def test_xgate(self):
"""XGATE: Flip along √i axis. 1 => 0, 0 => 1"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
cnot_tests = [
['Verify XGATE +|0>| = +|1>',
self.xgate(z), o],
['Verify XGATE +|1>| = +|0>',
self.xgate(o), z],
['Verify XGATE -|0>| = -|1>',
self.xgate(-z), -o],
['Verify XGATE -|1>| = -|0>',
self.xgate(-o), -z],
['Verify XGATE |00>| = |10>',
self.xgate(zz), oz],
['Verify XGATE |01>| =-|11>',
self.xgate(zo), -oo],
['Verify XGATE |10>| = |10>',
self.xgate(oz), zz],
['Verify XGATE |11>| = |01>',
self.xgate(oo), zo],
]
for test in cnot_tests:
title, calc, expect = test
self.assertEqual(calc, expect)
def test_16_steps(self):
"""16 Step Circle Walk test"""
z = Construct((1, 0))
steps = [
(0, 1),
(sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), sqrt(1 / 2)),
(0, -1),
(-1, 0),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-1, 0),
(0, -1),
(-sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), -sqrt(1 / 2)),
(0, 1),
(1, 0),
(sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), sqrt(1 / 2)),
(1, 0),
]
starting = Construct((z.flat()))
for i in range(16):
if i % 2:
gate = 'Hadamard'
z2 = self.hadamard(z)
else:
gate = ' XGate'
z2 = self.xgate(z)
z = z2
self.assertEqual(z, Construct(steps[i]))
self.assertEqual(z, starting)
def test_quaternion_unit_table(self):
"""quaternion table"""
x = Construct((1, 0, 0, 0))
i = Construct((0, 1, 0, 0))
j = Construct((0, 0, 1, 0))
k = Construct((0, 0, 0, 1))
timestable = [
['1*1 = 1', x * x, x],
['1*i = i', x * i, i],
['i*1 = i', i * x, i],
['i*i = -1', i * i, -x],
['1*j = 1', x * j, j],
['1*k = k', x * k, k],
['i*j = k', i * j, k],
['i*k = -j', i * k, -j],
['j*1 = j', j * x, j],
['j*i = -k', j * i, -k],
['j*j = -1', j * j, -x],
['j*k = i', j * k, i],
['k*1 = k', k * x, k],
['k*i = j', k * i, j],
['k*j = -i', k * j, -i],
['k*k = -1', k * k, -x],
]
for entry in timestable:
title, calc, expect = entry[::]
self.assertEqual(calc, expect)
def test_complex_unit_table(self):
"""complex table"""
x = Construct((1, 0))
i = Construct((0, 1))
timestable = [
['1*1 = 1', x * x, x],
['1*i = i', x * i, i],
['i*1 = i', i * x, i],
['i*i = -1', i * i, -x],
]
for entry in timestable:
title, calc, expect = entry[::]
self.assertEqual(calc, expect)
def test_identity(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, z)
self.assertEqual(target, z)
control = o.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, o)
self.assertEqual(target, z)
def test_constant_1(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, z)
self.assertEqual(target, o)
control = o.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, o)
self.assertEqual(target, o)
def test_sixteen_square_identity(self):
x = random_vector(16)
y = random_vector(16)
