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http://functions.wolfram.com/09.57.27.0002.01
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EllipticExpPrime[EllipticLog[{Subscript[z, 1], Subscript[z, 2]}, {a, b}],
{a, b}][[1]] == 2 Subscript[z, 2] /;
Subscript[z, 1]^3 + a Subscript[z, 1]^2 + b Subscript[z, 1] -
Subscript[z, 2]^2 == 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["EllipticExpPrime", "[", RowBox[List[RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]], ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]], "[", RowBox[List["[", "1", "]"]], "]"]], "\[Equal]", RowBox[List["2", SubscriptBox["z", "2"]]]]], "/;", " ", RowBox[List[RowBox[List[SubsuperscriptBox["z", "1", "3"], "+", RowBox[List["a", " ", SubsuperscriptBox["z", "1", "2"]]], "+", RowBox[List["b", " ", SubscriptBox["z", "1"]]], "-", SubsuperscriptBox["z", "2", "2"]]], "\[Equal]", "0"]]]]]]
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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> <mi> ξ </mi> <mo> ⩵ </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> { </mo> <mrow> <mi> ξ </mi> <mo> , </mo> <mi> η </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> = </mo> <mrow> <mrow> <msubsup> <mi> eexp </mi> <mi> z </mi> <mo> ′ </mo> </msubsup> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> elog </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> ∧ </mo> <mrow> <mrow> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Set </ci> <apply> <ci> Condition </ci> <apply> <eq /> <ci> ξ </ci> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <list> <ci> ξ </ci> <ci> η </ci> </list> </apply> <apply> <and /> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> eexp </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> elog </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> CompoundExpression </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> <ci> a </ci> </apply> <ci> b </ci> </apply> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["EllipticExpPrime", "[", RowBox[List[RowBox[List["EllipticLog", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List["a_", ",", "b_"]], "}"]]]], "]"]], ",", RowBox[List["{", RowBox[List["a_", ",", "b_"]], "}"]]]], "]"]], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", SubscriptBox["zz", "2"]]], "/;", RowBox[List[RowBox[List[SubsuperscriptBox["z", "1", "3"], "+", RowBox[List["a", " ", SubsuperscriptBox["z", "1", "2"]]], "+", RowBox[List["b", " ", SubscriptBox["z", "1"]]], "-", SubsuperscriptBox["zz", "2", "2"]]], "\[Equal]", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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