def test_probs():
d = Density([Ket(0), .75], [Ket(1), 0.25])
probs = d.probs()
assert probs[0] == 0.75 and probs[1] == 0.25
#probs can be symbols
x, y = symbols('x y')
d = Density([Ket(0), x], [Ket(1), y])
probs = d.probs()
assert probs[0] == x and probs[1] == y
def test_bra_ket_dagger():
x = symbols('x', complex=True)
k = Ket('k')
b = Bra('b')
assert Dagger(k) == Bra('k')
assert Dagger(b) == Ket('b')
assert Dagger(k).is_commutative == False
k2 = Ket('k2')
e = 2 * I * k + x * k2
assert Dagger(e) == conjugate(x) * Dagger(k2) - 2 * I * Dagger(k)
def test_bra_ket_dagger():
x = symbols("x", complex=True)
k = Ket("k")
b = Bra("b")
assert Dagger(k) == Bra("k")
assert Dagger(b) == Ket("b")
assert Dagger(k).is_commutative is False
k2 = Ket("k2")
e = 2 * I * k + x * k2
assert Dagger(e) == conjugate(x) * Dagger(k2) - 2 * I * Dagger(k)
def test_outer_product():
k = Ket('k')
b = Bra('b')
op = OuterProduct(k, b)
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = k*b
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = 2*k*b
assert op == Mul(Integer(2), k, b)
op = 2*(k*b)
assert op == Mul(Integer(2), OuterProduct(k, b))
assert Dagger(k*b) == OuterProduct(Dagger(b), Dagger(k))
assert Dagger(k*b).is_commutative is False
#test the _eval_trace
assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
# test scaled kets and bras
assert OuterProduct(2 * k, b) == 2 * OuterProduct(k, b)
assert OuterProduct(k, 2 * b) == 2 * OuterProduct(k, b)
# test sums of kets and bras
k1, k2 = Ket('k1'), Ket('k2')
b1, b2 = Bra('b1'), Bra('b2')
assert (OuterProduct(k1 + k2, b1) ==
OuterProduct(k1, b1) + OuterProduct(k2, b1))
assert (OuterProduct(k1, b1 + b2) ==
OuterProduct(k1, b1) + OuterProduct(k1, b2))
assert (OuterProduct(1 * k1 + 2 * k2, 3 * b1 + 4 * b2) ==
3 * OuterProduct(k1, b1) +
4 * OuterProduct(k1, b2) +
6 * OuterProduct(k2, b1) +
8 * OuterProduct(k2, b2))
def test_eval_args():
# check instance created
assert isinstance(Density([Ket(0), 0.5], [Ket(1), 0.5]), Density)
assert isinstance(Density([Qubit('00'), 1/sqrt(2)],
[Qubit('11'), 1/sqrt(2)]), Density)
#test if Qubit object type preserved
d = Density([Qubit('00'), 1/sqrt(2)], [Qubit('11'), 1/sqrt(2)])
for (state, prob) in d.args:
assert isinstance(state, Qubit)
# check for value error, when prob is not provided
raises(ValueError, lambda: Density([Ket(0)], [Ket(1)]))
def test_outer_product():
k = Ket('k')
b = Bra('b')
op = OuterProduct(k, b)
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative == False
op = k * b
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative == False
op = 2 * k * b
assert op == Mul(Integer(2), k, b)
op = 2 * (k * b)
assert op == Mul(Integer(2), OuterProduct(k, b))
assert Dagger(k * b) == OuterProduct(Dagger(b), Dagger(k))
assert Dagger(k * b).is_commutative == False
def test_bra():
b = Bra('0')
assert isinstance(b, Bra)
assert isinstance(b, BraBase)
assert isinstance(b, StateBase)
assert isinstance(b, QExpr)
assert b.label == (Symbol('0'), )
assert b.hilbert_space == HilbertSpace()
