def test_compare_recursive(self):
n = 20
seq_a = [ordinal([(1, 1)])]
seq_b = [ordinal([(1, 1), (0, 1)])]
while len(seq_a) < n:
seq_a.append(ordinal([(seq_a[-1], 2), (2, 1)]))
seq_b.append(ordinal([(seq_b[-1], 1)]))
for i in range(n):
a = seq_a[i]
b = seq_b[i]
self.assertTrue(a < b)
self.assertTrue(a <= b)
self.assertTrue(a != b)
self.assertFalse(a > b)
self.assertFalse(a >= b)
self.assertFalse(a == b)
for i in range(1, n):
b = seq_a[i]
for j in range(i):
a = seq_a[j]
self.assertTrue(a < b)
self.assertTrue(a <= b)
self.assertTrue(a != b)
self.assertFalse(a > b)
self.assertFalse(a >= b)
self.assertFalse(a == b)
b = seq_b[i]
for j in range(i):
a = seq_b[j]
self.assertTrue(a < b)
self.assertTrue(a <= b)
self.assertTrue(a != b)
self.assertFalse(a > b)
self.assertFalse(a >= b)
self.assertFalse(a == b)
def test_constants(self):
"""
Small test case to ensure all the provided constants,
such as omega, are actually the ordinals they're supposed to be.
"""
from ordinal import ordinal, omega, epsilon_0, zeta_0
self.assertEqual(omega, ordinal('omega'))
self.assertEqual(epsilon_0, ordinal('epsilon_0'))
self.assertEqual(zeta_0, ordinal('zeta_0'))
self.assertTrue(1 < omega)
self.assertTrue(omega < epsilon_0)
self.assertTrue(epsilon_0 < zeta_0)
def seasons(i):
"""Seasons as strings for searching"""
i = int(i)
if i == 0:
return 'Specials'
else:
return ordinal(i)
def test_add_large(self):
small = 2**8191 - 1
big = ordinal([(2, 1), (1, 2)])
huge = ordinal([(big, 3)])
operands = [
ordinal([(small, 7), (0, 2)]),
ordinal([(big, 2), (0, 5)]),
ordinal([(huge, 1), (small, 8), (0, 3)]),
ordinal([(huge, 4), (big, 3), (0, 6)])
]
results = [[(small, 14), (0, 2)], [(big, 2), (0, 5)],
[(huge, 1), (small, 8), (0, 3)],
[(huge, 4), (big, 3), (0, 6)], [(big, 2), (small, 7),
(0, 2)], [(big, 4), (0, 5)],
[(huge, 1), (small, 8), (0, 3)],
[(huge, 4), (big, 3), (0, 6)],
[(huge, 1), (small, 15), (0, 2)],
[(huge, 1), (big, 2), (0, 5)],
[(huge, 2), (small, 8), (0, 3)],
[(huge, 5), (big, 3), (0, 6)],
[(huge, 4), (big, 3), (small, 7), (0, 2)],
[(huge, 4), (big, 5), (0, 5)],
[(huge, 5), (small, 8), (0, 3)],
[(huge, 8), (big, 3), (0, 6)]]
for (a, b), r in zip(itertools.product(*[operands] * 2), results):
self.assertEqual(r, ordinal(a + b).cnf)
def mainMenu(scaleLetter, num, reps):
if len(sys.argv) < 3:
scaleLetter = input(
"Please enter a scale. eg: g# or ab or a: ").title()
num = float(input("Please enter flash interval: "))
reps = int(
input("Please enter number of reps or press enter to continue: "))
degrees = int(input("Please enter number of keys to use: "))
reps = 99 if reps == 0 else reps
for lvl in range(degrees, 8):
if lvl == 5:
reps = 49
# selected scale to practice
scale = scales[scaleLetter]
if os.name == "posix":
os.system("clear")
else:
os.system("cls")
print(f"Flashing keys in the {scaleLetter} scale")
print(f" Interval: {num}s")
print(f" Reps: {reps}")
print(f" Degree: {lvl}")
print(" Notes: " + ", ".join(scale[0:8]))
print("===================")
print()
print()
print(' Position: Key')
for r in range(1, lvl + 1):
print(' {} tone of {}: {}'.format(ordinal(r), scaleLetter,
scale[r - 1]))
input("Press enter to continue... ")
print()
print()
for i in range(reps):
r = randint(1, lvl)
