def test_1031_subs():
t, x, y, z = sp.symbols("t x y z")
q_sym = QHStates([QH([t, x, y, x * y * z])])
q_z = q_sym.subs({t: 1, x: 2, y: 3, z: 4})
print("t x y xyz sub 1 2 3 4: ", q_z)
assert q_z.equals(QHStates([QH([1, 2, 3, 24])]))
def test_1472_Lorentz_next_boost():
with pytest.raises(ValueError):
QH.Lorentz_next_boost(Q, q4321)
next_boost = QH.Lorentz_next_boost(Q, q1324)
print(f"next_boost: {next_boost}")
assert next_boost.t != 0
boost = q2244.rotation_and_or_boost(next_boost)
assert math.isclose(boost.square().t, q2244.square().t)
def test_1130_identity():
I2 = QHStates().identity(2, operator=True)
print("Operator Idenity, diagonal 2x2", I2)
assert I2.qs[0].equals(QH().q_1())
assert I2.qs[1].equals(QH().q_0())
I2 = QHStates().identity(2)
print("Idenity on 2 state ket", I2)
assert I2.qs[0].equals(QH().q_1())
assert I2.qs[1].equals(QH().q_1())
def test_1471_Lorentz_next_rotation():
with pytest.raises(ValueError):
QH.Lorentz_next_rotation(Q, q4321)
next_rotation = QH.Lorentz_next_rotation(Q, q1324)
print("next_rotation: ", next_rotation)
assert next_rotation.t == 0
rot = q2244.rotation_and_or_boost(next_rotation)
assert math.isclose(rot.t, 2)
assert math.isclose(rot.square().t, q2244.square().t)
next_rotation = QH.Lorentz_next_rotation(Q, Q)
assert next_rotation.equals(Q.vector().normalize())
def test_1570_ln():
assert Q.ln().exp().equals(Q)
assert Q.ln().equals(
QH([
1.7005986908310777,
-0.5151902926640850,
-0.7727854389961275,
-1.0303805853281700,
]))
assert P.ln().equals(
QH([1.6094379124341003, 1.2566370614359172, -0.9424777960769379, 0]))
assert R.ln().equals(QH([1.0986122886681098, 0, 0, 0]))
assert C.ln().equals(QH([1.4978661367769954, 1.1071487177940904, 0, 0]))
def test_1100_q_random():
q_z = QH().q_random()
print("q_random():", q_z)
assert -1 <= q_z.t <= 1
assert -1 <= q_z.x <= 1
assert -1 <= q_z.y <= 1
assert -1 <= q_z.z <= 1
def test_1060_q_1():
q_z: QH = QH.q_1()
print("q_1: ", q_z)
assert q_z.t == 1
assert q_z.x == 0
assert q_z.y == 0
assert q_z.z == 0
def test_1460_rotate():
q_z = Q.rotate(QH([0, 1, 0, 0]))
print("rotate: ", q_z)
assert q_z.t == 1
assert q_z.x == -2
assert q_z.y == 3
assert q_z.z == 4
def test_1580_q_2_q():
assert Q.q_2_q(P).equals(
QH([
-0.0197219653530713,
-0.2613955437374326,
0.6496281248064009,
-0.3265786562423951,
]))
def test_1470_rotation_and_or_boost():
q1_sq = Q.square()
beta: float = 0.003
gamma = 1 / math.sqrt(1 - beta**2)
h = QH([gamma, gamma * beta, 0, 0])
q_z = Q.rotation_and_or_boost(h)
q_z2 = q_z.square()
print("q1_sq: ", q1_sq)
print("boosted: ", q_z)
print("boosted squared: ", q_z2)
assert round(q_z2.t, 5) == round(q1_sq.t, 5)
def test_1304_rotation_and_or_boost():
q1_sq = Q_states.square()
beta = 0.003
gamma = 1 / math.sqrt(1 - beta**2)
h = QHStates([QH([gamma, gamma * beta, 0, 0])])
q_z = Q_states.rotation_and_or_boost(h)
q_z2 = q_z.square()
print("q1_sq: ", q1_sq)
print("boosted: ", q_z)
