Testing Wigner from sympy

diff_wigners

1c1
< r"""
---
> """
3a4,5
> form http://pydoc.net/Python/sympy/0.7.1/sympy.physics.wigner/
> 
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< References
< ~~~~~~~~~~
---
> REFERENCES:
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< Credits and Copyright
< ~~~~~~~~~~~~~~~~~~~~~
< 
31d28
< 
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< from sympy import Integer, pi, sqrt, sympify
---
> from sympy import Integer, pi, sqrt
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< _Factlist = [1]
< 
---
> _Factlist=[1]
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<     Examples
<     ========
---
>     EXAMPLES::
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<     >>> from sympy.physics.wigner import wigner_3j
<     >>> wigner_3j(2, 6, 4, 0, 0, 0)
<     sqrt(715)/143
<     >>> wigner_3j(2, 6, 4, 0, 0, 1)
<     0
---
>         sage: wigner_3j(2, 6, 4, 0, 0, 0)
>         sqrt(5/143)
>         sage: wigner_3j(2, 6, 4, 0, 0, 1)
>         0
>         sage: wigner_3j(0.5, 0.5, 1, 0.5, -0.5, 0)
>         sqrt(1/6)
>         sage: wigner_3j(40, 100, 60, -10, 60, -50)
>         95608/18702538494885*sqrt(21082735836735314343364163310/220491455010479533763)
>         sage: wigner_3j(2500, 2500, 5000, 2488, 2400, -4888, prec=64)
>         7.60424456883448589e-12
183c183
<     maxfact = max(j_1 + j_2 + j_3 + 1, j_1 + abs(m_1), j_2 + abs(m_2),
---
>     maxfact = max(j_1 + j_2 + j_3 + 1, j_1 + abs(m_1), j_2 + abs(m_2), \
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<     _calc_factlist(int(maxfact))
---
>     _calc_factlist(maxfact)
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<     argsqrt = Integer(_Factlist[int(j_1 + j_2 - j_3)] *
<                      _Factlist[int(j_1 - j_2 + j_3)] *
<                      _Factlist[int(-j_1 + j_2 + j_3)] *
<                      _Factlist[int(j_1 - m_1)] *
<                      _Factlist[int(j_1 + m_1)] *
<                      _Factlist[int(j_2 - m_2)] *
<                      _Factlist[int(j_2 + m_2)] *
<                      _Factlist[int(j_3 - m_3)] *
<                      _Factlist[int(j_3 + m_3)]) / \
<         _Factlist[int(j_1 + j_2 + j_3 + 1)]
---
>     argsqrt = Integer(_Factlist[int(j_1 + j_2 - j_3)] * \
>                           _Factlist[int(j_1 - j_2 + j_3)] * \
>                           _Factlist[int(-j_1 + j_2 + j_3)] * \
>                           _Factlist[int(j_1 - m_1)] * \
>                           _Factlist[int(j_1 + m_1)] * \
>                           _Factlist[int(j_2 - m_2)] * \
>                           _Factlist[int(j_2 + m_2)] * \
>                           _Factlist[int(j_3 - m_3)] * \
>                           _Factlist[int(j_3 + m_3)]) / \
>                           _Factlist[int(j_1 + j_2 + j_3 + 1)]
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<     for ii in range(int(imin), int(imax) + 1):
---
>     for ii in range(imin, imax + 1):
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<         sqrt(3)/2
---
>         3**(1/2)/2
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<         -sqrt(2)/2
---
>         -2**(1/2)/2
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<     res = (-1) ** sympify(j_1 - j_2 + m_3) * sqrt(2 * j_3 + 1) * \
---
>     res = (-1) ** int(j_1 - j_2 + m_3) * sqrt(2 * j_3 + 1) * \
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<     argsqrt = Integer(_Factlist[int(aa + bb - cc)] *
<                      _Factlist[int(aa + cc - bb)] *
<                      _Factlist[int(bb + cc - aa)]) / \
<         Integer(_Factlist[int(aa + bb + cc + 1)])
---
>     argsqrt = Integer(_Factlist[int(aa + bb - cc)] * \
>                           _Factlist[int(aa + cc - bb)] * \
>                           _Factlist[int(bb + cc - aa)]) / \
>                           Integer(_Factlist[int(aa + bb + cc + 1)])
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<     Examples
<     ========
---
>     EXAMPLES::
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<     >>> from sympy.physics.wigner import racah
<     >>> racah(3,3,3,3,3,3)
<     -1/14
---
>         sage: racah(3,3,3,3,3,3)
>         -1/14
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<     maxfact = max(imax + 1, aa + bb + cc + dd, aa + dd + ee + ff,
<                  bb + cc + ee + ff)
---
>     maxfact = max(imax + 1, aa + bb + cc + dd, aa + dd + ee + ff, \
>                       bb + cc + ee + ff)
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<     Examples
<     ========
---
>     EXAMPLES::
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<     >>> from sympy.physics.wigner import wigner_6j
<     >>> wigner_6j(3,3,3,3,3,3)
<     -1/14
