View source for 34.5

{{DISPLAYTITLE:3 j , 6 j , 9 j Symbols - 34.5 Basic Properties: <math>6j</math> Symbol}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/34.5.E1 34.5.E1] || <math qid="Q9741">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{0}{j_{3}}{j_{2}} = \frac{(-1)^{J}}{\left((2j_{2}+1)(2j_{3}+1)\right)^{\frac{1}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{0}{j_{3}}{j_{2}} = \frac{(-1)^{J}}{\left((2j_{2}+1)(2j_{3}+1)\right)^{\frac{1}{2}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {0, Subscript[j, 3], Subscript[j, 2]}] == Divide[(- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]),((2*Subscript[j, 2]+ 1)*(2*Subscript[j, 3]+ 1))^(Divide[1,2])]</syntaxhighlight> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[-1.3200489060811386*^-4, -0.0030849476982290776], Piecewise[{{Complex[-23.42903161903947, -30.25069364758892], Or[And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[0.8660254037844387, 0.<syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0012333518407666182, -2.9116132254363445*^-4], Piecewise[{{Complex[18.599052799749366, 155.48928543604504], Or[And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 0.0], Greater[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]]]}}, 0.0]]
Test Values: {Rule[Subscript[j, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/34.5.E2 34.5.E2] || <math qid="Q9742">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{\frac{1}{2}}{j_{3}-\frac{1}{2}}{j_{2}+\frac{1}{2}} = (-1)^{J}\left(\frac{(j_{1}+j_{3}-j_{2})(j_{1}+j_{2}-j_{3}+1)}{(2j_{2}+1)(2j_{2}+2)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{\frac{1}{2}}{j_{3}-\frac{1}{2}}{j_{2}+\frac{1}{2}} = (-1)^{J}\left(\frac{(j_{1}+j_{3}-j_{2})(j_{1}+j_{2}-j_{3}+1)}{(2j_{2}+1)(2j_{2}+2)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Divide[1,2], Subscript[j, 3]-Divide[1,2], Subscript[j, 2]+Divide[1,2]}] == (- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*(Divide[(Subscript[j, 1]+ Subscript[j, 3]- Subscript[j, 2])*(Subscript[j, 1]+ Subscript[j, 2]- Subscript[j, 3]+ 1),(2*Subscript[j, 2]+ 1)*(2*Subscript[j, 2]+ 2)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|- 
| [https://dlmf.nist.gov/34.5.E3 34.5.E3] || <math qid="Q9743">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{\frac{1}{2}}{j_{3}-\frac{1}{2}}{j_{2}-\frac{1}{2}} = (-1)^{J}\left(\frac{(j_{2}+j_{3}-j_{1})(j_{1}+j_{2}+j_{3}+1)}{2j_{2}(2j_{2}+1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{\frac{1}{2}}{j_{3}-\frac{1}{2}}{j_{2}-\frac{1}{2}} = (-1)^{J}\left(\frac{(j_{2}+j_{3}-j_{1})(j_{1}+j_{2}+j_{3}+1)}{2j_{2}(2j_{2}+1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Divide[1,2], Subscript[j, 3]-Divide[1,2], Subscript[j, 2]-Divide[1,2]}] == (- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*(Divide[(Subscript[j, 2]+ Subscript[j, 3]- Subscript[j, 1])*(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3]+ 1),2*Subscript[j, 2]*(2*Subscript[j, 2]+ 1)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|- 
| [https://dlmf.nist.gov/34.5.E4 34.5.E4] || <math qid="Q9744">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}-1} = (-1)^{J}\left(\frac{J(J+1)(J-2j_{1})(J-2j_{1}-1)}{(2j_{2}-1)2j_{2}(2j_{2}+1)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}-1} = (-1)^{J}\left(\frac{J(J+1)(J-2j_{1})(J-2j_{1}-1)}{(2j_{2}-1)2j_{2}(2j_{2}+1)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {1, Subscript[j, 3]- 1, Subscript[j, 2]- 1}] == (- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*(Divide[(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])+ 1)*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 1])*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 1]- 1),(2*Subscript[j, 2]- 1)*2*Subscript[j, 2]*(2*Subscript[j, 2]+ 1)*(2*Subscript[j, 3]- 1)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|- 
| [https://dlmf.nist.gov/34.5.E5 34.5.E5] || <math qid="Q9745">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}} = (-1)^{J}\left(\frac{2(J+1)(J-2j_{1})(J-2j_{2})(J-2j_{3}+1)}{2j_{2}(2j_{2}+1)(2j_{2}+2)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}} = (-1)^{J}\left(\frac{2(J+1)(J-2j_{1})(J-2j_{2})(J-2j_{3}+1)}{2j_{2}(2j_{2}+1)(2j_{2}+2)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {1, Subscript[j, 3]- 1, Subscript[j, 2]}] == (- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*(Divide[2*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])+ 1)*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 1])*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 2])*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 3]+ 1),2*Subscript[j, 2]*(2*Subscript[j, 2]+ 1)*(2*Subscript[j, 2]+ 2)*(2*Subscript[j, 3]- 1)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|- 
