WeierstrassP[z \[PlusMinus] Subscript[\[Omega], i], {Subscript[g, 2], Subscript[g, 3]}] == Subscript[e, i] + ((Subscript[e, i] - Subscript[e, j]) (Subscript[e, i] - Subscript[e, k]))/ (WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] - Subscript[e, i]) /; Element[{i, j, k}, {1, 2, 3}] && i != j != k

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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> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> z </mi> <mo> &#177; </mo> <msub> <mi> &#969; </mi> <mi> j </mi> </msub> </mrow> <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> <mo> &#10869; </mo> <mrow> <msub> <mi> e </mi> <mi> j </mi> </msub> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> l </mi> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <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> <mo> - </mo> <msub> <mi> e </mi> <mi> j </mi> </msub> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> i </mi> <mo> , </mo> <mi> j </mi> <mo> , </mo> <mi> k </mi> </mrow> <mo> } </mo> </mrow> <mo> &#8712; </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> i </mi> <mo> &#8800; </mo> <mi> j </mi> <mo> &#8800; </mo> <mi> k </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassP </ci> <apply> <ci> PlusMinus </ci> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <ci> j </ci> </apply> </apply> <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> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> l </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> WeierstrassP </ci> <ci> z </ci> <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> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </ci> <ci> k </ci> </list> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> <apply> <neq /> <ci> i </ci> <ci> j </ci> <ci> k </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29