print(' {} tone of {}: '.format(ordinal(r), scaleLetter),
end=' ',
flush=True)
sleep(num)
print(scale[r - 1])
sleep(1)
mainMenu(scaleLetter, num, reps)
def seasons(i):
"""Seasons as strings for searching"""
try:
i = int(i)
except:
i = 0
if i == 0:
return 'Specials'
else:
return ordinal(i)
def test_multiply_basic(self):
operands = [
ordinal([]), # 0
ordinal([(0, 1)]), # 1
ordinal([(0, 4)]), # 4
ordinal([(1, 1)]), # omega
ordinal([(2, 9)]), # omega**2 * 9
]
results = [[], [], [], [], [], [], [(0, 1)], [(0, 4)], [(1, 1)],
[(2, 9)], [], [(0, 4)], [(0, 16)], [(1, 1)], [(2, 9)], [],
[(1, 1)], [(1, 4)], [(2, 1)], [(3, 9)], [], [(2, 9)],
[(2, 36)], [(3, 1)], [(4, 9)]]
for (a, b), r in zip(itertools.product(*[operands] * 2), results):
self.assertEqual(r, ordinal(a * b).cnf)
def test_add_basic(self):
operands = [
ordinal([]), # 0
ordinal([(0, 1)]), # 1
ordinal([(0, 4)]), # 4
ordinal([(1, 1)]), # omega
ordinal([(2, 9)]), # omega**2 * 9
]
results = [[], [(0, 1)], [(0, 4)], [(1, 1)], [(2, 9)], [(0, 1)],
[(0, 2)], [(0, 5)], [(1, 1)], [(2, 9)], [(0, 4)], [(0, 5)],
[(0, 8)], [(1, 1)], [(2, 9)], [(1, 1)], [(1, 1), (0, 1)],
[(1, 1), (0, 4)], [(1, 2)], [(2, 9)], [(2, 9)],
[(2, 9), (0, 1)], [(2, 9), (0, 4)], [(2, 9), (1, 1)],
[(2, 18)]]
for (a, b), r in zip(itertools.product(*[operands] * 2), results):
self.assertEqual(r, ordinal(a + b).cnf)
def test_string(self):
self.assertEqual("Enter a number!", ordinal.ordinal('b'))
def test_third(self):
self.assertEqual("3rd", ordinal.ordinal(3))
def test_st(self):
self.assertEqual('21st',ordinal.ordinal(21))
def test_eleventh(self):
self.assertEqual("11th", ordinal.ordinal(11))
def test_instance_warn(self):
warnings.simplefilter('error')
with self.assertRaises(UserWarning):
ordinal(-1)
with self.assertRaises(UserWarning):
ordinal([], unchecked=True)
with self.assertRaises(UserWarning):
ordinal([(1 / 2, 1)], unchecked=True)
with self.assertRaises(UserWarning):
ordinal([(-1, 1)], unchecked=True)
with self.assertRaises(UserWarning):
ordinal([(1, 1 / 2)], unchecked=True)
with self.assertRaises(UserWarning):
ordinal([(1, -1)], unchecked=True)
warnings.resetwarnings()
def test_string(self):
self.assertEqual("Enter a number!", ordinal.ordinal('b'))
def test_third(self):
self.assertEqual("3rd", ordinal.ordinal(3))
def test_decimal(self):
self.assertEqual("1st", ordinal.ordinal(1.0))
def test_string_input(self):
self.assertEqual("1st", ordinal.ordinal("1"))
self.assertEqual("Improper input", ordinal.ordinal("abc"))
def test_one_thousand_two(self):
self.assertEqual("1002nd", ordinal.ordinal(1002))
def test_negative_one(self):
self.assertEqual("-1st", ordinal.ordinal(-1))
def test_twelfth(self):
self.assertEqual("12th", ordinal.ordinal(12))
def test_eleventh(self):
self.assertEqual("11th", ordinal.ordinal(11))
def test_fourth(self):
self.assertEqual("4th", ordinal.ordinal(4))
def test_negative_one(self):
self.assertEqual("-1st", ordinal.ordinal(-1))
def test_zero(self):
self.assertEqual("0th", ordinal.ordinal(0))
def test_integers(self):
"""
Sanity tests involving ordinals that are mathematically
integers and the builtin int objects.
Since integers are very straightforward and cheap to
test with, we do a lot of the low level sanity checks here.