print("boosted squared: ", q_z2)
assert round(q_z2.qs[0].t, 5) == round(q1_sq.qs[0].t, 5)
def test_1550_tanh():
assert QH([0, 0, 0, 0]).tanh().equals(QH().q_0())
assert Q.tanh().equals(
QH([
1.0248695360556623,
0.1022956817887642,
0.1534435226831462,
0.2045913635775283,
]))
assert P.tanh().equals(QH([0, -2.7044120049972684, 2.0283090037479505, 0]))
assert R.tanh().equals(QH([0.9950547536867305, 0, 0, 0]))
assert C.tanh().equals(QH([1.0046823121902353, 0.0364233692474038, 0, 0]))
def test_1520_tan():
assert QH([0, 0, 0, 0]).tan().equals(QH().q_0())
assert Q.tan().equals(
QH([
0.0000382163172501,
-0.3713971716439372,
-0.5570957574659058,
-0.7427943432878743,
]))
assert P.tan().equals(QH([0, 0.7999273634100760, -0.5999455225575570, 0]))
assert R.tan().equals(QH([-0.1425465430742778, 0, 0, 0]))
assert C.tan().equals(QH([-0.0005079806234700, 1.0004385132020521, 0, 0]))
def test_1530_sinh():
assert QH([0, 0, 0, 0]).sinh().equals(QH().q_0())
assert Q.sinh().equals(
QH([
0.7323376060463428,
0.4482074499805421,
0.6723111749708131,
0.8964148999610841,
]))
assert P.sinh().equals(QH([0, -0.7671394197305108, 0.5753545647978831, 0]))
assert R.sinh().equals(QH([10.0178749274099026, 0, 0, 0]))
assert C.sinh().equals(QH([-2.3706741693520015, -2.8472390868488278, 0,
0]))
def test_1560_exp():
assert QH([0, 0, 0, 0]).exp().equals(QH().q_1())
assert Q.exp().equals(
QH([
1.6939227236832994,
0.7895596245415588,
1.1843394368123383,
1.5791192490831176,
]))
assert P.exp().equals(
QH([0.2836621854632263, -0.7671394197305108, 0.5753545647978831, 0]))
assert R.exp().equals(QH([20.0855369231876679, 0, 0, 0]))
assert C.exp().equals(QH([-4.8298093832693851, -5.5920560936409816, 0, 0]))
def test_1510_cos():
assert QH([0, 0, 0, 0]).cos().equals(QH().q_1())
assert Q.cos().equals(
QH([
58.9336461679439481,
34.0861836904655959,
51.1292755356983974,
68.1723673809311919,
]))
assert P.cos().equals(QH([74.2099485247878476, 0, 0, 0]))
assert R.cos().equals(QH([-0.9899924966004454, 0, 0, 0]))
assert C.cos().equals(
QH([-11.3642347064010600, -24.8146514856341867, 0, 0]))
def test_1540_cosh():
assert QH([0, 0, 0, 0]).cosh().equals(QH().q_1())
assert Q.cosh().equals(
QH([
0.9615851176369565,
0.3413521745610167,
0.5120282618415251,
0.6827043491220334,
]))
assert P.cosh().equals(QH([0.2836621854632263, 0, 0, 0]))
assert R.cosh().equals(QH([10.0676619957777653, 0, 0, 0]))
assert C.cosh().equals(QH([-2.4591352139173837, -2.7448170067921538, 0,
0]))
def test_1500_sin():
assert QH([0, 0, 0, 0]).sin().equals(QH().q_0())
assert Q.sin().equals(
QH([
91.7837157840346691,
-21.8864868530291758,
-32.8297302795437673,
-43.7729737060583517,
]))
assert P.sin().equals(QH([0, 59.3625684622310033, -44.5219263466732542,
0]))
assert R.sin().equals(QH([0.1411200080598672, 0, 0, 0]))
assert C.sin().equals(QH([24.8313058489463785, -11.3566127112181743, 0,
0]))
def test_1250_product_AOp4i():
AOp4i = A.product(Op4i)
