def test_richcmp(self):
self.assertEqual(Transformation([1, 2, 2, 0]),
Transformation([1, 2, 2, 0]))
self.assertFalse(
Transformation([1, 2, 2, 0]) == Transformation([1, 2, 1, 3]))
self.assertNotEqual(Transformation([1, 2, 2, 0]),
Transformation([1, 2, 1, 3]))
self.assertFalse(Transformation([2, 2, 1]) < Transformation([0, 1, 2]))
self.assertGreater(Transformation([2, 2, 1]), Transformation([0, 1,
2]))
self.assertLessEqual(Transformation([2, 2, 1]),
Transformation([2, 2, 2]))
self.assertLessEqual(Transformation([2, 2, 2]),
Transformation([2, 2, 2]))
self.assertGreaterEqual(Transformation([2, 2, 2]),
Transformation([2, 2, 0]))
self.assertGreaterEqual(Transformation([3, 2, 3, 0]),
Transformation([3, 2, 0, 1]))
with self.assertRaises(TypeError):
Transformation([2, 2, 0]) == Bipartition([1, -1], [2, 3, -2], [-3])
with self.assertRaises(TypeError):
Bipartition([1, -1], [2, -2]) < Transformation([0, 1])
with self.assertRaises(TypeError):
Bipartition([1, -1], [2, -2]) != Transformation([0, 1])
def test_dealloc(self):
A = Bipartition([1, -1, 2, -2])
B = Bipartition([-7, -6, -5, -4], [3, 2, 1], [-3, -2, -1, 4, 5, 6, 7])
del A, B
with self.assertRaises(NameError):
A
with self.assertRaises(NameError):
B
def test_generator(self):
self.assertEqual(list(Bipartition([1, 2], [-2, -1])), [0, 0, 1, 1])
self.assertEqual(list(Bipartition([-1, -2], [2, -3], [1, 3])),
[0, 1, 0, 2, 2, 1])
self.assertEqual(
list(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7])),
[0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2])
def test_init_fail(self):
with self.assertRaises(ValueError):
Bipartition([1, -1, 2])
with self.assertRaises(ValueError):
Bipartition([1, 2, 3], [-3, -2])
with self.assertRaises(TypeError):
Bipartition([0, 1, 2], [-1, -2])
with self.assertRaises(TypeError):
Bipartition([1, 2, 3], (-1, -2, -3))
with self.assertRaises(TypeError):
Bipartition(1, 2, -1, -2)
def test_blocks1(self):
self.assertEqual(
Bipartition([1, 2], [-2, -1]).blocks(), [[1, 2], [-1, -2]])
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).blocks(),
[[1, 2, 3], [4, 5, 6, 7, -1, -2, -3], [-4, -5, -6, -7]])
self.assertEqual(
Bipartition([-1, -2], [2, -3], [1, 3]).blocks(),
[[1, 3], [2, -3], [-1, -2]])
x = Bipartition([-1, -2], [2, -3], [1, 3])
self.assertEqual((x * x).blocks(), [[1, 3], [2, -3], [-1, -2]])
def test_richcmp(self):
self.assertEqual(BooleanMat([[True, False], [False, True]]),
BooleanMat([[True, False], [False, True]]))
self.assertFalse(
BooleanMat([[True, False], [False, True]]) != BooleanMat(
[[True, False], [False, True]]))
self.assertFalse(
BooleanMat([[True, False], [False, True]]) == BooleanMat(
[[False, False], [False, True]]))
self.assertLess(BooleanMat([[False]]), BooleanMat([[True]]))
self.assertFalse(
BooleanMat([[False, True, True], [True, True, False],
[False, False, False]]) < BooleanMat([[
False, True, False
], [True, False, False], [False, False, True]]))
self.assertLessEqual(BooleanMat([[False]]), BooleanMat([[False]]))
self.assertGreater(BooleanMat([[True, False], [False, True]]),
BooleanMat([[True, False], [False, False]]))
