def _f_gen(l, lp, i2, i1, nu, lam2, lam1):
return Piecewise(
(0, (nu > l + lp) | (nu > lam1 + lam2) | ((lam1 > 2 * i2) &
(lam2 > 2 * i2))),
((sqrt(prod([2 * i + 1 for i in locals().values()])) *
(-1)**(lp + lam1 + lam2 + 1) * Wigner3j(l, 1, lp, -1, nu, 0) *
Wigner9j(i2, l, i1, i2, lp, i1, lam2, nu, lam1)), True))
def test_doit():
assert Wigner3j(1 / 2, -1 / 2, 1 / 2, 1 / 2, 0, 0).doit() == -sqrt(2) / 2
assert Wigner6j(1, 2, 3, 2, 1, 2).doit() == sqrt(21) / 105
assert Wigner9j(2, 1, 1,
S(3) / 2,
S(1) / 2, 1,
S(1) / 2,
S(1) / 2, 0).doit() == sqrt(2) / 12
assert CG(1 / 2, 1 / 2, 1 / 2, -1 / 2, 1, 0).doit() == sqrt(2) / 2
def test_doit():
assert (Wigner3j(S.Half, Rational(-1, 2), S.Half, S.Half, 0,
0).doit() == -sqrt(2) / 2)
assert Wigner6j(1, 2, 3, 2, 1, 2).doit() == sqrt(21) / 105
assert Wigner6j(3, 1, 2, 2, 2, 1).doit() == sqrt(21) / 105
assert (Wigner9j(2, 1, 1, Rational(3, 2), S.Half, 1, S.Half, S.Half,
0).doit() == sqrt(2) / 12)
assert CG(S.Half, S.Half, S.Half, Rational(-1, 2), 1,
0).doit() == sqrt(2) / 2
def test_cg():
cg = CG(1, 2, 3, 4, 5, 6)
wigner3j = Wigner3j(1, 2, 3, 4, 5, 6)
wigner6j = Wigner6j(1, 2, 3, 4, 5, 6)
wigner9j = Wigner9j(1, 2, 3, 4, 5, 6, 7, 8, 9)
assert str(cg) == 'CG(1, 2, 3, 4, 5, 6)'
ascii_str = \
"""\
5,6 \n\
C \n\
1,2,3,4\
"""
ucode_str = \
u"""\
5,6 \n\
C \n\
1,2,3,4\
"""
assert pretty(cg) == ascii_str
assert upretty(cg) == ucode_str
assert latex(cg) == r'C^{5,6}_{1,2,3,4}'
sT(
cg,
"CG(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))"
)
assert str(wigner3j) == 'Wigner3j(1, 2, 3, 4, 5, 6)'
ascii_str = \
"""\
/1 3 5\\\n\
| |\n\
\\2 4 6/\
"""
ucode_str = \
u"""\
⎛1 3 5⎞\n\
⎜ ⎟\n\
⎝2 4 6⎠\
"""
assert pretty(wigner3j) == ascii_str
assert upretty(wigner3j) == ucode_str
assert latex(wigner3j) == \
r'\left(\begin{array}{ccc} 1 & 3 & 5 \\ 2 & 4 & 6 \end{array}\right)'
sT(
wigner3j,
"Wigner3j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))"
)
assert str(wigner6j) == 'Wigner6j(1, 2, 3, 4, 5, 6)'
ascii_str = \
"""\
/1 2 3\\\n\
< >\n\
\\4 5 6/\
"""
ucode_str = \
u"""\
⎧1 2 3⎫\n\
⎨ ⎬\n\
⎩4 5 6⎭\
"""
assert pretty(wigner6j) == ascii_str
assert upretty(wigner6j) == ucode_str
assert latex(wigner6j) == \
r'\left\{\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}\right\}'
sT(
wigner6j,
"Wigner6j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6))"
)
assert str(wigner9j) == 'Wigner9j(1, 2, 3, 4, 5, 6, 7, 8, 9)'
ascii_str = \
"""\
/1 2 3\\\n\
| |\n\
<4 5 6>\n\
| |\n\
\\7 8 9/\
"""
ucode_str = \
u"""\
⎧1 2 3⎫\n\
⎪ ⎪\n\
⎨4 5 6⎬\n\
⎪ ⎪\n\
⎩7 8 9⎭\
"""
assert pretty(wigner9j) == ascii_str
assert upretty(wigner9j) == ucode_str
assert latex(wigner9j) == \
r'\left\{\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}\right\}'
sT(
wigner9j,
"Wigner9j(Integer(1), Integer(2), Integer(3), Integer(4), Integer(5), Integer(6), Integer(7), Integer(8), Integer(9))"
)