assert b.is_commutative is False
# Make sure this doesn't get converted to the number pi.
b = Bra('pi')
assert b.label == (Symbol('pi'), )
b = Bra(x, y)
assert b.label == (x, y)
assert b.hilbert_space == HilbertSpace()
assert b.is_commutative is False
assert b.dual_class() == Ket
assert b.dual == Ket(x, y)
assert b.subs(x, y) == Bra(y, y)
assert Bra() == Bra('psi')
def test_operator():
a = Operator('A')
b = Operator('B', Symbol('t'), S(1) / 2)
inv = a.inv()
f = Function('f')
x = symbols('x')
d = DifferentialOperator(Derivative(f(x), x), f(x))
op = OuterProduct(Ket(), Bra())
assert str(a) == 'A'
assert pretty(a) == 'A'
assert upretty(a) == u'A'
assert latex(a) == 'A'
sT(a, "Operator(Symbol('A'))")
assert str(inv) == 'A**(-1)'
ascii_str = \
"""\
-1\n\
A \
"""
ucode_str = \
u"""\
-1\n\
A \
"""
assert pretty(inv) == ascii_str
assert upretty(inv) == ucode_str
assert latex(inv) == r'\left(A\right)^{-1}'
sT(inv, "Pow(Operator(Symbol('A')), Integer(-1))")
assert str(d) == 'DifferentialOperator(Derivative(f(x), x),f(x))'
ascii_str = \
"""\
/d \\\n\
DifferentialOperator|--(f(x)),f(x)|\n\
\dx /\
"""
ucode_str = \
u"""\
⎛d ⎞\n\
DifferentialOperator⎜──(f(x)),f(x)⎟\n\
⎝dx ⎠\
"""
assert pretty(d) == ascii_str
assert upretty(d) == ucode_str
assert latex(d) == \
r'DifferentialOperator\left(\frac{\partial}{\partial x} \operatorname{f}{\left (x \right )},\operatorname{f}{\left (x \right )}\right)'
sT(
d,
"DifferentialOperator(Derivative(Function('f')(Symbol('x')), Symbol('x')),Function('f')(Symbol('x')))"
)
assert str(b) == 'Operator(B,t,1/2)'
assert pretty(b) == 'Operator(B,t,1/2)'
assert upretty(b) == u'Operator(B,t,1/2)'
assert latex(b) == r'Operator\left(B,t,\frac{1}{2}\right)'
sT(b, "Operator(Symbol('B'),Symbol('t'),Rational(1, 2))")
assert str(op) == '|psi><psi|'
assert pretty(op) == '|psi><psi|'
assert upretty(op) == u'❘ψ⟩⟨ψ❘'
assert latex(op) == r'{\left|\psi\right\rangle }{\left\langle \psi\right|}'
sT(op, "OuterProduct(Ket(Symbol('psi')),Bra(Symbol('psi')))")
def test_ket():
k = Ket('0')
assert isinstance(k, Ket)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Symbol('0'),)
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative is False
# Make sure this doesn't get converted to the number pi.
k = Ket('pi')
assert k.label == (Symbol('pi'),)
k = Ket(x, y)
assert k.label == (x, y)
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative is False
assert k.dual_class() == Bra
assert k.dual == Bra(x, y)
assert k.subs(x, y) == Ket(y, y)
k = CustomKet()
assert k == CustomKet("test")
k = CustomKetMultipleLabels()
assert k == CustomKetMultipleLabels("r", "theta", "phi")
assert Ket() == Ket('psi')
def test_operator():
a = Operator("A")
b = Operator("B", Symbol("t"), S.Half)
inv = a.inv()
f = Function("f")
x = symbols("x")
d = DifferentialOperator(Derivative(f(x), x), f(x))
op = OuterProduct(Ket(), Bra())
assert str(a) == "A"
assert pretty(a) == "A"
assert upretty(a) == u"A"
assert latex(a) == "A"
sT(a, "Operator(Symbol('A'))")
assert str(inv) == "A**(-1)"
ascii_str = """\
-1\n\
A \
"""
ucode_str = u("""\
-1\n\
A \
""")
assert pretty(inv) == ascii_str
assert upretty(inv) == ucode_str
assert latex(inv) == r"A^{-1}"
sT(inv, "Pow(Operator(Symbol('A')), Integer(-1))")
assert str(d) == "DifferentialOperator(Derivative(f(x), x),f(x))"
ascii_str = """\
/d \\\n\
DifferentialOperator|--(f(x)),f(x)|\n\
\\dx /\
"""
ucode_str = u("""\
⎛d ⎞\n\
DifferentialOperator⎜──(f(x)),f(x)⎟\n\
⎝dx ⎠\
""")
assert pretty(d) == ascii_str
assert upretty(d) == ucode_str
assert (
latex(d) ==
r"DifferentialOperator\left(\frac{d}{d x} f{\left(x \right)},f{\left(x \right)}\right)"
)
sT(
d,
"DifferentialOperator(Derivative(Function('f')(Symbol('x')), Tuple(Symbol('x'), Integer(1))),Function('f')(Symbol('x')))",