self.assertFalse(
BooleanMat([[True, False], [False, True]]) > BooleanMat(
[[True, False], [False, True]]))
self.assertGreaterEqual(BooleanMat([[False]]), BooleanMat([[False]]))
with self.assertRaises(TypeError):
(Bipartition([1, -2], [-1, 2]) >= BooleanMat([False, False],
[True, False]))
with self.assertRaises(TypeError):
BooleanMat([False, False], [True, False]) < Transformation([0, 1])
with self.assertRaises(TypeError):
(BooleanMat([True, False], [False, True]) == PartialPerm([0], [1],
2))
def test_richcmp(self):
self.assertEqual(PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]),
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]))
self.assertEqual(PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]),
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]))
self.assertNotEqual(
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]),
PBR([[1, 2], [-2, 1, 2], [3, -3]], [[2, 1], [-2, 2, 1], [1, -1]]))
self.assertTrue(
PBR([[1], [1, 2, -1]], [[1], [2, -1, 1]]) < PBR([[1], [2]],
[[-1], [-2]]))
self.assertTrue(
PBR([[1, -1, 3], [-2, -1, 2], [3, -2]], [[2], [-2], [1, -1, 2]]) >
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]))
self.assertTrue(
PBR([[1, -1, 3], [-2, -1, 2], [3, -2]], [[2], [-2], [1, -1, 2]]) >=
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]))
self.assertTrue(
PBR([[1, -1], [-2, -1, 2]], [[2], [-2]]) <= PBR(
[[1, -1], [-2, -1, 2]], [[2], [-2]]))
with self.assertRaises(TypeError):
(PBR([[1, -1, 3], [-2, -1, 2], [3, -2]],
[[2], [-2], [1, -1, 2]]) == Bipartition([1, -1], [2, 3, -2],
[-3]))
with self.assertRaises(TypeError):
PBR([[1, -1], [-2, -1]], [[1], [-2, -1]]) < Transformation([0, 1])
with self.assertRaises(TypeError):
(PBR([[1, -1], [-2, -1]], [[1], [-2, -1]]) != PartialPerm(
[0, 1], [1, 0], 2))
with self.assertRaises(TypeError):
PBR([[1, -1]], [[1]]) < 3
def test_richcmp(self):
self.assertEqual(PartialPerm([1, 2, 3], [2, 1, 0], 5),
PartialPerm([1, 2, 3], [2, 1, 0], 5))
self.assertFalse(
PartialPerm([1, 2, 3], [2, 1, 0], 5) != PartialPerm([1, 2, 3],
[2, 1, 0], 5))
self.assertFalse(
PartialPerm([1, 2, 4], [2, 1, 0], 5) == PartialPerm([1, 2, 3],
[2, 3, 0], 5))
self.assertNotEqual(PartialPerm([1, 2, 4], [2, 1, 0], 5),
PartialPerm([1, 2, 3], [2, 3, 0], 5))
self.assertFalse(
PartialPerm([1, 2, 4], [2, 1, 0], 5) < PartialPerm([1, 2, 3],
[2, 3, 0], 5))
self.assertLess(PartialPerm([1, 2], [0, 1], 3),
PartialPerm([2, 0], [0, 1], 3))
self.assertFalse(
PartialPerm([1, 2], [0, 1], 3) > PartialPerm([2, 0], [0, 1], 3))
self.assertGreater(PartialPerm([1, 2], [1, 2], 3),
PartialPerm([1, 2], [0, 1], 3))
self.assertGreaterEqual(PartialPerm([1, 2], [1, 2], 3),
PartialPerm([1, 2], [0, 1], 3))
self.assertLessEqual(PartialPerm([1, 2, 3], [2, 1, 0], 5),
PartialPerm([1, 2, 3], [2, 1, 0], 5))
with self.assertRaises(TypeError):
(PartialPerm([1, 2], [2, 1], 3) == Bipartition([1, -1], [2, 3, -2],
[-3]))
with self.assertRaises(TypeError):
PartialPerm([0, 1], [0, 1], 2) < Transformation([0, 1])
with self.assertRaises(TypeError):
PartialPerm([0, 1], [0, 1], 2) != Transformation([0, 1])
def test_mul(self):
