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_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 Wigner6j(3, 1, 2, 2, 2, 1).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 _f_5(l, lp, i2, i1, nu):
return Piecewise(
(((-1)**(i2 + i1 - 1) * sqrt(
(2 * l + 1) * (2 * lp + 1) * (2 * i1 + 1) * (2 * nu + 1)) *
Wigner3j(l, 1, lp, -1, nu, 0) * Wigner6j(l, lp, nu, i1, i1, i2)),
((l + lp >= nu) & (abs(l - lp) <= nu) & (lp + i1 >= i2) &
(abs(lp - i1) <= i2) & (l + i2 >= i1) & (abs(l - i2) <= i1) &
(abs(nu - i1) <= i1))), (0, True))
def _f_6(l, lp, i2, i1, lam2, lam1):
return Piecewise(
(((-1)**(i1 + i2 + l) * sqrt(
(2 * i1 + 1) * (2 * i2 + 1) *
(2 * lam1 + 1)) * Wigner6j(i1, i1, lam1, i2, i2, l)),
((l == lp) & (lam1 == lam2) & (i1 + i1 >= lam1) &
(abs(i1 - i1) <= lam1) & (i1 + i2 >= l) & (abs(i1 - i2) <= l) &
(i1 + l >= i2) & (abs(i1 - l) <= i2) & (abs(lam1 - i2) <= i2))),
(0, True))
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))"
)
