{Derivative[1][Subscript[e, 1]], Derivative[1][Subscript[e, 2]], Derivative[1][Subscript[e, 3]]} == WeierstrassPPrimeHalfPeriodValues[ {Subscript[g, 2], Subscript[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> <mo> { </mo> <mrow> <msubsup> <mi> e </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> <mo> , </mo> <msubsup> <mi> e </mi> <mn> 2 </mn> <mo> &#8242; </mo> </msubsup> <mo> , </mo> <msubsup> <mi> e </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mrow> <mo> } </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> e </mi> <mn> 1 </mn> <mo> &#8242; </mo> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> , </mo> </mstyle> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> e </mi> <mn> 2 </mn> <mo> &#8242; </mo> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mo> , </mo> <mrow> <mstyle scriptlevel='0'> <msubsup> <mi> e </mi> <mn> 3 </mn> <mo> &#8242; </mo> </msubsup> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <list> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <partialdiff /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> </apply> <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> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> </apply> <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> </apply> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> <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> </apply> </list> </apply> </annotation-xml> </semantics> </math>

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2007-05-02