self.assertEqual(
PBR([[1, -1]], [[1]]) * PBR([[1, -1]], [[1]]), PBR([[1, -1]],
[[1]]))
self.assertEqual(
PBR([[1, -1], [-2, -1]], [[1], [-2, -1]]) *
PBR([[-1, 1, 2], [2]], [[-1, 1], [-2, 2]]),
PBR([[1, -1], [1, -1]], [[1, -1], [1, -1, -2]]))
self.assertEqual(
PBR([[-1, 1, 2], [2]], [[-1, 1], [-2, 2]]) *
PBR([[1, -1], [-2, -1]], [[1], [-2, -1]]),
PBR([[-1, 1, 2], [2]], [[-1, 1], [-2, -1]]))
self.assertEqual(
PBR([[1, -1, 3], [-2, -1, 2], [3, -2]], [[2], [-2], [1, -1, 2]]) *
PBR([[1, -1, 3], [-2, -1, 2], [3, -3, -2]],
[[1, 2], [-2, 3, -3], [1, -1]]),
PBR([[-1, 1, 2, 3], [-2, -1, 1, 2], [-2, -1, 3]],
[[-2, -1, 2], [-3, -2, -1, 1, 2], [-1, 2]]))
with self.assertRaises(TypeError):
(Transformation([0, 2, 1]) *
PBR([[1, -1, 3], [-2, -1, 2], [3, -2]], [[2], [-2], [1, -1, 2]]))
with self.assertRaises(TypeError):
(PBR([[1, -1, 3], [-2, -1, 2], [3, -2]], [[2], [-2], [1, -1, 2]]) *
Bipartition([1, -1], [2, 3, -3], [-2]))
with self.assertRaises(TypeError):
PBR([[1, -1]], [[1]]) * 0.142857
with self.assertRaises(ValueError):
PBR([[1, -1, 3], [-2, -1, 2], [3, -2]],
[[2], [-2], [1, -1, 2]]) * PBR([[1, -1]], [[1]])
def test_mul(self):
(self.assertEqual(
BooleanMat([[True, False], [False, True]]) *
BooleanMat([[False, False], [False, True]]),
BooleanMat([[False, False], [False, True]])))
self.assertEqual(
BooleanMat([[False]]) * BooleanMat([[True]]),
BooleanMat([[False]]))
(self.assertEqual(
BooleanMat([[False, True, True], [True, True, False],
[False, False, False]]) *
BooleanMat([[False, True, False], [True, False, False],
[False, False, True]]),
BooleanMat([[True, False, True], [True, True, False],
[False, False, False]])))
with self.assertRaises(TypeError):
BooleanMat([[True, True], [False, False]]) * Transformation([1, 1])
with self.assertRaises(TypeError):
BooleanMat([[False, True, True], [True, True, False],
[False, False, False]]) * PartialPerm([0, 1], [1, 2],
3)
with self.assertRaises(TypeError):
BooleanMat([[True]]) * [[True]]
with self.assertRaises(TypeError):
BooleanMat([[True, False], [False, True]]) * Bipartition(
[1, 2], [-1], [-2])
with self.assertRaises(ValueError):
(BooleanMat([[False, True, True], [True, True, False],
[False, False, False]]) *
BooleanMat([[True, False], [False, True]]))
def test_init(self):
Semigroup(-1)
Semigroup(Transformation([1, 0, 1]), Transformation([0, 0, 0]))
with self.assertRaises(ValueError):
Semigroup()
with self.assertRaises(TypeError):
Semigroup(Bipartition([1, -1], [2], [-2]), Transformation([0, 1]))
with self.assertRaises(TypeError):
Semigroup({2, 3})
def test_repr(self):
self.assertEqual(eval(Bipartition([1, 2], [-2, -1]).__repr__()),
Bipartition([1, 2], [-2, -1]))
self.assertEqual(
eval(Bipartition([-1, -2], [2, -3], [1, 3]).__repr__()),
Bipartition([-1, -2], [2, -3], [1, 3]))
self.assertEqual(
eval(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).__repr__()),
Bipartition([-7, -6, -5, -4], [3, 2, 1], [-3, -2, -1, 4, 5, 6, 7]))
def test_identity(self):
self.assertEqual(
Bipartition([1, 2], [-2, -1]).identity(),
Bipartition([1, -1], [2, -2]))
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).identity(),