)
assert str(b) == "Operator(B,t,1/2)"
assert pretty(b) == "Operator(B,t,1/2)"
assert upretty(b) == u"Operator(B,t,1/2)"
assert latex(b) == r"Operator\left(B,t,\frac{1}{2}\right)"
sT(b, "Operator(Symbol('B'),Symbol('t'),Rational(1, 2))")
assert str(op) == "|psi><psi|"
assert pretty(op) == "|psi><psi|"
assert upretty(op) == u"❘ψ⟩⟨ψ❘"
assert latex(op) == r"{\left|\psi\right\rangle }{\left\langle \psi\right|}"
sT(op, "OuterProduct(Ket(Symbol('psi')),Bra(Symbol('psi')))")
def test_op_to_state():
assert operators_to_state(XOp) == XKet()
assert operators_to_state(PxOp) == PxKet()
assert operators_to_state(Operator) == Ket()
assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
assert state_to_operators(operators_to_state(XOp())) == XOp()
raises(NotImplementedError, lambda: operators_to_state(XKet))
def test_innerproduct():
k = Ket('k')
b = Bra('b')
ip = InnerProduct(b, k)
assert isinstance(ip, InnerProduct)
assert ip.bra == b
assert ip.ket == k
assert b*k == InnerProduct(b, k)
assert k*(b*k)*b == k*InnerProduct(b, k)*b
assert InnerProduct(b, k).subs(b, Dagger(k)) == Dagger(k)*k
def test_ket():
k = Ket('0')
assert isinstance(k, Ket)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Symbol('0'),)
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative == False
# Make sure this doesn't get converted to the number pi.
k = Ket('pi')
assert k.label == (Symbol('pi'),)
k = Ket(x,y)
assert k.label == (x,y)
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative == False
assert k.dual_class == Bra
assert k.dual == Bra(x,y)
assert k.subs(x,y) == Ket(y,y)
def test_op_to_state():
assert operators_to_state(XOp) == XKet()
assert operators_to_state(PxOp) == PxKet()
assert operators_to_state(Operator) == Ket()
assert operators_to_state(set([J2Op, JxOp])) == JxKet()
assert operators_to_state(set([J2Op, JyOp])) == JyKet()
assert operators_to_state(set([J2Op, JzOp])) == JzKet()
assert operators_to_state(set([J2Op(), JxOp()])) == JxKet()
assert operators_to_state(set([J2Op(), JyOp()])) == JyKet()
assert operators_to_state(set([J2Op(), JzOp()])) == JzKet()
assert state_to_operators(operators_to_state(XOp("Q"))) == XOp("Q")
assert state_to_operators(operators_to_state(XOp())) == XOp()
raises(NotImplementedError, 'operators_to_state(XKet)')
def convert_atom(atom):
if atom.LETTER():
subscriptName = ''
if atom.subexpr():
subscript = None
if atom.subexpr().expr(): # subscript is expr
subscript = convert_expr(atom.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(atom.subexpr().atom())
subscriptName = '_{' + StrPrinter().doprint(subscript) + '}'
return sympy.Symbol(atom.LETTER().getText() + subscriptName)
elif atom.SYMBOL():
s = atom.SYMBOL().getText()[1:]
if s == "infty":
return sympy.oo
else:
if atom.subexpr():
subscript = None
if atom.subexpr().expr(): # subscript is expr
subscript = convert_expr(atom.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(atom.subexpr().atom())
subscriptName = StrPrinter().doprint(subscript)
s += '_{' + subscriptName + '}'
return sympy.Symbol(s)
elif atom.NUMBER():
s = atom.NUMBER().getText().replace(",", "")
return sympy.Number(s)
elif atom.DIFFERENTIAL():
var = get_differential_var(atom.DIFFERENTIAL())
return sympy.Symbol('d' + var.name)
elif atom.mathit():
text = rule2text(atom.mathit().mathit_text())
return sympy.Symbol(text)
elif atom.frac():
return convert_frac(atom.frac())
elif atom.binom():
return convert_binom(atom.binom())
elif atom.bra():
val = convert_expr(atom.bra().expr())
return Bra(val)
elif atom.ket():
val = convert_expr(atom.ket().expr())
return Ket(val)
def test_ket():
k = Ket('0')
assert isinstance(k, Ket)
assert isinstance(k, KetBase)
assert isinstance(k, StateBase)
assert isinstance(k, QExpr)
assert k.label == (Symbol('0'), )