| [https://dlmf.nist.gov/34.5.E6 34.5.E6] || <math qid="Q9746">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}+1} = (-1)^{J}\left(\frac{(J-2j_{2}-1)(J-2j_{2})(J-2j_{3}+1)(J-2j_{3}+2)}{(2j_{2}+1)(2j_{2}+2)(2j_{2}+3)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}-1}{j_{2}+1} = (-1)^{J}\left(\frac{(J-2j_{2}-1)(J-2j_{2})(J-2j_{3}+1)(J-2j_{3}+2)}{(2j_{2}+1)(2j_{2}+2)(2j_{2}+3)(2j_{3}-1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {1, Subscript[j, 3]- 1, Subscript[j, 2]+ 1}] == (- 1)^(Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])*(Divide[((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 2]- 1)*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 2])*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 3]+ 1)*((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])- 2*Subscript[j, 3]+ 2),(2*Subscript[j, 2]+ 1)*(2*Subscript[j, 2]+ 2)*(2*Subscript[j, 2]+ 3)*(2*Subscript[j, 3]- 1)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
|- 
| [https://dlmf.nist.gov/34.5.E7 34.5.E7] || <math qid="Q9747">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}}{j_{2}} = (-1)^{J+1}\frac{2(j_{2}(j_{2}+1)+j_{3}(j_{3}+1)-j_{1}(j_{1}+1))}{\left(2j_{2}(2j_{2}+1)(2j_{2}+2)2j_{3}(2j_{3}+1)(2j_{3}+2)\right)^{\frac{1}{2}}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{1}{j_{3}}{j_{2}} = (-1)^{J+1}\frac{2(j_{2}(j_{2}+1)+j_{3}(j_{3}+1)-j_{1}(j_{1}+1))}{\left(2j_{2}(2j_{2}+1)(2j_{2}+2)2j_{3}(2j_{3}+1)(2j_{3}+2)\right)^{\frac{1}{2}}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {1, Subscript[j, 3], Subscript[j, 2]}] == (- 1)^((Subscript[j, 1]+ Subscript[j, 2]+ Subscript[j, 3])+ 1)*Divide[2*(Subscript[j, 2]*(Subscript[j, 2]+ 1)+ Subscript[j, 3]*(Subscript[j, 3]+ 1)- Subscript[j, 1]*(Subscript[j, 1]+ 1)),(2*Subscript[j, 2]*(2*Subscript[j, 2]+ 1)*(2*Subscript[j, 2]+ 2)*2*Subscript[j, 3]*(2*Subscript[j, 3]+ 1)*(2*Subscript[j, 3]+ 2))^(Divide[1,2])]</syntaxhighlight> || Missing Macro Error || Aborted || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[6.600244530405688*^-5, 0.0015424738491145388], Piecewise[{{Complex[11.71451580951971, 15.125346823794441], Or[And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Com<syntaxhighlight lang=mathematica>Result: Plus[Complex[2.6655716865160955*^-4, 3.69824455184698*^-4], Piecewise[{{Complex[-49.11676072361018, 27.586829738396876], Or[And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.36602540378443893, 1.3660254037844386]]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Or[And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]], And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0]]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 1.5], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Or[And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.36602540378443893, 1.3660254037844386]]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.36602540378443893, 1.3660254037844386]]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 1.5], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5]], And[Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 1.5], Inequality[Complex[2.220446049250313*^-16, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Or[And[Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.5], 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Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.1339745962155613, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.5], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.5], Inequality[1.5, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[2.