Bipartition([1, -1], [2, -2], [3, -3], [4, -4], [5, -5], [6, -6],
[7, -7]))
self.assertEqual(
Bipartition([-1, -2], [2, -3], [1, 3]).identity(),
Bipartition([1, -1], [2, -2], [3, -3]))
def test_block(self):
self.assertEqual(Bipartition([1, 2], [-2, -1]).block(-2), 1)
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).block(3), 0)
self.assertEqual(Bipartition([-1, -2], [2, -3], [1, 3]).block(-1), 2)
with self.assertRaises(IndexError):
Bipartition([1, 2], [-2, -1]).block(-3)
with self.assertRaises(IndexError):
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).block(26)
with self.assertRaises(TypeError):
Bipartition([-1, -2], [2, -3], [1, 3]).block('a')
def test_mul(self):
(self.assertEqual(
PartialPerm([0, 1], [0, 1], 2) * PartialPerm([0, 1], [0, 1], 2),
PartialPerm([0, 1], [0, 1], 2)))
(self.assertEqual(
PartialPerm([1, 2, 4, 6, 7, 23], [0, 5, 2, 4, 6, 7], 26) *
PartialPerm([2, 4, 3, 5, 0, 19], [7, 8, 2, 3, 23, 0], 26),
PartialPerm([1, 2, 4, 6], [23, 3, 7, 8], 26)))
(self.assertEqual(
PartialPerm([0, 3, 7, 2], [5, 7, 1, 3], 8) *
PartialPerm([4, 7, 3, 6], [5, 0, 3, 2], 8),
PartialPerm([2, 3], [3, 0], 8)))
with self.assertRaises(TypeError):
PartialPerm([0, 1], [0, 1], 2) * Transformation([0, 1])
with self.assertRaises(TypeError):
PartialPerm([0, 1], [0, 1], 2) * Bipartition([-2, 1], [-1, 2])
with self.assertRaises(ValueError):
PartialPerm([1, 2], [0, 1], 3) * PartialPerm([1, 2], [0, 1], 4)
def test_mul(self):
(self.assertEqual(
Transformation([1, 3, 2, 1]) * Transformation([0, 3, 2, 2]),
Transformation([3, 2, 2, 3])))
self.assertEqual(
Transformation([2, 2, 2]) * Transformation([1, 0, 1]),
Transformation([1, 1, 1]))
(self.assertEqual(
Transformation([0, 1, 2, 3, 4, 5]) *
Transformation([3, 2, 2, 3, 1, 4]),
Transformation([3, 2, 2, 3, 1, 4])))
with self.assertRaises(TypeError):
Transformation([0, 2, 1]) * PartialPerm([0, 1], [1, 2], 3)
with self.assertRaises(TypeError):
Transformation([0, 2, 1]) * Bipartition([1, -1], [2, 3, -3], [-2])
with self.assertRaises(TypeError):
Transformation([0, 1, 2, 3, 4, 5]) * 8
with self.assertRaises(ValueError):
Transformation([0, 2, 1]) * Transformation([1, 2, 3, 0])
def test_is_transverse_block(self):
self.assertEqual(
Bipartition([1, 2], [-2, -1]).is_transverse_block(1), False)
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).is_transverse_block(1), True)
self.assertEqual(
Bipartition([-1, -2], [2, -3], [1, 3]).is_transverse_block(1),
True)
with self.assertRaises(IndexError):
Bipartition([1, 2], [-2, -1]).is_transverse_block(-3)
with self.assertRaises(IndexError):
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).is_transverse_block(26)
with self.assertRaises(TypeError):
Bipartition([-1, -2], [2, -3], [1, 3]).is_transverse_block('a')
with self.assertRaises(TypeError):
Bipartition([-1, -2], [2, -3], [1, 3]).is_transverse_block([7, 26])
def test_blocks2(self):
x = Bipartition([1, 2], [-2, -1, 3], [-3])
self.assertEqual(x.blocks(), [[1, 2], [3, -1, -2], [-3]])
self.assertEqual((x * x.identity()).blocks(),
[[1, 2], [3, -1, -2], [-3]])
def test_pow(self):