"""
from ordinal import ordinal, ordinal_type
for i in range(100):
self.assertTrue(isinstance(i, ordinal_type))
self.assertTrue(isinstance(ordinal(i), ordinal_type))
self.assertEqual(i == i, ordinal(i) == i)
self.assertEqual(i == i, ordinal(i) == ordinal(i))
self.assertEqual(i != i, ordinal(i) != i)
self.assertEqual(i != i, ordinal(i) != ordinal(i))
self.assertEqual(i > i, ordinal(i) > i)
self.assertEqual(i > i, ordinal(i) > ordinal(i))
self.assertEqual(i >= i, ordinal(i) >= i)
self.assertEqual(i >= i, ordinal(i) >= ordinal(i))
self.assertEqual(i < i, ordinal(i) < i)
self.assertEqual(i < i, ordinal(i) < ordinal(i))
self.assertEqual(i <= i, ordinal(i) <= i)
self.assertEqual(i <= i, ordinal(i) <= ordinal(i))
for j in range(1, 100):
for i in range(j):
self.assertEqual(i == j, ordinal(i) == j)
self.assertEqual(i == j, ordinal(i) == ordinal(j))
self.assertEqual(i != j, ordinal(i) != j)
self.assertEqual(i != j, ordinal(i) != ordinal(j))
self.assertEqual(i > j, ordinal(i) > j)
self.assertEqual(i > j, ordinal(i) > ordinal(j))
self.assertEqual(i >= j, ordinal(i) >= j)
self.assertEqual(i >= j, ordinal(i) >= ordinal(j))
self.assertEqual(i < j, ordinal(i) < j)
self.assertEqual(i < j, ordinal(i) < ordinal(j))
self.assertEqual(i <= j, ordinal(i) <= j)
self.assertEqual(i <= j, ordinal(i) <= ordinal(j))
self.assertEqual(j == i, ordinal(j) == i)
self.assertEqual(j == i, ordinal(j) == ordinal(i))
self.assertEqual(j != i, ordinal(j) != i)
self.assertEqual(j != i, ordinal(j) != ordinal(i))
self.assertEqual(j > i, ordinal(j) > i)
self.assertEqual(j > i, ordinal(j) > ordinal(i))
self.assertEqual(j >= i, ordinal(j) >= i)
self.assertEqual(j >= i, ordinal(j) >= ordinal(i))
self.assertEqual(j < i, ordinal(j) < i)
self.assertEqual(j < i, ordinal(j) < ordinal(i))
self.assertEqual(j <= i, ordinal(j) <= i)
self.assertEqual(j <= i, ordinal(j) <= ordinal(i))
with self.assertRaises(ValueError):
ordinal(-1)
with self.assertRaises(TypeError):
ordinal(0.5)
def test_first(self):
self.assertEqual("1st", ordinal.ordinal(1))
def test_st(self):
self.assertEqual('21st', ordinal.ordinal(21))
def test_multiply_mid(self):
operands = [
ordinal([(6, 8), (5, 7), (3, 6), (0, 5)]),
ordinal([(ordinal([(1, 1), (0, 2)]), 3), (0, 4)]),
ordinal([(ordinal([(1, 1), (0, 4)]), 3), (0, 2)])
]
results = [[(12, 8), (11, 7), (9, 6), (6, 40)],
[(ordinal([(1, 1), (0, 2)]), 3), (6, 32)],
[(ordinal([(1, 1), (0, 4)]), 3), (6, 16)],
[(ordinal([(1, 1), (0, 8)]), 8),
(ordinal([(1, 1), (0, 7)]), 7),
(ordinal([(1, 1), (0, 5)]), 6),
(ordinal([(1, 1), (0, 2)]), 15)],
[(ordinal([(1, 2), (0, 2)]), 3),
(ordinal([(1, 1), (0, 2)]), 12)],
[(ordinal([(1, 2), (0, 4)]), 3),
(ordinal([(1, 1), (0, 2)]), 6)],
[(ordinal([(1, 1), (0, 10)]), 8),
(ordinal([(1, 1), (0, 9)]), 7),
(ordinal([(1, 1), (0, 7)]), 6),
(ordinal([(1, 1), (0, 4)]), 15)],
[(ordinal([(1, 2), (0, 2)]), 3),
(ordinal([(1, 1), (0, 4)]), 12)],
[(ordinal([(1, 2), (0, 4)]), 3),
(ordinal([(1, 1), (0, 4)]), 6)]]
for (a, b), r in zip(itertools.product(*[operands] * 2), results):
self.assertEqual(r, ordinal(a * b).cnf)
def test_forth(self):
self.assertEqual("4th", ordinal.ordinal(4))
def test_instance_eq(self):
self.assertEqual(ordinal(0), 0)
self.assertEqual(ordinal(1), 1)