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 3.0], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, 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And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Or[And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Greater[Complex[0.8660254037844387, 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LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.5], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.5], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Or[And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.5], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.5], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[1.0, Less, Complex[0.8660254037844387, 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0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 1.5], Inequality[Complex[-0.9999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.5], 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Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[1.5, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 2.0], Inequality[Complex[-0.9999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[1.5, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.9999999999999998, 0.8660254037844387]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 2.5], Inequality[Complex[-1.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 2.5], Inequality[Complex[-0.9999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0]], And[Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.5], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.9999999999999998, 0.8660254037844387]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[2.5, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 3.0], Inequality[Complex[-1.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Or[And[Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.5], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 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0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, 3.0], Inequality[Complex[-1.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 3.0], Inequality[Complex[-0.2499999999999999, 0.43301270189221935], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-1.4999999999999998, 0.8660254037844387]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 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Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-1.4999999999999998, 0.8660254037844387]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Greater[Complex[-0.4999999999999998, 0.8660254037844387], 4.0], Inequality[Complex[-0.2499999999999999, 0.43301270189221935], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-1.4999999999999998, 0.8660254037844387]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.2499999999999999, 0.43301270189221935]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.5], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.5], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[2.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 3.0], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Or[And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.5], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.5], Inequality[Complex[0.3660254037844387, 0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]]]], And[Inequality[2.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 3.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 3.0], Inequality[Complex[-0.1339745962155613, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.3660254037844387, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 4.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 4.0], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 4.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 4.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 4.0], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 4.0], Inequality[Complex[0.43301270189221935, 0.24999999999999997], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[0.8660254037844387, 0.49999999999999994]], Inequality[Complex[1.3660254037844384, -0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.16666666666666666], Inequality[Complex[0.1339745962155613, -0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.16666666666666666], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.6666666666666666], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.16666666666666666], Inequality[0.6666666666666666, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.8333333333333334], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.16666666666666666], Inequality[0.8333333333333334, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[0.1339745962155613, -0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