a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16 = x
b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = y
# assuming i^2 = -1 ...
z1 = a1 * b1 - a2 * b2 - a3 * b3 - a4 * b4 - b5 * a5 - b6 * a6 - b7 * a7 - b8 * a8 - b9 * a9 - b10 * a10 - b11 * a11 - b12 * a12 - a13 * b13 - a14 * b14 - a15 * b15 - a16 * b16
z2 = a1 * b2 + a2 * b1 + a3 * b4 - a4 * b3 - b5 * a6 + b6 * a5 + b7 * a8 - b8 * a7 - b9 * a10 + b10 * a9 + b11 * a12 - b12 * a11 - a13 * b14 + a14 * b13 + a15 * b16 - a16 * b15
z3 = a1 * b3 - a2 * b4 + a3 * b1 + a4 * b2 - b5 * a7 - b6 * a8 + b7 * a5 + b8 * a6 - b9 * a11 - b10 * a12 + b11 * a9 + b12 * a10 - a13 * b15 - a14 * b16 + a15 * b13 + a16 * b14
z4 = a1 * b4 + a2 * b3 - a3 * b2 + a4 * b1 - b5 * a8 + b6 * a7 - b7 * a6 + b8 * a5 - b9 * a12 + b10 * a11 - b11 * a10 + b12 * a9 - a13 * b16 + a14 * b15 - a15 * b14 + a16 * b13
z5 = b5 * a1 - b6 * a2 - b7 * a3 - b8 * a4 + a5 * b1 + a6 * b2 + a7 * b3 + a8 * b4 - a13 * b9 - a14 * b10 - a15 * b11 - a16 * b12 + b13 * a9 + b14 * a10 + b15 * a11 + b16 * a12
z6 = b5 * a2 + b6 * a1 + b7 * a4 - b8 * a3 - a5 * b2 + a6 * b1 - a7 * b4 + a8 * b3 + a13 * b10 - a14 * b9 + a15 * b12 - a16 * b11 - b13 * a10 + b14 * a9 - b15 * a12 + b16 * a11
z7 = b5 * a3 - b6 * a4 + b7 * a1 + b8 * a2 - a5 * b3 + a6 * b4 + a7 * b1 - a8 * b2 + a13 * b11 - a14 * b12 - a15 * b9 + a16 * b10 - b13 * a11 + b14 * a12 + b15 * a9 - b16 * a10
z8 = b5 * a4 + b6 * a3 - b7 * a2 + b8 * a1 - a5 * b4 - a6 * b3 + a7 * b2 + a8 * b1 + a13 * b12 + a14 * b11 - a15 * b10 - a16 * b9 - b13 * a12 - b14 * a11 + b15 * a10 + b16 * a9
z9 = b9 * a1 - b10 * a2 - b11 * a3 - b12 * a4 - a5 * b13 - a6 * b14 - a7 * b15 - a8 * b16 + a9 * b1 + a10 * b2 + a11 * b3 + a12 * b4 + b5 * a13 + b6 * a14 + b7 * a15 + b8 * a16
z10 = b9 * a2 + b10 * a1 + b11 * a4 - b12 * a3 - a5 * b14 + a6 * b13 + a7 * b16 - a8 * b15 - a9 * b2 + a10 * b1 - a11 * b4 + a12 * b3 + b5 * a14 - b6 * a13 - b7 * a16 + b8 * a15
z11 = b9 * a3 - b10 * a4 + b11 * a1 + b12 * a2 - a5 * b15 - a6 * b16 + a7 * b13 + a8 * b14 - a9 * b3 + a10 * b4 + a11 * b1 - a12 * b2 + b5 * a15 + b6 * a16 - b7 * a13 - b8 * a14
z12 = b9 * a4 + b10 * a3 - b11 * a2 + b12 * a1 - a5 * b16 + a6 * b15 - a7 * b14 + a8 * b13 - a9 * b4 - a10 * b3 + a11 * b2 + a12 * b1 + b5 * a16 - b6 * a15 + b7 * a14 - b8 * a13
z13 = a5 * b9 - a6 * b10 - a7 * b11 - a8 * b12 + b13 * a1 + b14 * a2 + b15 * a3 + b16 * a4 - b5 * a9 + b6 * a10 + b7 * a11 + b8 * a12 + a13 * b1 - a14 * b2 - a15 * b3 - a16 * b4
z14 = a5 * b10 + a6 * b9 + a7 * b12 - a8 * b11 - b13 * a2 + b14 * a1 - b15 * a4 + b16 * a3 - b5 * a10 - b6 * a9 - b7 * a12 + b8 * a11 + a13 * b2 + a14 * b1 + a15 * b4 - a16 * b3
z15 = a5 * b11 - a6 * b12 + a7 * b9 + a8 * b10 - b13 * a3 + b14 * a4 + b15 * a1 - b16 * a2 - b5 * a11 + b6 * a12 - b7 * a9 - b8 * a10 + a13 * b3 - a14 * b4 + a15 * b1 + a16 * b2