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative == False
# Make sure this doesn't get converted to the number pi.
k = Ket('pi')
assert k.label == (Symbol('pi'), )
k = Ket(x, y)
assert k.label == (x, y)
assert k.hilbert_space == HilbertSpace()
assert k.is_commutative == False
assert k.dual_class == Bra
assert k.dual == Bra(x, y)
assert k.subs(x, y) == Ket(y, y)
def test_outer_product():
k = Ket('k')
b = Bra('b')
op = OuterProduct(k, b)
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = k * b
assert isinstance(op, OuterProduct)
assert isinstance(op, Operator)
assert op.ket == k
assert op.bra == b
assert op.label == (k, b)
assert op.is_commutative is False
op = 2 * k * b
assert op == Mul(Integer(2), k, b)
op = 2 * (k * b)
assert op == Mul(Integer(2), OuterProduct(k, b))
assert Dagger(k * b) == OuterProduct(Dagger(b), Dagger(k))
assert Dagger(k * b).is_commutative is False
#test the _eval_trace
assert Tr(OuterProduct(JzKet(1, 1), JzBra(1, 1))).doit() == 1
def test_get_prob():
x, y = symbols('x y')
d = Density([Ket(0), x], [Ket(1), y])
probs = (d.get_prob(0), d.get_prob(1))
assert probs[0] == x and probs[1] == y
def test_get_state():
x, y = symbols('x y')
d = Density([Ket(0), x], [Ket(1), y])
states = (d.get_state(0), d.get_state(1))
assert states[0] == Ket(0) and states[1] == Ket(1)
def test_states():
d = Density([Ket(0), 0.5], [Ket(1), 0.5])
states = d.states()
assert states[0] == Ket(0) and states[1] == Ket(1)
def test_apply_op():
d = Density([Ket(0), 0.5], [Ket(1), 0.5])
assert d.apply_op(XOp()) == Density([XOp() * Ket(0), 0.5],
[XOp() * Ket(1), 0.5])
def test_sympy__physics__quantum__state__Ket():
from sympy.physics.quantum.state import Ket
assert _test_args(Ket(0))
f5 = 1 / 2 * acom(com(U11, U10), com(U11, U00)) + 1 / 2 * acom(
com(U11, U10), com(U01, U10))
f6 = com(U11, U10)**2
sumf = f1 + f2 + f3 + f4 + f5 + f6
combUpsi0 = U11 * U00 * U10 * U00 - U01 * U10 * U10 * U00 - U11 * U00 * U00 * U10 + U01 * U10 * U00 * U10 + U10 * U00 * U10 * U00 - U00 * U10 * U10 * U00 - U10 * U00 * U00 * U10 + U00 * U10 * U00 * U10 + U10 * U00 * U11 * U00 - U00 * U10 * U11 * U00 - U10 * U00 * U01 * U10 + U00 * U10 * U01 * U10 + U10 * U01 * U10 * U00 - U00 * U11 * U10 * U00 - U10 * U01 * U00 * U10 + U00 * U11 * U00 * U10 + U10 * U00 * U10 * U01 - U00 * U10 * U10 * U01 - U10 * U00 * U00 * U11 + U00 * U10 * U00 * U11 + U11 * U01 * U10 * U00 - U01 * U11 * U10 * U00 - U11 * U01 * U00 * U10 + U01 * U11 * U00 * U10 + U10 * U00 * U11 * U01 - U00 * U10 * U11 * U01 - U10 * U00 * U01 * U11 + U00 * U10 * U01 * U11 + U10 * U01 * U10 * U01 - U00 * U11 * U10 * U01 - U10 * U01 * U00 * U11 + U00 * U11 * U00 * U11 + U11 * U00 * U11 * U00 - U01 * U10 * U11 * U00 - U11 * U00 * U01 * U10 + U01 * U10 * U01 * U10 + U11 * U00 * U10 * U01 - U01 * U10 * U10 * U01 - U11 * U00 * U00 * U11 + U01 * U10 * U00 * U11 + U10 * U01 * U11 * U00 - U00 * U11 * U11 * U00 - U10 * U01 * U01 * U10 + U00 * U11 * U01 * U10 + U10 * U01 * U11 * U01 - U00 * U11 * U11 * U01 - U10 * U01 * U01 * U11 + U00 * U11 * U01 * U11 + U11 * U00 * U11 * U01 - U01 * U10 * U11 * U01 - U11 * U00 * U01 * U11 + U01 * U10 * U01 * U11 + U11 * U01 * U10 * U01 - U01 * U11 * U10 * U01 - U11 * U01 * U00 * U11 + U01 * U11 * U00 * U11 + U11 * U01 * U11 * U00 - U01 * U11 * U11 * U00 - U11 * U01 * U01 * U10 + U01 * U11 * U01 * U10 + U11 * U01 * U11 * U01 - U01 * U11 * U11 * U01 - U11 * U01 * U01 * U11 + U01 * U11 * U01 * U11
norm = 1 / 2 * Dagger(combUpsi0 * psi) * combUpsi0 * psi
mel = Dagger(sumf * psi) * (sumf * psi)
pprint("Numérateur : ")
pprint(mel[0])
print("")
pprint("Dénominateurs : ")
pprint(norm[0])
print("")
return mel[0] / norm[0]
a = Ket('0')
b = Ket('1')
#psi = Ket('ψ')
alpha, beta = symbols('α β')
psi0 = Matrix([[alpha], [beta]])
U = 1 / sqrt(2) * Matrix([[0, 0, 1, 1], [0, 0, 1, -1], [1, -1, 0, 0],
[-1, -1, 0, 0]])
pprint(proba(U, psi0))
def test_sympy__physics__quantum__innerproduct__InnerProduct():
from sympy.physics.quantum import Bra, Ket, InnerProduct
b = Bra('b')
k = Ket('k')
assert _test_args(InnerProduct(b, k))
def test_sympy__physics__quantum__dagger__Dagger():
from sympy.physics.quantum.dagger import Dagger
from sympy.physics.quantum.state import Ket
assert _test_args(Dagger(Dagger(Ket('psi'))))
def test_eval_args():
# check instance created
assert isinstance(Density([Ket(0), 0.5], [Ket(1), 0.5]), Density)
# check for value error, when prob is not provided
raises(ValueError, 'Density([Ket(0)], [Ket(1)])')
def test_innerproduct_dagger():
k = Ket('k')
b = Bra('b')
ip = b*k
assert Dagger(ip) == Dagger(k)*Dagger(b)
(r"1+1", _Add(1, 1)),
(r"0+1", _Add(0, 1)),
(r"1*2", _Mul(1, 2)),
(r"0*1", _Mul(0, 1)),
(r"x = y", Eq(x, y)),
(r"x \neq y", Ne(x, y)),
(r"x < y", Lt(x, y)),
(r"x > y", Gt(x, y)),
(r"x \leq y", Le(x, y)),
(r"x \geq y", Ge(x, y)),
(r"x \le y", Le(x, y)),
(r"x \ge y", Ge(x, y)),
(r"\lfloor x \rfloor", floor(x)),
(r"\lceil x \rceil", ceiling(x)),
(r"\langle x |", Bra('x')),
(r"| x \rangle", Ket('x')),
(r"\sin \theta", sin(theta)),
(r"\sin(\theta)", sin(theta)),
(r"\sin^{-1} a", asin(a)),
(r"\sin a \cos b", _Mul(sin(a), cos(b))),
(r"\sin \cos \theta", sin(cos(theta))),
(r"\sin(\cos \theta)", sin(cos(theta))),
(r"\frac{a}{b}", a / b),
(r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