.16666666666666666], Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.16666666666666666, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.75], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.16666666666666666, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[0.75, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.1339745962155613, -0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.16666666666666666, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.6666666666666666], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.16666666666666666, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[0.6666666666666666, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.16666666666666666, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[Complex[0.1339745962155613, -0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.8333333333333334], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.16666666666666666, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.25], Inequality[0.8333333333333334, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.25, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.5], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.25, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.5], Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.1339745962155613, -0.49999999999999994]], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.25, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.5], Inequality[Complex[0.1339745962155613, -0.49999999999999994], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.75], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.25, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.5], Inequality[0.75, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.5], Inequality[Complex[0.1339745962155613, -0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.75], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.75, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.75, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Or[And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 1.5], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.3660254037844388, 0.49999999999999994]]]]], And[Inequality[1.0, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.5], Inequality[2.0, LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[GreaterEqual[Complex[0.8660254037844387, 0.49999999999999994], 1.5], Inequality[Complex[1.3660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.5], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 0.75], Inequality[Complex[1.7320508075688774, 0.9999999999999999], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.5], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 0.75], Inequality[1.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[0.75, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[1.7320508075688774, 0.9999999999999999], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[2.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 1.0], Inequality[Complex[1.8660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, Complex[1.8660254037844388, 0.49999999999999994]], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[1.8660254037844388, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[0.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.43301270189221935, 0.24999999999999997]], Inequality[0.0, LessEqual, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, Complex[1.7320508075688774, 0.9999999999999999]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 1.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 1.0], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[0.5, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 1.0], Inequality[1.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], Less, 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], LessEqual, 2.0], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Inequality[1.0, Less, Complex[0.8660254037844387, 0.49999999999999994], LessEqual, 2.0], Inequality[2.0, Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]], And[Greater[Complex[0.8660254037844387, 0.49999999999999994], 2.0], Inequality[Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[-0.4999999999999998, 0.8660254037844387], Less, Complex[1.7320508075688774, 0.9999999999999999]], Inequality[Complex[-1.3660254037844384, 0.36602540378443876], LessEqual, Complex[0.8660254037844387, 0.49999999999999994], Less, Complex[0.8660254037844387, 0.49999999999999994]]]]}}, 0.0]]