<     >>> wigner_6j(5,5,5,5,5,5)
<     1/52
---
>         sage: wigner_6j(3,3,3,3,3,3)
>         -1/14
>         sage: wigner_6j(5,5,5,5,5,5)
>         1/52
>         sage: wigner_6j(6,6,6,6,6,6)
>         309/10868
>         sage: wigner_6j(8,8,8,8,8,8)
>         -12219/965770
>         sage: wigner_6j(30,30,30,30,30,30)
>         36082186869033479581/87954851694828981714124
>         sage: wigner_6j(0.5,0.5,1,0.5,0.5,1)
>         1/6
>         sage: wigner_6j(200,200,200,200,200,200, prec=1000)*1.0
>         0.000155903212413242
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<     Examples
<     ========
---
>     EXAMPLES:
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<     >>> from sympy.physics.wigner import wigner_9j
<     >>> wigner_9j(1,1,1, 1,1,1, 1,1,0 ,prec=64) # ==1/18
<     0.05555555...
---
>     A couple of examples and test cases, note that for speed reasons a
>     precision is given::
> 
>         sage: wigner_9j(1,1,1, 1,1,1, 1,1,0 ,prec=64) # ==1/18
>         0.0555555555555555555
>         sage: wigner_9j(1,1,1, 1,1,1, 1,1,1)
>         0
>         sage: wigner_9j(1,1,1, 1,1,1, 1,1,2 ,prec=64) # ==1/18
>         0.0555555555555555556
>         sage: wigner_9j(1,2,1, 2,2,2, 1,2,1 ,prec=64) # ==-1/150
>         -0.00666666666666666667
>         sage: wigner_9j(3,3,2, 2,2,2, 3,3,2 ,prec=64) # ==157/14700
>         0.0106802721088435374
>         sage: wigner_9j(3,3,2, 3,3,2, 3,3,2 ,prec=64) # ==3221*sqrt(70)/(246960*sqrt(105)) - 365/(3528*sqrt(70)*sqrt(105))
>         0.00944247746651111739
>         sage: wigner_9j(3,3,1, 3.5,3.5,2, 3.5,3.5,1 ,prec=64) # ==3221*sqrt(70)/(246960*sqrt(105)) - 365/(3528*sqrt(70)*sqrt(105))
>         0.0110216678544351364
>         sage: wigner_9j(100,80,50, 50,100,70, 60,50,100 ,prec=1000)*1.0
>         1.05597798065761e-7
>         sage: wigner_9j(30,30,10, 30.5,30.5,20, 30.5,30.5,10 ,prec=1000)*1.0 # ==(80944680186359968990/95103769817469)*sqrt(1/682288158959699477295)
>         0.0000325841699408828
>         sage: wigner_9j(64,62.5,114.5, 61.5,61,112.5, 113.5,110.5,60, prec=1000)*1.0
>         -3.41407910055520e-39
>         sage: wigner_9j(15,15,15, 15,3,15, 15,18,10, prec=1000)*1.0
>         -0.0000778324615309539
>         sage: wigner_9j(1.5,1,1.5, 1,1,1, 1.5,1,1.5)
>         0
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<     Examples
<     ========
---
>     EXAMPLES::
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<     >>> from sympy.physics.wigner import gaunt
<     >>> gaunt(1,0,1,1,0,-1)
<     -1/(2*sqrt(pi))
<     >>> gaunt(1000,1000,1200,9,3,-12).n(64)
<     0.00689500421922113448...
---
>         sage: gaunt(1,0,1,1,0,-1)
>         -1/2/sqrt(pi)
>         sage: gaunt(1,0,1,1,0,0)
>         0
>         sage: gaunt(29,29,34,10,-5,-5)
>         1821867940156/215552371055153321*sqrt(22134)/sqrt(pi)
>         sage: gaunt(20,20,40,1,-1,0)
>         28384503878959800/74029560764440771/sqrt(pi)
>         sage: gaunt(12,15,5,2,3,-5)
>         91/124062*sqrt(36890)/sqrt(pi)
>         sage: gaunt(10,10,12,9,3,-12)
>         -98/62031*sqrt(6279)/sqrt(pi)
>         sage: gaunt(1000,1000,1200,9,3,-12).n(64)
>         0.00689500421922113448
625c662
<       `J = l_1 + l_2 + l_3 = 2n` for `n` in `\mathbb{N}`
---
>       `J=l_1+l_2+l_3=2n` for `n` in `\Bold{N}`
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<     prefac = Integer(_Factlist[bigL] * _Factlist[l_2 - l_1 + l_3] *
---
>     prefac = Integer(_Factlist[bigL] * _Factlist[l_2 - l_1 + l_3] * \
681,683c718,719
<         _Factlist[2 * bigL + 1]/ \
<         (_Factlist[bigL - l_1] *
<          _Factlist[bigL - l_2] * _Factlist[bigL - l_3])
---
>                      _Factlist[2 * bigL+1]/ \
>                      (_Factlist[bigL - l_1] * _Factlist[bigL - l_2] * _Factlist[bigL - l_3])
693c729
<     if prec is not None:
---
>     if prec != None:
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< 

test_wigner

In [1]: from sympy import S

In [2]: S
Out[2]: S

In [3]: S.
S.Catalan           S.EulerGamma        S.Half              S.Infinity          S.Naturals          S.NegativeOne       S.Reals
S.ComplexInfinity   S.Exp1              S.IdentityFunction  S.Integers          S.Naturals0         S.One               S.UniversalSet
S.EmptySet          S.GoldenRatio       S.ImaginaryUnit     S.NaN               S.NegativeInfinity  S.Pi                S.Zero

In [3]: from sympy.physics.wigner import clebsch_gordan

In [4]: clebsch_gordan(S(1)/2, S(1)/2, 1, S(1)/2, S(1)/2, 1)
Out[4]: 1

In [5]: clebsch_gordan(.5, .5, 1, .5, .5, 1, prec=None)
Out[5]: 1.00000000000000

Okay just narrowed it down. Importing S is unnecessary.

The error was coming because I was earlier importing the wigner file you gave me.