z16 = a5 * b12 + a6 * b11 - a7 * b10 + a8 * b9 - b13 * a4 - b14 * a3 + b15 * a2 + b16 * a1 - b5 * a12 - b6 * a11 + b7 * a10 - b8 * a9 + a13 * b4 + a14 * b3 - a15 * b2 + a16 * b1
form = Construct((z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, z12,
z13, z14, z15, z16))
self.assertEqual(form, x * y)
def test_two_square_identity(self):
x = random_vector(2)
y = random_vector(2)
a, b = x
c, d = y
form = Construct((a * c - d * b, d * a + b * c))
self.assertEqual(form, x * y)
def test_cnot(self):
"""CNOT: second bit flip controlled by the first"""
z = Construct((1, 0))
o = Construct((0, 1))
cnot_tests = [
['Verify CNOT |00>| = |00>',
self.cnot(z, z), (1, 0, 0, 0)],
['Verify CNOT |01>| = |01>',
self.cnot(z, o), (0, 1, 0, 0)],
['Verify CNOT |10>| = |11>',
self.cnot(o, z), (0, 0, 0, 1)],
['Verify CNOT |11>| = -|10>',
self.cnot(o, o), (0, 0, -1, 0)]
]
for test in cnot_tests:
title, calc, expected = test
expect = Construct(expected)
self.assertEqual(calc, expect)
def test_32ion(self):
"""Check that a number intended to be 32 dimensional knows that it is"""
for n in range(self.LOOPS):
z = Construct([random() for _ in range(32)])
self.assertFalse(z.is_complex())
self.assertFalse(z.is_quaternion())
self.assertFalse(z.is_octonion())
self.assertFalse(z.is_sedenion())
self.assertEqual(z.dimension(), 32)
def test_octonion_dimensions(self):
"""Check that a number intended to be a octonion says that it is"""
for n in range(self.LOOPS):
z = Construct([random() for _ in range(8)])
self.assertFalse(z.is_complex())
self.assertFalse(z.is_quaternion())
self.assertTrue(z.is_octonion())
self.assertFalse(z.is_sedenion())
self.assertNotEqual(z.dimension(), 32)
def test_hadamard(self):
"""Hadamard gate test"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
hadamard_tests = [
['Verify HADAMARD +| 0>| = + | +>',
self.hadamard(z), rz],
['Verify HADAMARD +| 1>| = + | ->',
self.hadamard(o), ro],
['Verify HADAMARD -| 0>| = - | +>',
self.hadamard(-z), -rz],
['Verify HADAMARD -| 1>| = - | ->',
self.hadamard(-o), -ro],
[
'Verify HADAMARD +|00>| = + |1+>',
self.hadamard(zz),
rz.tensor(z)
],
[
'Verify HADAMARD +|01>| = - |11>',
self.hadamard(zo), -rz.tensor(o)
],
[
'Verify HADAMARD +|10>| = + |00>',
self.hadamard(oz),
ro.tensor(z)
],
[
'Verify HADAMARD +|11>| = + |01>',
self.hadamard(oo),
ro.tensor(o)
],
]
for test in hadamard_tests:
title, calc, expected = test
self.assertEqual(calc, expected)
def test_four_square_identity(self):
x = random_vector(4)
y = random_vector(4)
a, b, c, d = x
e, f, g, h = y
r = a * e - b * f - c * g - d * h
s = a * f + b * e + c * h - d * g
t = a * g - b * h + c * e + d * f
u = a * h + b * g - c * f + d * e
form = Construct((r, s, t, u))
self.assertEqual(form, x * y)
def test_eight_square_identity(self):
x = random_vector(8)
y = random_vector(8)