Test Values: {Rule[Subscript[j, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[j, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/34.5.E8 34.5.E8] || <math qid="Q9748">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{j_{2}}{j_{1}}{j_{3}}{l_{2}}{l_{1}}{l_{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{j_{2}}{j_{1}}{j_{3}}{l_{2}}{l_{1}}{l_{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}] == SixJSymbol[{Subscript[j, 2], Subscript[j, 1], Subscript[j, 3]}, {Subscript[l, 2], Subscript[l, 1], Subscript[l, 3]}]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 300]
|- 
| [https://dlmf.nist.gov/34.5.E8 34.5.E8] || <math qid="Q9748">\Wignersixjsym{j_{2}}{j_{1}}{j_{3}}{l_{2}}{l_{1}}{l_{3}} = \Wignersixjsym{j_{1}}{l_{2}}{l_{3}}{l_{1}}{j_{2}}{j_{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{2}}{j_{1}}{j_{3}}{l_{2}}{l_{1}}{l_{3}} = \Wignersixjsym{j_{1}}{l_{2}}{l_{3}}{l_{1}}{j_{2}}{j_{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 2], Subscript[j, 1], Subscript[j, 3]}, {Subscript[l, 2], Subscript[l, 1], Subscript[l, 3]}] == SixJSymbol[{Subscript[j, 1], Subscript[l, 2], Subscript[l, 3]}, {Subscript[l, 1], Subscript[j, 2], Subscript[j, 3]}]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 300]
|- 
| [https://dlmf.nist.gov/34.5.E9 34.5.E9] || <math qid="Q9749">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{j_{1}}{\frac{1}{2}(j_{2}+l_{2}+j_{3}-l_{3})}{\frac{1}{2}(j_{2}-l_{2}+j_{3}+l_{3})}{l_{1}}{\frac{1}{2}(j_{2}+l_{2}-j_{3}+l_{3})}{\frac{1}{2}(-j_{2}+l_{2}+j_{3}+l_{3})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{j_{1}}{\frac{1}{2}(j_{2}+l_{2}+j_{3}-l_{3})}{\frac{1}{2}(j_{2}-l_{2}+j_{3}+l_{3})}{l_{1}}{\frac{1}{2}(j_{2}+l_{2}-j_{3}+l_{3})}{\frac{1}{2}(-j_{2}+l_{2}+j_{3}+l_{3})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}] == SixJSymbol[{Subscript[j, 1], Divide[1,2]*(Subscript[j, 2]+ Subscript[l, 2]+ Subscript[j, 3]- Subscript[l, 3]), Divide[1,2]*(Subscript[j, 2]- Subscript[l, 2]+ Subscript[j, 3]+ Subscript[l, 3])}, {Subscript[l, 1], Divide[1,2]*(Subscript[j, 2]+ Subscript[l, 2]- Subscript[j, 3]+ Subscript[l, 3]), Divide[1,2]*(- Subscript[j, 2]+ Subscript[l, 2]+ Subscript[j, 3]+ Subscript[l, 3])}]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 300]
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| [https://dlmf.nist.gov/34.5.E10 34.5.E10] || <math qid="Q9750">\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{\frac{1}{2}(j_{2}+l_{2}+j_{3}-l_{3})}{\frac{1}{2}(j_{1}-l_{1}+j_{3}+l_{3})}{\frac{1}{2}(j_{1}+l_{1}+j_{2}-l_{2})}{\frac{1}{2}(j_{2}+l_{2}-j_{3}+l_{3})}{\frac{1}{2}(-j_{1}+l_{1}+j_{3}+l_{3})}{\frac{1}{2}(j_{1}+l_{1}-j_{2}+l_{2})}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}} = \Wignersixjsym{\frac{1}{2}(j_{2}+l_{2}+j_{3}-l_{3})}{\frac{1}{2}(j_{1}-l_{1}+j_{3}+l_{3})}{\frac{1}{2}(j_{1}+l_{1}+j_{2}-l_{2})}{\frac{1}{2}(j_{2}+l_{2}-j_{3}+l_{3})}{\frac{1}{2}(-j_{1}+l_{1}+j_{3}+l_{3})}{\frac{1}{2}(j_{1}+l_{1}-j_{2}+l_{2})}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}] == SixJSymbol[{Divide[1,2]*(Subscript[j, 2]+ Subscript[l, 2]+ Subscript[j, 3]- Subscript[l, 3]), Divide[1,2]*(Subscript[j, 1]- Subscript[l, 1]+ Subscript[j, 3]+ Subscript[l, 3]), Divide[1,2]*(Subscript[j, 1]+ Subscript[l, 1]+ Subscript[j, 2]- Subscript[l, 2])}, {Divide[1,2]*(Subscript[j, 2]+ Subscript[l, 2]- Subscript[j, 3]+ Subscript[l, 3]), Divide[1,2]*(- Subscript[j, 1]+ Subscript[l, 1]+ Subscript[j, 3]+ Subscript[l, 3]), Divide[1,2]*(Subscript[j, 1]+ Subscript[l, 1]- Subscript[j, 2]+ Subscript[l, 2])}]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 300]