print("A Op4i: ", AOp4i)
assert AOp4i.qs[0].equals(QH([0, 16, 0, 0]))
assert AOp4i.qs[1].equals(QH([-4, 0, 0, 0]))
def test_1210_product_OpB():
OpB: QHStates = Op.product(B)
print("Op B: ", OpB)
assert OpB.qs[0].equals(QH([0, 10, 3, 0]))
assert OpB.qs[1].equals(QH([-18, 0, 0, 1]))
def test_1230_product_AOpB():
AOpB = A.product(Op).product(B)
print("A Op B: ", AOpB)
assert AOpB.equals(QHStates([QH([0, 22, 11, 0])]))
def test_1150_product_AA():
Aket = deepcopy(A).ket()
AA = A.product(Aket)
print("<A|A>: ", AA)
assert AA.equals(QHStates([QH([17, 0, 0, 0])]))
def test_1170_product_AOp():
AOp: QHStates = A.product(Op)
print("A Op: ", AOp)
assert AOp.qs[0].equals(QH([11, 0, 0, 0]))
assert AOp.qs[1].equals(QH([0, 0, 5, 0]))
assert AOp.qs[2].equals(QH([4, 0, 0, 0]))
def test_1140_product():
assert b.product(o).equals(
QHStates([QH([10, 0, 0, 0]),
QH([20, 0, 0, 0]),
QH([30, 0, 0, 0])]))
assert b.product(k).equals(QHStates([QH([32, 0, 0, 0])]))
assert b.product(o).product(k).equals(QHStates([QH([320, 0, 0, 0])]))
assert b.product(b).equals(
QHStates([QH([1, 0, 0, 0]),
QH([4, 0, 0, 0]),
QH([9, 0, 0, 0])]))
assert o.product(k).equals(
QHStates([QH([40, 0, 0, 0]),
QH([50, 0, 0, 0]),
QH([60, 0, 0, 0])]))
assert o.product(o).equals(QHStates([QH([100, 0, 0, 0])]))
assert k.product(k).equals(
QHStates([QH([16, 0, 0, 0]),
QH([25, 0, 0, 0]),
QH([36, 0, 0, 0])]))
assert k.product(b).equals(
QHStates([
QH([4, 0, 0, 0]),
QH([5, 0, 0, 0]),
QH([6, 0, 0, 0]),
QH([8, 0, 0, 0]),
QH([10, 0, 0, 0]),
QH([12, 0, 0, 0]),
QH([12, 0, 0, 0]),
QH([15, 0, 0, 0]),
QH([18, 0, 0, 0]),
]))
def test_1010_subs():
q_z = q_sym.subs({t: 1, x: 2, y: 3, z: 4})
print("t x y xyz sub 1 2 3 4: ", q_z)
assert q_z.equals(QH([1, 2, 3, 24]))
def test_txyz_2_representation():
qr = QH(Q12.txyz_2_representation(""))
assert qr.equals(Q12)
qr = QH(Q12.txyz_2_representation("polar"))
assert qr.equals(QH([2.23606797749979, 1.10714871779409, 0, 0]))
qr = QH(Q1123.txyz_2_representation("spherical"))
assert qr.equals(
QH([1.0, 3.7416573867739413, 0.640522312679424, 1.10714871779409]))
def test_1270_product_Op4iB():
Op4iB = Op4i.product(B)
print("Op4i B: ", Op4iB)
assert Op4iB.qs[0].equals(QH([0, 6, 0, 4]))
assert Op4iB.qs[1].equals(QH([0, 9, -8, 0]))
def test_representation_2_txyz():
qr = QH(Q12.representation_2_txyz(""))
assert qr.equals(Q12)
qr = QH(Q12.representation_2_txyz("polar"))
assert qr.equals(QH([-0.4161468365471424, 0.9092974268256817, 0, 0]))
qr = QH(Q1123.representation_2_txyz("spherical"))
assert qr.equals(
QH([
1.0,
-0.9001976297355174,
0.12832006020245673,
-0.4161468365471424,
]))
def test_1290_product_AOp4iB():
AOp4iB = A.product(Op4i).product(B)
print("A* Op4i B: ", AOp4iB)
assert AOp4iB.equals(QHStates([QH([-9, 24, 0, 8])]))
def test_1120_diagonal():
Op4iDiag2 = Op_scalar.diagonal(2)
print("Op4i on a diagonal 2x2", Op4iDiag2)
assert Op4iDiag2.qs[0].equals(q_i4)
assert Op4iDiag2.qs[1].equals(QH().q_0())