
self.assertEqual(self.group1.order(), 24)
# Dopuszczam permutacje parzyste - grupa alternujaca.
self.group2 = self.group1.subgroup_search(lambda x: x.is_even())
self.assertEqual(self.group2.order(), 12)
self.assertTrue(self.group2.is_transitive(points=range(self.N)))
#print self.group2
def test_stabilizer(self):
self.group2 = self.group1.stabilizer(3)
self.assertEqual(self.group2.order(), 6)
#print self.group2
def test_centralizer(self):
# Tworze grupe cykliczna.
self.group2 = Group()
self.group2.insert(Perm()(*range(self.N)))
self.assertEqual(self.group2.order(), self.N)
# centrum grupy abelowej cyklicznej to cala grupa
self.group3 = self.group2.center()
self.assertEqual(self.group3.order(), self.N)
# Dalej dla grupy symetrycznej.
self.group2 = self.group1.center()
self.assertEqual(self.group2.order(), 1)
def test_is_subgroup(self):
self.group2 = Group()
# Tworze grupe cykliczna.
self.group2.insert(Perm()(*range(self.N)))
self.assertTrue(self.group2.is_subgroup(self.group1))
self.assertTrue(self.group2.is_abelian())
self.assertFalse(self.group1.is_abelian())
self.assertFalse(self.group2.is_normal(self.group1))
def tearDown(self): pass
class TestSubgroup(unittest.TestCase):
def setUp(self):
self.N = 4
# Make symmetric group S_N.
self.group1 = Group()
self.group1.insert(Perm()(0, 1))
self.group1.insert(Perm()(*range(self.N)))
def test_subgroup_search(self):
self.assertEqual(self.group1.order(), 24)
# Dopuszczam permutacje parzyste - grupa alternujaca A_N.
self.group2 = self.group1.subgroup_search(lambda x: x.is_even())
self.assertEqual(self.group2.order(), 12)
self.assertTrue(self.group2.is_transitive(points=range(self.N)))
#print self.group2
def test_stabilizer(self):
self.group2 = self.group1.stabilizer(3)
self.assertEqual(self.group2.order(), 6)
#print self.group2
def test_centralizer(self):
# Tworze grupe cykliczna.
self.group2 = Group()
self.group2.insert(Perm()(*range(self.N)))
self.assertEqual(self.group2.order(), self.N)
# centrum grupy abelowej cyklicznej to cala grupa
self.group3 = self.group2.center()
self.assertEqual(self.group3.order(), self.N)
# Dalej dla grupy symetrycznej.
self.group2 = self.group1.center()
self.assertEqual(self.group2.order(), 1)
def test_normalizer(self):
pass
def test_normal_closure(self):
n = 5
# Tworze grupe cykliczna C_5.
C5 = Group()
C5.insert(Perm()(*range(n)))
self.assertEqual(C5.order(), n)
# Make Sym(5).
S5 = Group()
S5.insert(Perm()(*range(n)))
S5.insert(Perm()(0, 1))
self.assertEqual(S5.order(), 120)
A5 = S5.normal_closure(C5)
self.assertEqual(A5.order(), 60)
for perm in A5.iterperms():
self.assertTrue(perm.is_even())
def test_derived_subgroup(self):
pass
def test_is_subgroup(self):
self.group2 = Group()
# Make cyclic group C_N.
self.group2.insert(Perm()(*range(self.N)))
self.assertEqual(self.group2.order(), self.N)
self.assertTrue(self.group2.is_subgroup(self.group1))
self.assertTrue(self.group2.is_abelian())
self.assertFalse(self.group1.is_abelian())
self.assertFalse(self.group2.is_normal(self.group1))
def test_is_normal(self):
a = Perm()(0, 1, 2)
b = Perm()(0, 1)
c = Perm()(0, 2, 1)
G = Group()
G.insert(a)
G.insert(b)
self.assertEqual(G.order(), 6) # G = S_3
H = Group()
H.insert(a)
H.insert(c)
self.assertEqual(H.order(), 3) # H = A_3
self.assertTrue(H.is_normal(G))
def tearDown(self): pass
class TestSubgroup(unittest.TestCase):
def setUp(self):
self.N = 4
# Make symmetric group S_N.
self.group1 = Group()
self.group1.insert(Perm()(0, 1))
self.group1.insert(Perm()(*range(self.N)))
def test_subgroup_search(self):
self.assertEqual(self.group1.order(), 24)
# Dopuszczam permutacje parzyste - grupa alternujaca A_N.
self.group2 = self.group1.subgroup_search(lambda x: x.is_even())
self.assertEqual(self.group2.order(), 12)
self.assertTrue(self.group2.is_transitive(points=range(self.N)))
#print self.group2
def test_stabilizer(self):
self.group2 = self.group1.stabilizer(3)
self.assertEqual(self.group2.order(), 6)
#print self.group2
def test_centralizer(self):
# Tworze grupe cykliczna.
self.group2 = Group()
self.group2.insert(Perm()(*range(self.N)))
self.assertEqual(self.group2.order(), self.N)
# centrum grupy abelowej cyklicznej to cala grupa
self.group3 = self.group2.center()
self.assertEqual(self.group3.order(), self.N)
# Dalej dla grupy symetrycznej.
self.group2 = self.group1.center()
self.assertEqual(self.group2.order(), 1)
def test_normalizer(self):
pass
def test_normal_closure(self):
n = 5
# Tworze grupe cykliczna C_5.
C5 = Group()
C5.insert(Perm()(*range(n)))
self.assertEqual(C5.order(), n)
# Make Sym(5).
S5 = Group()
S5.insert(Perm()(*range(n)))
S5.insert(Perm()(0, 1))
self.assertEqual(S5.order(), 120)
A5 = S5.normal_closure(C5)
self.assertEqual(A5.order(), 60)
for perm in A5.iterperms():
self.assertTrue(perm.is_even())
def test_derived_subgroup(self):
pass
def test_is_subgroup(self):
self.group2 = Group()
# Make cyclic group C_N.
self.group2.insert(Perm()(*range(self.N)))
self.assertEqual(self.group2.order(), self.N)
self.assertTrue(self.group2.is_subgroup(self.group1))
self.assertTrue(self.group2.is_abelian())
self.assertFalse(self.group1.is_abelian())
self.assertFalse(self.group2.is_normal(self.group1))
def test_is_normal(self):
a = Perm()(0, 1, 2)
b = Perm()(0, 1)
c = Perm()(0, 2, 1)
G = Group()
G.insert(a)
G.insert(b)
self.assertEqual(G.order(), 6) # G = S_3
H = Group()
H.insert(a)
H.insert(c)
self.assertEqual(H.order(), 3) # H = A_3
self.assertTrue(H.is_normal(G))
def tearDown(self):
pass