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| [https://dlmf.nist.gov/34.5.E11 34.5.E11] || <math qid="Q9751">{(2j_{1}+1)\left((J_{3}+J_{2}-J_{1})(L_{3}+L_{2}-J_{1})-2(J_{3}L_{3}+J_{2}L_{2}-J_{1}L_{1})\right)\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}}\\ = j_{1}E(j_{1}+1)\Wignersixjsym{j_{1}+1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}+(j_{1}+1)E(j_{1})\Wignersixjsym{j_{1}-1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>{(2j_{1}+1)\left((J_{3}+J_{2}-J_{1})(L_{3}+L_{2}-J_{1})-2(J_{3}L_{3}+J_{2}L_{2}-J_{1}L_{1})\right)\Wignersixjsym{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}}\\ = j_{1}E(j_{1}+1)\Wignersixjsym{j_{1}+1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}+(j_{1}+1)E(j_{1})\Wignersixjsym{j_{1}-1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(2*Subscript[j, 1]+ 1)*((Subscript[J, 3]+ Subscript[J, 2]- Subscript[J, 1])*(Subscript[L, 3]+ Subscript[L, 2]- Subscript[J, 1])- 2*(Subscript[J, 3]*Subscript[L, 3]+ Subscript[J, 2]*Subscript[L, 2]- Subscript[J, 1]*Subscript[L, 1]))*SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}] == Subscript[j, 1]*E[Subscript[j, 1]+ 1]* SixJSymbol[{Subscript[j, 1]+ 1, Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}]+(Subscript[j, 1]+ 1)*E[Subscript[j, 1]]* SixJSymbol[{Subscript[j, 1]- 1, Subscript[j, 2], Subscript[j, 3]}, {Subscript[l, 1], Subscript[l, 2], Subscript[l, 3]}]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"></div></div>
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| [https://dlmf.nist.gov/34.5.E19 34.5.E19] || <math qid="Q9760">\sum_{l}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{l}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = 0</syntaxhighlight> || <math>\mu = \min(j_{1}</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[SixJSymbol[{Subscript[j, 1], Subscript[j, 2], l}, {Subscript[j, 2], Subscript[j, 1], j}], {l, - Infinity, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/34.5.E20 34.5.E20] || <math qid="Q9761">\sum_{l}(-1)^{l+j}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{1}}{j_{2}}{j} = \frac{(-1)^{2\mu}}{2j+1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{l}(-1)^{l+j}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{1}}{j_{2}}{j} = \frac{(-1)^{2\mu}}{2j+1}</syntaxhighlight> || <math>\mu = \min(j_{1}</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(l + j)* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], l}, {Subscript[j, 1], Subscript[j, 2], j}], {l, - Infinity, Infinity}, GenerateConditions->None] == Divide[(- 1)^(2*\[Mu]),2*j + 1]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/34.5.E21 34.5.E21] || <math qid="Q9762">\sum_{l}(-1)^{l+j+j_{1}+j_{2}}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = \frac{1}{2j+1}\left(\frac{(2j_{1}-j)!(2j_{2}+j+1)!}{(2j_{2}-j)!(2j_{1}+j+1)!}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{l}(-1)^{l+j+j_{1}+j_{2}}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = \frac{1}{2j+1}\left(\frac{(2j_{1}-j)!(2j_{2}+j+1)!}{(2j_{2}-j)!(2j_{1}+j+1)!}\right)^{\frac{1}{2}}</syntaxhighlight> || <math>j_{2} \leq j_{1}</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(l + j + Subscript[j, 1]+ Subscript[j, 2])* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], l}, {Subscript[j, 2], Subscript[j, 1], j}], {l, - Infinity, Infinity}, GenerateConditions->None] == Divide[1,2*j + 1]*(Divide[(2*Subscript[j, 1]- j)!*(2*Subscript[j, 2]+ j + 1)!,(2*Subscript[j, 2]- j)!*(2*Subscript[j, 1]+ j + 1)!])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [38 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[j, 1], Rule[Subscript[j, 1], -1.5], Rule[Subscript[j, 2], -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
Test Values: {Rule[j, 2], Rule[Subscript[j, 1], -1.5], Rule[Subscript[j, 2], -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/34.5.E22 34.5.E22] || <math qid="Q9763">\sum_{l}(-1)^{l+j+j_{1}+j_{2}}\frac{1}{l(l+1)}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = \frac{1}{j_{1}(j_{1}+1)-j_{2}(j_{2}+1)}\left(\frac{(2j_{1}-j)!(2j_{2}+j+1)!}{(2j_{2}-j)!(2j_{1}+j+1)!}\right)^{\frac{1}{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{l}(-1)^{l+j+j_{1}+j_{2}}\frac{1}{l(l+1)}\Wignersixjsym{j_{1}}{j_{2}}{l}{j_{2}}{j_{1}}{j} = \frac{1}{j_{1}(j_{1}+1)-j_{2}(j_{2}+1)}\left(\frac{(2j_{1}-j)!(2j_{2}+j+1)!}{(2j_{2}-j)!(2j_{1}+j+1)!}\right)^{\frac{1}{2}}</syntaxhighlight> || <math>j_{2} < j_{1}</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(l + j + Subscript[j, 1]+ Subscript[j, 2])*Divide[1,l*(l + 1)]*SixJSymbol[{Subscript[j, 1], Subscript[j, 2], l}, {Subscript[j, 2], Subscript[j, 1], j}], {l, - Infinity, Infinity}, GenerateConditions->None] == Divide[1,Subscript[j, 1]*(Subscript[j, 1]+ 1)- Subscript[j, 2]*(Subscript[j, 2]+ 1)]*(Divide[(2*Subscript[j, 1]- j)!*(2*Subscript[j, 2]+ j + 1)!,(2*Subscript[j, 2]- j)!*(2*Subscript[j, 1]+ j + 1)!])^(Divide[1,2])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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