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http://functions.wolfram.com/07.38.04.0001.01
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DomainAndRange[Function[{{Subscript[j, 1], Subscript[m, 1]},
{Subscript[j, 2], Subscript[m, 2]}, {j, m}},
ClebschGordan[{Subscript[j, 1], Subscript[m, 1]},
{Subscript[j, 2], Subscript[m, 2]}, {j, m}]]] ==
PowerSet[SetUnion[Rationals, Rationals], 3] \[LongRightArrow] Complexes
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Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m"]], "}"]]]], "}"]], ",", " ", "\[IndentingNewLine]", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m"]], "}"]]]], "]"]]]], " ", "]"]], " ", "]"]], "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List[RowBox[List["SetUnion", "[", RowBox[List["Rationals", ",", " ", "Rationals"]], "]"]], ",", "3"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> * </mo> <msub> <mi> m </mi> <mn> 1 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⋆ </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> * </mo> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> * </mo> <mrow> <mo> { </mo> <mrow> <mi> j </mi> <mo> * </mo> <mi> m </mi> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mrow> <mo> 〈 </mo> <mrow> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> m </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> m </mi> <mn> 2 </mn> </msub> </mrow> <mtext>   </mtext> <mo> ❘ </mo> <mtext>   </mtext> <mrow> <msub> <mi> j </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <mtext>   </mtext> <msub> <mi> j </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mtext>   </mtext> <mi> j </mi> <mo> ⁢ </mo> <mtext>   </mtext> <mi> m </mi> </mrow> </mrow> <mo> 〉 </mo> </mrow> </mrow> <mo> ∷ </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> ℚ </mi> <mo> ⊗ </mo> <mi> ℚ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mrow> <mo> { </mo> <mrow> <mi> ℚ </mi> <mo> ⊗ </mo> <mi> ℚ </mi> </mrow> <mo> } </mo> </mrow> <mo> ⊗ </mo> <mrow> <mo> { </mo> <mrow> <mi> ℚ </mi> <mo> ⊗ </mo> <mi> ℚ </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⟶ </mo> <mi> ℂ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <list> <apply> <times /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> </apply> </list> <apply> <times /> <list> <apply> <times /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </list> <list> <apply> <times /> <ci> j </ci> <ci> m </ci> </apply> </list> </apply> </apply> <apply> <ci> AngleBracket </ci> <apply> <ci> VerticalSeparator </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> j </ci> <cn type='integer'> 2 </cn> </apply> <ci> j </ci> <ci> m </ci> </apply> </apply> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <list> <apply> <ci> CircleTimes </ci> <ci> ℚ </ci> <ci> ℚ </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> ℚ </ci> <ci> ℚ </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> ℚ </ci> <ci> ℚ </ci> </apply> </list> </apply> <ci> ℂ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m_"]], "}"]]]], "}"]], ",", RowBox[List["ClebschGordan", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["j", "1"], ",", SubscriptBox["m_", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["j", "2"], ",", SubscriptBox["m_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["j", ",", "m_"]], "}"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerSet", "[", RowBox[List[RowBox[List["SetUnion", "[", RowBox[List["Rationals", ",", "Rationals"]], "]"]], ",", "3"]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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