a, b, c, d, e, f, g, h = x
i, j, k, l, m, n, o, p = y
# assuming i^2 = -1 ...
z1 = a * i - b * j - c * k - d * l - m * e - n * f - o * g - p * h
z2 = a * j + b * i + c * l - d * k - m * f + n * e + o * h - p * g
z3 = a * k - b * l + c * i + d * j - m * g - n * h + o * e + p * f
z4 = a * l + b * k - c * j + d * i - m * h + n * g - o * f + p * e
z5 = m * a - n * b - o * c - p * d + e * i + f * j + g * k + h * l
z6 = m * b + n * a + o * d - p * c - e * j + f * i - g * l + h * k
z7 = m * c - n * d + o * a + p * b - e * k + f * l + g * i - h * j
z8 = m * d + n * c - o * b + p * a - e * l - f * k + g * j + h * i
form = Construct((z1, z2, z3, z4, z5, z6, z7, z8))
self.assertEqual(form, x * y)
def test_constant_0(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = Construct(z.flat())
target = Construct(z.flat())
self.assertEqual(control, z)
self.assertEqual(target, z)
control = Construct(o.flat())
target = Construct(z.flat())
self.assertEqual(control, o)
self.assertEqual(target, z)
def random_vector(dimension=2):
"""generate a random complex number"""
return Construct([random() for _ in range(dimension)])
class TestBlackBox(unittest.TestCase):
"""Black box: constant 0, constant 1, identity and negate"""
gate_cnot = Construct((sqrt(1 / 2), sqrt(1 / 2), 0, 0))
gate_x = Construct((0, 1))
gate_hadamard = Construct((sqrt(1 / 2), sqrt(1 / 2)))
def cnot(self, z1, z2):
c = z1.tensor(z2)
return self.gate_cnot * c * ~self.gate_cnot
def xgate(self, z):
return self.gate_x / z
def hadamard(self, z):
return self.gate_hadamard / z
def test_constant_0(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = Construct(z.flat())
target = Construct(z.flat())
self.assertEqual(control, z)
self.assertEqual(target, z)
control = Construct(o.flat())
target = Construct(z.flat())
self.assertEqual(control, o)
self.assertEqual(target, z)
def test_constant_1(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, z)
self.assertEqual(target, o)
control = o.copy()
target = z.copy()
target = self.xgate(target)
self.assertEqual(control, o)
self.assertEqual(target, o)
def test_identity(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, z)
self.assertEqual(target, z)
control = o.copy()
target = z.copy()
self.cnot(control, target)
self.assertEqual(control, o)
self.assertEqual(target, z)
def test_negate(self):
z = Construct((1, 0))
o = Construct((0, 1))
control = z.copy()
target = z.copy()
self.cnot(control, target)
target = self.xgate(target)
self.assertEqual(control, z)
self.assertEqual(target, o)
control = o.copy()
target = z.copy()
self.cnot(control, target)
target = self.xgate(target)
self.assertEqual(control, o)
self.assertEqual(target, o)
def test_tensor(self):
z1 = Construct((1, 2))
z2 = Construct((3, 4))
z = Construct((1, 0))
o = Construct((0, 1))
brakets = [
[z1.tensor(z2), (3, 4, 6, 8)],
[o.tensor(z.tensor(z)), (0, 0, 0, 0, 1, 0, 0, 0)],
[o.tensor(z.tensor(o)), (0, 0, 0, 0, 0, 1, 0, 0)],
[o.tensor(o.tensor(z)), (0, 0, 0, 0, 0, 0, 1, 0)],
[o.tensor(o.tensor(o)), (0, 0, 0, 0, 0, 0, 0, 1)],
[
o.tensor(z.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
]
for item in brakets:
calc, expected = item
expect = Construct(expected)
self.assertEqual(calc, expect)
class TestQuantumEmulator(unittest.TestCase):
"""Quatum Tests"""
gate_cnot = Construct((sqrt(1 / 2), sqrt(1 / 2), 0, 0))