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7])**20,
Bipartition([1, 2, 3], [4, 5, 6, 7], [-1, -2, -3],
[-4, -5, -6, -7]))
self.assertEqual(
Bipartition([1, -1, 2, -2])**26, Bipartition([1, 2, -1, -2]))
self.assertEqual(
Bipartition([-1, -2], [2, -3], [1, 3])**3,
Bipartition([1, 3], [2, -3], [-1, -2]))
with self.assertRaises(ValueError):
Bipartition([1, -1, 2, -2])**-26
self.assertEqual(
Bipartition([1], [-1, 2, -2])**0,
Bipartition([1], [-1, 2, -2]).identity())
with self.assertRaises(TypeError):
Bipartition([1, 2], [-1], [-2])**3.141592653589793238462643383279
with self.assertRaises(TypeError):
Bipartition([1, 2], [-1], [-2])**'c'
def test_degree(self):
self.assertEqual(Bipartition([1, 2], [-2, -1]).degree(), 2)
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).degree(), 7)
self.assertEqual(Bipartition([-1, -2], [2, -3], [1, 3]).degree(), 3)
def test_richcmp(self):
self.assertEqual(Bipartition([3, -4, -1], [2, -3], [4, -2], [1]),
Bipartition([4, -2], [3, -4, -1], [1], [2, -3]))
self.assertFalse(
Bipartition([3, -4, -1], [2, -3], [4, -2], [1]) != Bipartition(
[4, -2], [3, -4, -1], [1], [2, -3]))
self.assertLessEqual(Bipartition([1, -1, 3], [-3, 2, -2]),
Bipartition([1, -1], [2, 3, -2], [-3]))
self.assertLess(Bipartition([1, -1], [2, -2]),
Bipartition([1, -2], [2, -1]))
self.assertLessEqual(Bipartition([1, -1], [2, -2]),
Bipartition([1, -2], [2, -1]))
self.assertGreaterEqual(Bipartition([1, -1, 3], [-3, 2, -2]),
Bipartition([1, -2], [2, -1]))
self.assertFalse(
Bipartition([1, -1, 3], [-3, 2, -2]) > Bipartition(
[1, -1], [2, 3, -2], [-3]))
with self.assertRaises(TypeError):
(PartialPerm([1, 2], [2, 1], 3) == Bipartition([1, -1], [2, 3, -2],
[-3]))
with self.assertRaises(TypeError):
Bipartition([1, -1], [2, -2]) < Transformation([0, 1])
with self.assertRaises(TypeError):
Bipartition([1, -1], [2, -2]) != Transformation([0, 1])
def test_init(self):
Bipartition([-1, -2], [2, -3], [1, 3])
Bipartition([-7, -6, -5, -4], [3, 2, 1], [-3, -2, -1, 4, 5, 6, 7])
Bipartition([1, -1, 2, -2])
def test_mul(self):
(self.assertEqual(
Bipartition([1, -1, 2, -2]) * Bipartition([1, -1, 2, -2]),
Bipartition([1, 2, -1, -2])))
(self.assertEqual(
Bipartition([1, 2], [-1], [-2]) * Bipartition([1, -1], [2, -2]),
Bipartition([1, 2], [-1], [-2])))
(self.assertEqual(
Bipartition([1, -1], [2, 3, -2], [-3]) *
Bipartition([1, 3, 2, -3], [-2], [-1]),
Bipartition([1, 2, 3, -3], [-1], [-2])))
with self.assertRaises(TypeError):
(Bipartition([1, -1], [2, 3, -3], [-2]) *
PartialPerm([0, 1], [1, 2], 3))
with self.assertRaises(TypeError):
Transformation([0, 2, 1]) * Bipartition([1, -1], [2, 3, -3], [-2])
with self.assertRaises(TypeError):
Bipartition([1, -1], [2, 3, -3], [-2]) * 26
with self.assertRaises(ValueError):
(Bipartition([1, -1], [2, 3, -3], [-2]) *
Bipartition([1, -1, 2, -2]))
def test_nr_blocks(self):
self.assertEqual(Bipartition([1, 2], [-2, -1]).nr_blocks(), 2)
self.assertEqual(
Bipartition([-7, -6, -5, -4], [3, 2, 1],
[-3, -2, -1, 4, 5, 6, 7]).nr_blocks(), 3)
self.assertEqual(Bipartition([-1, -2], [2, -3], [1, 3]).nr_blocks(), 3)