def test_sympy__physics__quantum__spin__JzBraCoupled():
from sympy.physics.quantum.spin import JzBraCoupled
assert _test_args(JzBraCoupled(0, 1))
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')))")
def test_spin():
lz = JzOp('L')
ket = JzKet(1, 0)
bra = JzBra(1, 0)
cket = JzKetCoupled(1, 0, (1, 2))
cbra = JzBraCoupled(1, 0, (1, 2))
cket_big = JzKetCoupled(1, 0, (1, 2, 3))
cbra_big = JzBraCoupled(1, 0, (1, 2, 3))
rot = Rotation(1, 2, 3)
bigd = WignerD(1, 2, 3, 4, 5, 6)
smalld = WignerD(1, 2, 3, 0, 4, 0)
assert str(lz) == 'Lz'
ascii_str = \
"""\
L \n\
z\
"""
ucode_str = \
u"""\
L \n\
z\
"""
assert pretty(lz) == ascii_str
assert upretty(lz) == ucode_str
assert latex(lz) == 'L_z'
sT(lz, "JzOp(Symbol('L'))")
assert str(J2) == 'J2'
ascii_str = \
"""\
2\n\
J \
"""
ucode_str = \
u"""\
2\n\
J \
"""
assert pretty(J2) == ascii_str
assert upretty(J2) == ucode_str
assert latex(J2) == r'J^2'
sT(J2, "J2Op(Symbol('J'))")
assert str(Jz) == 'Jz'
ascii_str = \
"""\
J \n\
z\
"""
ucode_str = \
u"""\
J \n\
z\
"""
assert pretty(Jz) == ascii_str
assert upretty(Jz) == ucode_str
assert latex(Jz) == 'J_z'
sT(Jz, "JzOp(Symbol('J'))")
assert str(ket) == '|1,0>'
assert pretty(ket) == '|1,0>'
assert upretty(ket) == u'❘1,0⟩'
assert latex(ket) == r'{\left|1,0\right\rangle }'
sT(ket, "JzKet(Integer(1),Integer(0))")
assert str(bra) == '<1,0|'
assert pretty(bra) == '<1,0|'
assert upretty(bra) == u'⟨1,0❘'
assert latex(bra) == r'{\left\langle 1,0\right|}'
sT(bra, "JzBra(Integer(1),Integer(0))")
assert str(cket) == '|1,0,j1=1,j2=2>'
assert pretty(cket) == '|1,0,j1=1,j2=2>'
assert upretty(cket) == u'❘1,0,j₁=1,j₂=2⟩'
assert latex(cket) == r'{\left|1,0,j_{1}=1,j_{2}=2\right\rangle }'
sT(
cket,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))"
)
assert str(cbra) == '<1,0,j1=1,j2=2|'
assert pretty(cbra) == '<1,0,j1=1,j2=2|'
assert upretty(cbra) == u'⟨1,0,j₁=1,j₂=2❘'
assert latex(cbra) == r'{\left\langle 1,0,j_{1}=1,j_{2}=2\right|}'
sT(
cbra,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))"
)
assert str(cket_big) == '|1,0,j1=1,j2=2,j3=3,j(1,2)=3>'
# TODO: Fix non-unicode pretty printing
# i.e. j1,2 -> j(1,2)
assert pretty(cket_big) == '|1,0,j1=1,j2=2,j3=3,j1,2=3>'
assert upretty(cket_big) == u'❘1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3⟩'
assert latex(cket_big) == \
r'{\left|1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right\rangle }'
sT(
cket_big,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))"
)
assert str(cbra_big) == '<1,0,j1=1,j2=2,j3=3,j(1,2)=3|'
assert pretty(cbra_big) == u'<1,0,j1=1,j2=2,j3=3,j1,2=3|'
assert upretty(cbra_big) == u'⟨1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3❘'
assert latex(cbra_big) == \
r'{\left\langle 1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right|}'
sT(
cbra_big,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))"
)
assert str(rot) == 'R(1,2,3)'
assert pretty(rot) == 'R (1,2,3)'
assert upretty(rot) == u'ℛ (1,2,3)'
assert latex(rot) == r'\mathcal{R}\left(1,2,3\right)'
sT(rot, "Rotation(Integer(1),Integer(2),Integer(3))")
assert str(bigd) == 'WignerD(1, 2, 3, 4, 5, 6)'
ascii_str = \
"""\
1 \n\
D (4,5,6)\n\
2,3 \
"""
ucode_str = \
u"""\
1 \n\
D (4,5,6)\n\
2,3 \
"""
assert pretty(bigd) == ascii_str
assert upretty(bigd) == ucode_str
assert latex(bigd) == r'D^{1}_{2,3}\left(4,5,6\right)'
sT(
bigd,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))"
)
assert str(smalld) == 'WignerD(1, 2, 3, 0, 4, 0)'
ascii_str = \
"""\
1 \n\
d (4)\n\
2,3 \
"""
ucode_str = \
u"""\
1 \n\
d (4)\n\
2,3 \
"""
assert pretty(smalld) == ascii_str
assert upretty(smalld) == ucode_str
assert latex(smalld) == r'd^{1}_{2,3}\left(4\right)'
sT(
smalld,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(0), Integer(4), Integer(0))"