gate_x = Construct((0, 1))
gate_hadamard = Construct((sqrt(1 / 2), sqrt(1 / 2)))
def cnot(self, z1, z2):
c = z1.tensor(z2)
return self.gate_cnot * c * ~self.gate_cnot
def xgate(self, z):
return self.gate_x / z
def hadamard(self, z):
return self.gate_hadamard / z
def test_instantiate(self):
for t in [(1, 2), (3, 4), (-1, 2)]:
self.assertEqual(RootFraction(t).flat(), t)
def test_tensor(self):
z1 = Construct((1, 2))
z2 = Construct((3, 4))
z = Construct((1, 0))
o = Construct((0, 1))
brakets = [
[z1.tensor(z2), (3, 4, 6, 8)],
[o.tensor(z.tensor(z)), (0, 0, 0, 0, 1, 0, 0, 0)],
[o.tensor(z.tensor(o)), (0, 0, 0, 0, 0, 1, 0, 0)],
[o.tensor(o.tensor(z)), (0, 0, 0, 0, 0, 0, 1, 0)],
[o.tensor(o.tensor(o)), (0, 0, 0, 0, 0, 0, 0, 1)],
[
o.tensor(z.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(z.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(z.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(z.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(z)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0)
],
[
o.tensor(o.tensor(o.tensor(o.tensor(o)))),
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
],
]
for item in brakets:
calc, expected = item
expect = Construct(expected)
self.assertEqual(calc, expect)
def test_xgate(self):
"""XGATE: Flip along √i axis. 1 => 0, 0 => 1"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
cnot_tests = [
['Verify XGATE +|0>| = +|1>',
self.xgate(z), o],
['Verify XGATE +|1>| = +|0>',
self.xgate(o), z],
['Verify XGATE -|0>| = -|1>',
self.xgate(-z), -o],
['Verify XGATE -|1>| = -|0>',
self.xgate(-o), -z],
['Verify XGATE |00>| = |10>',
self.xgate(zz), oz],
['Verify XGATE |01>| =-|11>',
self.xgate(zo), -oo],
['Verify XGATE |10>| = |10>',
self.xgate(oz), zz],
['Verify XGATE |11>| = |01>',
self.xgate(oo), zo],
]
for test in cnot_tests:
title, calc, expect = test
self.assertEqual(calc, expect)
def test_cnot(self):
"""CNOT: second bit flip controlled by the first"""
z = Construct((1, 0))
o = Construct((0, 1))
cnot_tests = [
['Verify CNOT |00>| = |00>',
self.cnot(z, z), (1, 0, 0, 0)],
['Verify CNOT |01>| = |01>',
self.cnot(z, o), (0, 1, 0, 0)],
['Verify CNOT |10>| = |11>',
self.cnot(o, z), (0, 0, 0, 1)],
['Verify CNOT |11>| = -|10>',
self.cnot(o, o), (0, 0, -1, 0)]
]
for test in cnot_tests:
title, calc, expected = test
expect = Construct(expected)
self.assertEqual(calc, expect)
def test_hadamard(self):
"""Hadamard gate test"""
z = Construct((1, 0))
o = Construct((0, 1))
zz = z.tensor(z)
zo = z.tensor(o)
oz = o.tensor(z)
oo = o.tensor(o)
rz = self.hadamard(z)
ro = self.hadamard(o)
hadamard_tests = [
['Verify HADAMARD +| 0>| = + | +>',
self.hadamard(z), rz],
['Verify HADAMARD +| 1>| = + | ->',
self.hadamard(o), ro],
['Verify HADAMARD -| 0>| = - | +>',
self.hadamard(-z), -rz],
['Verify HADAMARD -| 1>| = - | ->',
self.hadamard(-o), -ro],
[
'Verify HADAMARD +|00>| = + |1+>',
self.hadamard(zz),
rz.tensor(z)
],
[
'Verify HADAMARD +|01>| = - |11>',
self.hadamard(zo), -rz.tensor(o)
],
[
'Verify HADAMARD +|10>| = + |00>',
self.hadamard(oz),
ro.tensor(z)
],
[
'Verify HADAMARD +|11>| = + |01>',
self.hadamard(oo),
ro.tensor(o)
],
]
for test in hadamard_tests:
title, calc, expected = test
self.assertEqual(calc, expected)
def test_16_steps(self):
"""16 Step Circle Walk test"""
z = Construct((1, 0))
steps = [
(0, 1),
(sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), sqrt(1 / 2)),
(0, -1),
(-1, 0),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-sqrt(1 / 2), -sqrt(1 / 2)),
(-1, 0),
(0, -1),
(-sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), -sqrt(1 / 2)),
(0, 1),
(1, 0),
(sqrt(1 / 2), sqrt(1 / 2)),
(sqrt(1 / 2), sqrt(1 / 2)),
(1, 0),
]
starting = Construct((z.flat()))
for i in range(16):
if i % 2:
gate = 'Hadamard'
z2 = self.hadamard(z)
else:
gate = ' XGate'
z2 = self.xgate(z)
z = z2
self.assertEqual(z, Construct(steps[i]))
self.assertEqual(z, starting)
def test_octonion_unit_table(self):
"""octonion table"""
x = Construct((1, 0, 0, 0, 0, 0, 0, 0))
i = Construct((0, 1, 0, 0, 0, 0, 0, 0))
j = Construct((0, 0, 1, 0, 0, 0, 0, 0))
k = Construct((0, 0, 0, 1, 0, 0, 0, 0))
l = Construct((0, 0, 0, 0, 1, 0, 0, 0))
m = Construct((0, 0, 0, 0, 0, 1, 0, 0))
n = Construct((0, 0, 0, 0, 0, 0, 1, 0))
o = Construct((0, 0, 0, 0, 0, 0, 0, 1))
timestable = [
['1*1 = 1', x * x, x],
['1*i = i', x * i, i],
['i*1 = i', i * x, i],
['i*i = -1', i * i, -x],
['1*j = 1', x * j, j],
['1*k = k', x * k, k],
['i*j = k', i * j, k],
['i*k = -j', i * k, -j],
['j*1 = j', j * x, j],
['j*i = -k', j * i, -k],
['j*j = -1', j * j, -x],
['j*k = i', j * k, i],
['k*1 = k', k * x, k],
['k*i = j', k * i, j],
['k*j = -i', k * j, -i],
['k*k = -1', k * k, -x],
['1*l = 1', x * l, l],
['1*m = m', x * m, m],
['1*n = n', x * n, n],
['1*o = o', x * o, o],
['i*l = m', i * l, m],
['i*m = -l', i * m, -l],
['i*n = -o', i * n, -o],
['i*o = n', i * o, n],
['j*l = n', j * l, n],
['j*m = o', j * m, o],
['j*n = -l', j * n, -l],
['j*o = -m', j * o, -m],
['k*l = o', k * l, o],
['k*m = -n', k * m, -n],
['k*n = m', k * n, m],
['k*o = -l', k * o, -l],
['l*1 = 1', l * x, l],
['l*i = -m', l * i, -m],
['l*j = -n', l * j, -n],
['l*k = -o', l * k, -o],
['l*l = -1', l * l, -x],
['l*m = i', l * m, i],
['l*n = j', l * n, j],
['1*o = k', l * o, k],
['m*1 = m', m * x, m],
['m*i = l', m * i, l],
['m*j = -o', m * j, -o],
['m*k = n', m * k, n],
['m*l = -i', m * l, -i],
['m*m = -1', m * m, -x],
['m*n = -k', m * n, -k],
['m*o = j', m * o, j],
['n*1 = n', n * x, n],
['n*i = o', n * i, o],
['n*j = l', n * j, l],
['n*k = -m', n * k, -m],
['n*l = -j', n * l, -j],
['n*m = k', n * m, k],
['n*n = -1', n * n, -x],
['n*o = -i', n * o, -i],
['o*1 = o', o * x, o],
['o*i = -n', o * i, -n],
['o*j = m', o * j, m],
['o*k = l', o * k, l],
['o*l = -k', o * l, -k],
['o*m = -j', o * m, -j],
['o*n = i', o * n, i],
['o*o = -1', o * o, -x],
]
for entry in timestable:
title, calc, expect = entry[::]
self.assertEqual(calc, expect)
def test_sedenion_unit_table(self):
"""sedenion table"""
x = Construct((1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
i = Construct((0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
j = Construct((0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
k = Construct((0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
l = Construct((0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
m = Construct((0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
n = Construct((0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0))
o = Construct((0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0))
p = Construct((0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0))
q = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0))
r = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0))
s = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0))
t = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0))
u = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0))
v = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0))
w = Construct((0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1))
timestable = [
['1*1 = 1', x * x, x],
['1*i = i', x * i, i],
['i*1 = i', i * x, i],
['i*i = -1', i * i, -x],
['1*j = 1', x * j, j],
['1*k = k', x * k, k],
['i*j = k', i * j, k],
['i*k = -j', i * k, -j],
['j*1 = j', j * x, j],
['j*i = -k', j * i, -k],
['j*j = -1', j * j, -x],
['j*k = i', j * k, i],
['k*1 = k', k * x, k],
['k*i = j', k * i, j],
['k*j = -i', k * j, -i],
['k*k = -1', k * k, -x],
['1*l = 1', x * l, l],
['1*m = m', x * m, m],
['1*n = n', x * n, n],
['1*o = o', x * o, o],
['i*l = m', i * l, m],
['i*m = -l', i * m, -l],
['i*n = -o', i * n, -o],
['i*o = n', i * o, n],
['j*l = n', j * l, n],
['j*m = o', j * m, o],
['j*n = -l', j * n, -l],
['j*o = -m', j * o, -m],
['k*l = o', k * l, o],
['k*m = -n', k * m, -n],
['k*n = m', k * n, m],
['k*o = -l', k * o, -l],
['l*1 = 1', l * x, l],
['l*i = -m', l * i, -m],
['l*j = -n', l * j, -n],
['l*k = -o', l * k, -o],
['l*l = -1', l * l, -x],
['l*m = i', l * m, i],
['l*n = j', l * n, j],
['1*o = k', l * o, k],
['m*1 = m', m * x, m],
['m*i = l', m * i, l],
['m*j = -o', m * j, -o],
['m*k = n', m * k, n],
['m*l = -i', m * l, -i],
['m*m = -1', m * m, -x],
['m*n = -k', m * n, -k],
['m*o = j', m * o, j],
['n*1 = n', n * x, n],
['n*i = o', n * i, o],
['n*j = l', n * j, l],
['n*k = -m', n * k, -m],
['n*l = -j', n * l, -j],
['n*m = k', n * m, k],
['n*n = -1', n * n, -x],
['n*o = -i', n * o, -i],
['o*1 = o', o * x, o],
['o*i = -n', o * i, -n],
['o*j = m', o * j, m],
['o*k = l', o * k, l],
['o*l = -k', o * l, -k],
['o*m = -j', o * m, -j],
['o*n = i', o * n, i],
['o*o = -1', o * o, -x],
['1*p = p', x * p, p],
['1*q = q', x * q, q],
['1*r = r', x * r, r],
['1*s = s', x * s, s],
['1*t = t', x * t, t],
['1*u = u', x * u, u],
['1*v = v', x * v, v],
['1*w = w', x * w, w],
['i*p = i', i * p, q],
['i*q = -x', i * q, -p],
['i*r = k', i * r, -s],
['i*s = -j', i * s, r],
['i*t = m', i * t, -u],
['i*u = -l', i * u, t],
['i*v = -o', i * v, w],
['i*w = n', i * w, -v],
['j*p = 1', j * p, r],
['j*q = i', j * q, s],
['j*r = 1', j * r, -p],
['j*s = k', j * s, -q],
['j*t = 1', j * t, -v],
['j*u = i', j * u, -w],
['j*v = 1', j * v, t],
['j*w = k', j * w, u],
['k*p = 1', k * p, s],
['k*q = i', k * q, -r],
['k*r = 1', k * r, q],
['k*s = k', k * s, -p],
['k*t = 1', k * t, -w],
['k*u = i', k * u, v],
['k*v = 1', k * v, -u],
['k*w = k', k * w, t],
['l*p = 1', l * p, t],
['l*q = i', l * q, u],
['l*r = 1', l * r, v],
['l*s = k', l * s, w],
['l*t = 1', l * t, -p],
['l*u = i', l * u, -q],
['l*v = 1', l * v, -r],
['1*w = k', l * w, -s],
['m*p = 1', m * p, u],
['m*q = i', m * q, -t],
['m*r = 1', m * r, w],
['m*s = k', m * s, -v],
['m*t = 1', m * t, q],
['m*u = i', m * u, -p],
['m*v = 1', m * v, s],
['m*w = k', m * w, -r],
['n*p = 1', n * p, v],
['n*q = i', n * q, -w],
['n*r = 1', n * r, -t],
['n*s = k', n * s, u],
['n*t = 1', n * t, r],
['n*u = i', n * u, -s],
['n*v = 1', n * v, -p],
['n*w = k', n * w, q],
['o*p = 1', o * p, w],
['o*q = i', o * q, v],