self.assertEqual(ordinal(3), ordinal(3))
self.assertEqual(ordinal('omega'), omega)
self.assertEqual(ordinal(omega), omega)
def test_first(self):
self.assertEqual("1st", ordinal.ordinal(1)) # first ordinal is document from importing
def test_nd(self):
self.assertEqual('2nd',ordinal.ordinal(2))
def test_first(self):
self.assertEqual("1st", ordinal.ordinal(1))
def test_second(self):
self.assertEqual("2nd", ordinal.ordinal(2))
def test_third(self): self.assertEqual(ordinal.ordinal(3), "3rd")
def test_eleven(self): self.assertNotEqual(ordinal.ordinal(111), "111st")
def test_instance_cnf(self):
self.assertEqual(ordinal(0).cnf, [])
self.assertEqual(ordinal(1).cnf, [(0, 1)])
self.assertEqual(ordinal(7).cnf, [(0, 7)])
self.assertEqual(ordinal('omega').cnf, [(1, 1)])
self.assertEqual(ordinal([(4, 3), (2, 1)]).cnf, [(4, 3), (2, 1)])
def test_other(self): self.assertEqual(ordinal.ordinal(34), "34th")
def test_compare(self):
self.assertTrue(ordinal(omega) == omega)
self.assertTrue(ordinal(omega) >= omega)
self.assertTrue(ordinal(omega) <= omega)
self.assertFalse(ordinal(omega) != omega)
self.assertFalse(ordinal(omega) > omega)
self.assertFalse(ordinal(omega) < omega)
self.assertTrue(ordinal(0) == 0)
self.assertTrue(ordinal(0) < 1)
self.assertFalse(ordinal(1) < 0)
self.assertFalse(ordinal(omega) < 0)
self.assertTrue(ordinal(omega) > 1)
ord_ref = ordinal([(3, 2), (1, 4), (0, 1)])
for cnf in [[(1, 4), (0, 1)], [(1, 9)], [(3, 1), (1, 8)],
[(3, 1), (2, 6), (1, 7), (0, 8)], [(3, 2), (1, 3), (0, 7)],
[(3, 2), (1, 4)]]:
ord_cmp = ordinal(cnf)
self.assertTrue(ord_ref > ord_cmp)
self.assertTrue(ord_ref >= ord_cmp)
self.assertTrue(ord_ref != ord_cmp)
self.assertFalse(ord_ref < ord_cmp)
self.assertFalse(ord_ref <= ord_cmp)
self.assertFalse(ord_ref == ord_cmp)
for cnf in [[(3, 2), (1, 4), (0, 1)]]:
ord_cmp = ordinal(cnf)
self.assertTrue(ord_ref == ord_cmp)
self.assertTrue(ord_ref >= ord_cmp)
self.assertTrue(ord_ref <= ord_cmp)
self.assertFalse(ord_ref < ord_cmp)
self.assertFalse(ord_ref > ord_cmp)
self.assertFalse(ord_ref != ord_cmp)
for cnf in [[(3, 2), (1, 4), (0, 2)], [(3, 2), (1, 5)], [(3, 2),
(2, 1)],
[(3, 3), (0, 1)], [(4, 1)]]:
ord_cmp = ordinal(cnf)
self.assertTrue(ord_ref < ord_cmp)
self.assertTrue(ord_ref <= ord_cmp)
self.assertTrue(ord_ref != ord_cmp)
self.assertFalse(ord_ref > ord_cmp)
self.assertFalse(ord_ref >= ord_cmp)
self.assertFalse(ord_ref == ord_cmp)
def test_second(self):
self.assertEqual("2nd", ordinal.ordinal(2))
def ordinal(self, number):
return ordinal.ordinal(number)
def test_second(self):
self.assertEqual("11th", ordinal.ordinal(11))
def test_first(self): self.assertEqual(ordinal.ordinal(self.value), "1st")
def test_eleven(self):
self.assertEqual('11th',ordinal.ordinal(11))
def test_second(self):
self.assertEqual("3rd", ordinal.ordinal(3))
def test_second(self): self.assertEqual(ordinal.ordinal(2), "2nd")
def test_string_input(self):
self.assertEqual("Input is not a number.", ordinal.ordinal("1"))
def test_nd(self):
self.assertEqual('2nd', ordinal.ordinal(2))
def test_first(self):
self.assertEqual("1st", ordinal.ordinal(1)) # first ordinal: module, second ordinal: method
def test_eleven(self):
self.assertEqual('11th', ordinal.ordinal(11))
