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http://functions.wolfram.com/09.23.13.0001.01
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(4 Subscript[z, 1]^3 - Subscript[g, 2] Subscript[z, 1] - Subscript[g, 3])
Derivative[1][w][Subscript[z, 1]]^2 - 1 == 0 /;
w[Subscript[z, 1]] == InverseWeierstrassP[{Subscript[z, 1],
Subscript[z, 2]}, {Subscript[g, 2], Subscript[g, 3]}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", SubsuperscriptBox["z", "1", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", SubscriptBox["z", "1"]]], "-", SubscriptBox["g", "3"]]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", SubscriptBox["z", "1"], "]"]], "2"]]], "-", "1"]], "\[Equal]", "0"]], "/;", " ", RowBox[List[RowBox[List["w", "[", SubscriptBox["z", "1"], "]"]], "\[Equal]", RowBox[List["InverseWeierstrassP", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]
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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> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mrow> <msup> <mi> w </mi> <mo> ′ </mo> </msup> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> w </mi> <mo> ⁡ </mo> <mo> ( </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msup> <mi> ℘ </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> D </ci> <apply> <ci> w </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <apply> <ci> w </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> InverseWeierstrassP </ci> <list> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["4", " ", SubsuperscriptBox["z_", "1", "3"]]], "-", RowBox[List[SubscriptBox["g_", "2"], " ", SubscriptBox["z_", "1"]]], "-", SubscriptBox["g_", "3"]]], ")"]], " ", SuperscriptBox[RowBox[List[SuperscriptBox["w", "\[Prime]", Rule[MultilineFunction, None]], "[", SubscriptBox["z_", "1"], "]"]], "2"]]], "-", "1"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", SubscriptBox["z", "1"], "]"]], "\[Equal]", RowBox[List["InverseWeierstrassP", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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