(r"\frac{7}{3}", _Mul(7, _Pow(3, -1))),
(r"(\csc x)(\sec y)", csc(x) * sec(y)),
(r"\lim_{x \to 3} a", Limit(a, x, 3)),
(r"\lim_{x \rightarrow 3} a", Limit(a, x, 3)),
(r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3)),
(r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3)),
(r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3)),
def test_issue_6073():
x, y = symbols('x y', commutative=False)
A = Ket(x, y)
B = Operator('B')
assert qapply(A) == A
assert qapply(A.dual * B) == A.dual * B
def test_sympy__physics__quantum__operator__OuterProduct():
from sympy.physics.quantum.operator import OuterProduct
from sympy.physics.quantum import Ket, Bra
b = Bra('b')
k = Ket('k')
assert _test_args(OuterProduct(k, b))
def test_state():
x = symbols('x')
bra = Bra()
ket = Ket()
bra_tall = Bra(x / 2)
ket_tall = Ket(x / 2)
tbra = TimeDepBra()
tket = TimeDepKet()
assert str(bra) == '<psi|'
assert pretty(bra) == '<psi|'
assert upretty(bra) == u'⟨ψ❘'
assert latex(bra) == r'{\left\langle \psi\right|}'
sT(bra, "Bra(Symbol('psi'))")
assert str(ket) == '|psi>'
assert pretty(ket) == '|psi>'
assert upretty(ket) == u'❘ψ⟩'
assert latex(ket) == r'{\left|\psi\right\rangle }'
sT(ket, "Ket(Symbol('psi'))")
assert str(bra_tall) == '<x/2|'
ascii_str = \
"""\
/ |\n\
/ x|\n\
\\ -|\n\
\\2|\
"""
ucode_str = \
u"""\
╱ │\n\
╱ x│\n\
╲ ─│\n\
╲2│\
"""
assert pretty(bra_tall) == ascii_str
assert upretty(bra_tall) == ucode_str
assert latex(bra_tall) == r'{\left\langle \frac{1}{2} x\right|}'
sT(bra_tall, "Bra(Mul(Rational(1, 2), Symbol('x')))")
assert str(ket_tall) == '|x/2>'
ascii_str = \
"""\
| \\ \n\
|x \\\n\
|- /\n\
|2/ \
"""
ucode_str = \
u"""\
│ ╲ \n\
│x ╲\n\
│─ ╱\n\
│2╱ \
"""
assert pretty(ket_tall) == ascii_str
assert upretty(ket_tall) == ucode_str
assert latex(ket_tall) == r'{\left|\frac{1}{2} x\right\rangle }'
sT(ket_tall, "Ket(Mul(Rational(1, 2), Symbol('x')))")
assert str(tbra) == '<psi;t|'
assert pretty(tbra) == u'<psi;t|'
assert upretty(tbra) == u'⟨ψ;t❘'
assert latex(tbra) == r'{\left\langle \psi;t\right|}'
sT(tbra, "TimeDepBra(Symbol('psi'),Symbol('t'))")
assert str(tket) == '|psi;t>'
assert pretty(tket) == '|psi;t>'
assert upretty(tket) == u'❘ψ;t⟩'
assert latex(tket) == r'{\left|\psi;t\right\rangle }'
sT(tket, "TimeDepKet(Symbol('psi'),Symbol('t'))")
def test_innerproduct():
x = symbols('x')
ip1 = InnerProduct(Bra(), Ket())
ip2 = InnerProduct(TimeDepBra(), TimeDepKet())
ip3 = InnerProduct(JzBra(1, 1), JzKet(1, 1))
ip4 = InnerProduct(JzBraCoupled(1, 1, (1, 1)), JzKetCoupled(1, 1, (1, 1)))
ip_tall1 = InnerProduct(Bra(x / 2), Ket(x / 2))
ip_tall2 = InnerProduct(Bra(x), Ket(x / 2))
