def test_left_inverse(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertEqual(semigroup.left_inverse(0), 0)
self.assertEqual(semigroup.left_inverse(1), 2)
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertEqual(semigroup.left_inverse('0'), '0')
self.assertEqual(semigroup.left_inverse('1'), '2')
semigroup = SemiGroup('Z3', '012',
[['0', '0', '1', '2'], ['0', '0', '1', '2'],
['1', '1', '2', '0'], ['2', '2', '2', '1']])
self.assertRaises(ElementWithoutInverse, semigroup.left_inverse, '1')
def test_initializationWithMatrix(self):
# tabla correcta
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertIsInstance(semigroup, SemiGroup)
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 2, 1], [0, 0, 2, 1], [2, 2, 1, 0], [1, 1, 0, 2]])
self.assertIsInstance(semigroup, SemiGroup)
semigroup = SemiGroup('Z3', '012',
[['0', '0', '1', '2'], ['0', '0', '1', '2'],
['1', '1', '2', '0'], ['2', '2', '0', '1']])
self.assertIsInstance(semigroup, SemiGroup)
# tabla con operaciones fuera del conjunto de elementos
self.assertRaises(
OperationOutOfDomainError, SemiGroup, 'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 4]])
# tabla sin especificacion de operacion para pares de elementos
self.assertRaises(ElementsWithoutOperationError, SemiGroup, 'Z3',
[0, 1, 2],
[[0, 0, 1], [0, 0, 1], [1, 1, 2], [2, 2, 0]])
self.assertRaises(ElementsWithoutOperationError, SemiGroup, 'Z3',
[0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 0], [2, 2, 0, 2]])
# tablas con operacion multivaluada para pares de elementos
self.assertRaises(MultivaluedOperation, SemiGroup, 'Z3', [0, 1, 2],
[[0, 0, 1, 2, 2], [0, 0, 1, 2, 1], [1, 1, 2, 0, 2],
[2, 2, 0, 1, 0]])
self.assertRaises(MultivaluedOperation, SemiGroup, 'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0],
[2, 2, 0, 1], [1, 0, 1, 2]])
self.assertRaises(MultivaluedOperation, SemiGroup, 'Z3', [0, 1, 2],
[[0, 0, 1, 2, 2], [0, 0, 1, 2, 1], [1, 1, 2, 0, 2],
[2, 2, 0, 1, 0], [1, 0, 1, 2, 2]])
def test_table2map(self):
tableMatrix = [[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]]
tableDict = {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 1): 2,
(1, 2): 0,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}
semigroup = SemiGroup('Z3', [0, 1, 2], tableMatrix)
self.assertEqual(semigroup._table2map(tableMatrix), tableDict)
def test_has_left_inverse(self):
# se llamara 2 veces al metodo has_left_inverse para verificar que
# la cache funciones bien
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
for element in range(3):
self.assertTrue(semigroup.has_left_inverse(element))
self.assertTrue(semigroup.has_left_inverse(element))
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 2, 1]])
self.assertTrue(semigroup.has_left_inverse(0))
self.assertFalse(semigroup.has_left_inverse(1))
semigroup = SemiGroup('Z3', '012',
[['0', '0', '1', '2'], ['0', '0', '2', '2'],
['1', '1', '2', '2'], ['2', '2', '0', '1']])
self.assertRaises(SemigroupWithoutUnit, semigroup.has_left_inverse,
'1')
def test_commutators(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
for element in [0, 1, 2]:
self.assertEqual(semigroup.commutators(element), set([0, 1, 2]))
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 0], [1, 2, 1, 0], [2, 2, 0, 1]])
self.assertEqual(semigroup.commutators(1), [1, 2])
def test_inverse(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
for element in range(3):
self.assertTrue(semigroup.has_inverse(element))
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 2, 1]])
self.assertFalse(semigroup.has_inverse(1))
def test_isin(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertTrue(semigroup.isin(1))
self.assertFalse(semigroup.isin(4))
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertFalse(semigroup.isin('4'))
self.assertFalse(semigroup.isin(4))
self.assertTrue(semigroup.isin('0'))
def test_op(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertEqual(semigroup.op(1, 2), 0)
self.assertEqual(semigroup.op(2, 2), 1)
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertEqual(semigroup.op('1', '1'), '2')
self.assertEqual(semigroup.op('0', '2'), '2')
def test_initializationWithDict(self):
# tabla correcta
semigroup = SemiGroup(
'Z3', [0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 1): 2,
(1, 2): 0,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}, DICT)
self.assertIsInstance(semigroup, SemiGroup)
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertIsInstance(semigroup, SemiGroup)
# tabla con operaciones fuera del conjunto de elementos
self.assertRaises(