['o*r = 1', o * r, -u],
['o*s = k', o * s, -t],
['o*t = 1', o * t, s],
['o*u = i', o * u, r],
['o*v = 1', o * v, -q],
['o*w = k', o * w, -p],
['p*1 = p', p * x, p],
['p*i = -q', p * i, -q],
['p*j = -r', p * j, -r],
['p*k = -s', p * k, -s],
['p*l = -t', p * l, -t],
['p*m = -u', p * m, -u],
['p*n = -v', p * n, -v],
['p*o = -w', p * o, -w],
['p*p = -1', p * p, -x],
['p*q = i', p * q, i],
['p*r = j', p * r, j],
['p*s = k', p * s, k],
['p*t = l', p * t, l],
['p*u = m', p * u, m],
['p*v = n', p * v, n],
['p*w = o', p * w, o],
['q*1 = q', q * x, q],
['q*i = p', q * i, p],
['q*j = -s', q * j, -s],
['q*k = r', q * k, r],
['q*l = -u', q * l, -u],
['q*m = t', q * m, t],
['q*n = w', q * n, w],
['q*o = -v', q * o, -v],
['q*p = -i', q * p, -i],
['q*q = -1', q * q, -x],
['q*r = -k', q * r, -k],
['q*s = j', q * s, j],
['q*t = -m', q * t, -m],
['q*u = l', q * u, l],
['q*v = o', q * v, o],
['q*w = -n', q * w, -n],
['r*1 = r', r * x, r],
['r*i = s', r * i, s],
['r*j = p', r * j, p],
['r*k = -q', r * k, -q],
['r*l = -v', r * l, -v],
['r*m = -w', r * m, -w],
['r*n = t', r * n, t],
['r*o = u', r * o, u],
['r*p = -j', r * p, -j],
['r*q = k', r * q, k],
['r*r = -1', r * r, -x],
['r*s = -i', r * s, -i],
['r*t = -n', r * t, -n],
['r*u = -o', r * u, -o],
['r*v = l', r * v, l],
['r*w = m', r * w, m],
['s*1 = s', s * x, s],
['s*i = -r', s * i, -r],
['s*j = q', s * j, q],
['s*k = p', s * k, p],
['s*l = -w', s * l, -w],
['s*m = v', s * m, v],
['s*n = -u', s * n, -u],
['s*o = t', s * o, t],
['s*p = -k', s * p, -k],
['s*q = -j', s * q, -j],
['s*r = i', s * r, i],
['s*s = -1', s * s, -x],
['s*t = -o', s * t, -o],
['s*u = n', s * u, n],
['s*v = -m', s * v, -m],
['s*w = l', s * w, l],
['t*1 = t', t * x, t],
['t*i = u', t * i, u],
['t*j = v', t * j, v],
['t*k = w', t * k, w],
['t*l = p', t * l, p],
['t*m = -q', t * m, -q],
['t*n = -r', t * n, -r],
['t*o = -s', t * o, -s],
['t*p = -l', t * p, -l],
['t*q = m', t * q, m],
['t*r = n', t * r, n],
['t*s = o', t * s, o],
['t*t = -1', t * t, -x],
['t*u = -i', t * u, -i],
['t*v = -j', t * v, -j],
['t*w = -k', t * w, -k],
['u*1 = u', u * x, u],
['u*i = -t', u * i, -t],
['u*j = w', u * j, w],
['u*k = -v', u * k, -v],
['u*l = q', u * l, q],
['u*m = p', u * m, p],
['u*n = s', u * n, s],
['u*o = -r', u * o, -r],
['u*p = -m', u * p, -m],
['u*q = -l', u * q, -l],
['u*r = o', u * r, o],
['u*s = -n', u * s, -n],
['u*t = i', u * t, i],
['u*u = -1', u * u, -x],
['u*v = k', u * v, k],
['u*w = -j', u * w, -j],
['v*1 = v', v * x, v],
['v*i = -w', v * i, -w],
['v*j = -t', v * j, -t],
['v*k = u', v * k, u],
['v*l = r', v * l, r],
['v*m = -s', v * m, -s],
['v*n = p', v * n, p],
['v*o = q', v * o, q],
['v*p = -n', v * p, -n],
['v*q = -o', v * q, -o],
['v*r = -l', v * r, -l],
['v*s = m', v * s, m],
['v*t = j', v * t, j],
['v*u = -k', v * u, -k],
['v*v = -1', v * v, -x],
['v*w = i', v * w, i],
['w*1 = w', w * x, w],
['w*i = v', w * i, v],
['w*j = -u', w * j, -u],
['w*k = -t', w * k, -t],
['w*l = s', w * l, s],
['w*m = r', w * m, r],
['w*n = -q', w * n, -q],
['w*o = p', w * o, p],
['w*p = -o', w * p, -o],
['w*q = n', w * q, n],
['w*r = -m', w * r, -m],
['w*s = -l', w * s, -l],
['w*t = k', w * t, k],
['w*u = j', w * u, j],
['w*v = -i', w * v, -i],
['w*w = -1', w * w, -x],
]
for entry in timestable:
title, calc, expect = entry[::]
self.assertEqual(calc, expect)