ip_tall3 = InnerProduct(Bra(x / 2), Ket(x))
assert str(ip1) == '<psi|psi>'
assert pretty(ip1) == '<psi|psi>'
assert upretty(ip1) == u'⟨ψ❘ψ⟩'
assert latex(
ip1) == r'\left\langle \psi \right. {\left|\psi\right\rangle }'
sT(ip1, "InnerProduct(Bra(Symbol('psi')),Ket(Symbol('psi')))")
assert str(ip2) == '<psi;t|psi;t>'
assert pretty(ip2) == '<psi;t|psi;t>'
assert upretty(ip2) == u'⟨ψ;t❘ψ;t⟩'
assert latex(ip2) == \
r'\left\langle \psi;t \right. {\left|\psi;t\right\rangle }'
sT(
ip2,
"InnerProduct(TimeDepBra(Symbol('psi'),Symbol('t')),TimeDepKet(Symbol('psi'),Symbol('t')))"
)
assert str(ip3) == "<1,1|1,1>"
assert pretty(ip3) == '<1,1|1,1>'
assert upretty(ip3) == u'⟨1,1❘1,1⟩'
assert latex(ip3) == r'\left\langle 1,1 \right. {\left|1,1\right\rangle }'
sT(
ip3,
"InnerProduct(JzBra(Integer(1),Integer(1)),JzKet(Integer(1),Integer(1)))"
)
assert str(ip4) == "<1,1,j1=1,j2=1|1,1,j1=1,j2=1>"
assert pretty(ip4) == '<1,1,j1=1,j2=1|1,1,j1=1,j2=1>'
assert upretty(ip4) == u'⟨1,1,j₁=1,j₂=1❘1,1,j₁=1,j₂=1⟩'
assert latex(ip4) == \
r'\left\langle 1,1,j_{1}=1,j_{2}=1 \right. {\left|1,1,j_{1}=1,j_{2}=1\right\rangle }'
sT(
ip4,
"InnerProduct(JzBraCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))),JzKetCoupled(Integer(1),Integer(1),Tuple(Integer(1), Integer(1)),Tuple(Tuple(Integer(1), Integer(2), Integer(1)))))"
)
assert str(ip_tall1) == '<x/2|x/2>'
ascii_str = \
"""\
/ | \\ \n\
/ x|x \\\n\
\\ -|- /\n\
\\2|2/ \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ x│x ╲\n\
╲ ─│─ ╱\n\
╲2│2╱ \
"""
assert pretty(ip_tall1) == ascii_str
assert upretty(ip_tall1) == ucode_str
assert latex(ip_tall1) == \
r'\left\langle \frac{1}{2} x \right. {\left|\frac{1}{2} x\right\rangle }'
sT(
ip_tall1,
"InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Mul(Rational(1, 2), Symbol('x'))))"
)
assert str(ip_tall2) == '<x|x/2>'
ascii_str = \
"""\
/ | \\ \n\
/ |x \\\n\
\\ x|- /\n\
\\ |2/ \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ │x ╲\n\
╲ x│─ ╱\n\
╲ │2╱ \
"""
assert pretty(ip_tall2) == ascii_str
assert upretty(ip_tall2) == ucode_str
assert latex(ip_tall2) == \
r'\left\langle x \right. {\left|\frac{1}{2} x\right\rangle }'
sT(ip_tall2,
"InnerProduct(Bra(Symbol('x')),Ket(Mul(Rational(1, 2), Symbol('x'))))")
assert str(ip_tall3) == '<x/2|x>'
ascii_str = \
"""\
/ | \\ \n\
/ x| \\\n\
\\ -|x /\n\
\\2| / \
"""
ucode_str = \
u"""\
╱ │ ╲ \n\
╱ x│ ╲\n\
╲ ─│x ╱\n\
╲2│ ╱ \
"""
assert pretty(ip_tall3) == ascii_str
assert upretty(ip_tall3) == ucode_str
assert latex(ip_tall3) == \
r'\left\langle \frac{1}{2} x \right. {\left|x\right\rangle }'
sT(ip_tall3,
"InnerProduct(Bra(Mul(Rational(1, 2), Symbol('x'))),Ket(Symbol('x')))")