)
def test_spin():
lz = JzOp("L")
ket = JzKet(1, 0)
bra = JzBra(1, 0)
cket = JzKetCoupled(1, 0, (1, 2))
cbra = JzBraCoupled(1, 0, (1, 2))
cket_big = JzKetCoupled(1, 0, (1, 2, 3))
cbra_big = JzBraCoupled(1, 0, (1, 2, 3))
rot = Rotation(1, 2, 3)
bigd = WignerD(1, 2, 3, 4, 5, 6)
smalld = WignerD(1, 2, 3, 0, 4, 0)
assert str(lz) == "Lz"
ascii_str = """\
L \n\
z\
"""
ucode_str = u("""\
L \n\
z\
""")
assert pretty(lz) == ascii_str
assert upretty(lz) == ucode_str
assert latex(lz) == "L_z"
sT(lz, "JzOp(Symbol('L'))")
assert str(J2) == "J2"
ascii_str = """\
2\n\
J \
"""
ucode_str = u("""\
2\n\
J \
""")
assert pretty(J2) == ascii_str
assert upretty(J2) == ucode_str
assert latex(J2) == r"J^2"
sT(J2, "J2Op(Symbol('J'))")
assert str(Jz) == "Jz"
ascii_str = """\
J \n\
z\
"""
ucode_str = u("""\
J \n\
z\
""")
assert pretty(Jz) == ascii_str
assert upretty(Jz) == ucode_str
assert latex(Jz) == "J_z"
sT(Jz, "JzOp(Symbol('J'))")
assert str(ket) == "|1,0>"
assert pretty(ket) == "|1,0>"
assert upretty(ket) == u"❘1,0⟩"
assert latex(ket) == r"{\left|1,0\right\rangle }"
sT(ket, "JzKet(Integer(1),Integer(0))")
assert str(bra) == "<1,0|"
assert pretty(bra) == "<1,0|"
assert upretty(bra) == u"⟨1,0❘"
assert latex(bra) == r"{\left\langle 1,0\right|}"
sT(bra, "JzBra(Integer(1),Integer(0))")
assert str(cket) == "|1,0,j1=1,j2=2>"
assert pretty(cket) == "|1,0,j1=1,j2=2>"
assert upretty(cket) == u"❘1,0,j₁=1,j₂=2⟩"
assert latex(cket) == r"{\left|1,0,j_{1}=1,j_{2}=2\right\rangle }"
sT(
cket,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))",
)
assert str(cbra) == "<1,0,j1=1,j2=2|"
assert pretty(cbra) == "<1,0,j1=1,j2=2|"
assert upretty(cbra) == u"⟨1,0,j₁=1,j₂=2❘"
assert latex(cbra) == r"{\left\langle 1,0,j_{1}=1,j_{2}=2\right|}"
sT(
cbra,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2)),Tuple(Tuple(Integer(1), Integer(2), Integer(1))))",
)
assert str(cket_big) == "|1,0,j1=1,j2=2,j3=3,j(1,2)=3>"
# TODO: Fix non-unicode pretty printing
# i.e. j1,2 -> j(1,2)
assert pretty(cket_big) == "|1,0,j1=1,j2=2,j3=3,j1,2=3>"
assert upretty(cket_big) == u"❘1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3⟩"
assert (latex(cket_big) ==
r"{\left|1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right\rangle }")
sT(
cket_big,
"JzKetCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))",
)
assert str(cbra_big) == "<1,0,j1=1,j2=2,j3=3,j(1,2)=3|"
assert pretty(cbra_big) == u"<1,0,j1=1,j2=2,j3=3,j1,2=3|"
assert upretty(cbra_big) == u"⟨1,0,j₁=1,j₂=2,j₃=3,j₁,₂=3❘"
assert (latex(cbra_big) ==
r"{\left\langle 1,0,j_{1}=1,j_{2}=2,j_{3}=3,j_{1,2}=3\right|}")
sT(
cbra_big,
"JzBraCoupled(Integer(1),Integer(0),Tuple(Integer(1), Integer(2), Integer(3)),Tuple(Tuple(Integer(1), Integer(2), Integer(3)), Tuple(Integer(1), Integer(3), Integer(1))))",
)
assert str(rot) == "R(1,2,3)"
assert pretty(rot) == "R (1,2,3)"
assert upretty(rot) == u"ℛ (1,2,3)"
assert latex(rot) == r"\mathcal{R}\left(1,2,3\right)"
sT(rot, "Rotation(Integer(1),Integer(2),Integer(3))")
assert str(bigd) == "WignerD(1, 2, 3, 4, 5, 6)"
ascii_str = """\
1 \n\
D (4,5,6)\n\
2,3 \
"""
ucode_str = u("""\
1 \n\
D (4,5,6)\n\
2,3 \
""")
assert pretty(bigd) == ascii_str
assert upretty(bigd) == ucode_str
assert latex(bigd) == r"D^{1}_{2,3}\left(4,5,6\right)"
sT(
bigd,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))",
)
assert str(smalld) == "WignerD(1, 2, 3, 0, 4, 0)"
ascii_str = """\
1 \n\
d (4)\n\
2,3 \
"""
ucode_str = u("""\
1 \n\
d (4)\n\
2,3 \
""")
assert pretty(smalld) == ascii_str
assert upretty(smalld) == ucode_str
assert latex(smalld) == r"d^{1}_{2,3}\left(4\right)"
sT(
smalld,
"WignerD(Integer(1), Integer(2), Integer(3), Integer(0), Integer(4), Integer(0))",
)