OperationOutOfDomainError, SemiGroup, 'Z3', [0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 1): 2,
(1, 2): 0,
(2, 0): 2,
(2, 1): 0,
(2, 2): 4
}, DICT)
# tabla sin especificacion de operacion para pares de elementos
self.assertRaises(ElementsWithoutOperationError, SemiGroup, 'Z3',
[0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(1, 0): 1,
(1, 1): 2,
(2, 0): 2,
(2, 1): 0
}, DICT)
self.assertRaises(ElementsWithoutOperationError, SemiGroup, 'Z3',
[0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}, DICT)
self.assertRaises(
ElementsWithoutOperationError, SemiGroup, 'Z3', [0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 2): 0,
(0, 4): 1,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}, DICT)
def test_check_commutativity(self):
# se llamara 2 veces al metodo check_commutativity para verificar que
# la cache funciones bien
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertTrue(semigroup.check_commutativity())
self.assertTrue(semigroup.check_commutativity())
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 0], [1, 2, 1, 0], [2, 2, 0, 1]])
self.assertFalse(semigroup.check_commutativity())
self.assertEqual(semigroup.check_commutativity(True), {
(0, 1): 1,
(1, 0): 2,
(2, 0): 2,
(0, 2): 0
})
# tabla no conmutativa '2' * '1' = '0' pero '1' * '2' = '2'
semigroup = SemiGroup('Z3', '012',
[['0', '0', '1', '2'], ['0', '0', '1', '2'],
['1', '1', '2', '2'], ['2', '2', '0', '1']])
self.assertEqual(semigroup.check_commutativity(True), {
('1', '2'): '2',
('2', '1'): '0'
})
self.assertFalse(semigroup.check_commutativity())
self.assertEqual(semigroup.check_commutativity(True), {
('1', '2'): '2',
('2', '1'): '0'
})
self.assertFalse(semigroup.check_commutativity())
# tabla conmutativa
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertTrue(semigroup.check_commutativity())
self.assertTrue(semigroup.check_commutativity())
# tabla no conmutativa 2 * 1 = 0 pero 1 * 2 = 2
semigroup = SemiGroup(
'Z3', [0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 1): 2,
(1, 2): 2,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}, DICT)
self.assertEqual(semigroup.check_commutativity(True), {
(2, 1): 0,
(1, 2): 2
})
self.assertFalse(semigroup.check_commutativity())
def test_unit(self):
# se llamara 2 veces al metodo unit para verificar que la cache
# funciones bien
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertEqual(semigroup.unit(), 0)
self.assertEqual(semigroup.unit(), 0)
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertEqual(semigroup.unit(), '0')
self.assertEqual(semigroup.unit(), '0')
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 1], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertIsNone(semigroup.unit())
self.assertIsNone(semigroup.unit())
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '2',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertIsNone(semigroup.unit())
self.assertIsNone(semigroup.unit())
def test_has_unit(self):
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertTrue(semigroup.has_unit())
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertTrue(semigroup.has_unit())
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 1], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertFalse(semigroup.has_unit())
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '2',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertFalse(semigroup.has_unit())
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 1, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
print(semigroup.unit())
self.assertFalse(semigroup.has_unit())
def test_check_associativity(self):
# tabla asociativa
semigroup = SemiGroup(
'Z3', [0, 1, 2],
[[0, 0, 1, 2], [0, 0, 1, 2], [1, 1, 2, 0], [2, 2, 0, 1]])
self.assertTrue(semigroup._check_associativity())
# tabla no asociativa '2' * '1' = '0' pero '1' * '2' = '2'
semigroup = SemiGroup('Z3', '012',
[['0', '0', '1', '2'], ['0', '0', '1', '2'],
['1', '1', '2', '2'], ['2', '2', '0', '1']])
self.assertFalse(semigroup._check_associativity())
# tabla asociativa
semigroup = SemiGroup(
'Z3', '012', {
('0', '0'): '0',
('0', '1'): '1',
('0', '2'): '2',
('1', '0'): '1',
('1', '1'): '2',
('1', '2'): '0',
('2', '0'): '2',
('2', '1'): '0',
('2', '2'): '1'
}, DICT)
self.assertTrue(semigroup._check_associativity())
# tabla no asociativa 2 * 1 = 0 pero 1 * 2 = 2
semigroup = SemiGroup(
'Z3', [0, 1, 2], {
(0, 0): 0,
(0, 1): 1,
(0, 2): 2,
(1, 0): 1,
(1, 1): 2,
(1, 2): 2,
(2, 0): 2,
(2, 1): 0,
(2, 2): 1
}, DICT)
self.assertFalse(semigroup._check_associativity())