(Subscript[e, k] - Subscript[e, j]) WeierstrassSigma[i, z, {Subscript[g, 2], Subscript[g, 3]}]^2 + (Subscript[e, i] - Subscript[e, k]) WeierstrassSigma[j, z, {Subscript[g, 2], Subscript[g, 3]}]^2 + (Subscript[e, j] - Subscript[e, i]) WeierstrassSigma[k, z, {Subscript[g, 2], Subscript[g, 3]}]^2 == 0 /; Element[{i, j}, {1, 2, 3}] && i != j

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e", "k"], "-", SubscriptBox["e", "j"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["i", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e", "i"], "-", SubscriptBox["e", "k"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["j", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e", "j"], "-", SubscriptBox["e", "i"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", "z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "2"]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "\[And]", RowBox[List["i", "\[NotEqual]", "j"]]]]]]]]

<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> <msub> <mi> e </mi> <mi> k </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> j </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> &#963; </mi> <mi> i </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> k </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> &#963; </mi> <mi> j </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mi> j </mi> </msub> <mo> - </mo> <msub> <mi> e </mi> <mi> i </mi> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> &#963; </mi> <mi> k </mi> </msub> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox[&quot;z&quot;, Rule[Editable, True]] </annotation> </semantics> <mo> ; </mo> <semantics> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> , </mo> <semantics> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]] </annotation> </semantics> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <mi> i </mi> <mo> , </mo> <mi> j </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> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <apply> <apply> <ci> Subscript </ci> <ci> &#963; </ci> <ci> i </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> i </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <apply> <apply> <ci> Subscript </ci> <ci> &#963; </ci> <ci> j </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </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> i </ci> </apply> </apply> </apply> <apply> <power /> <apply> <apply> <ci> Subscript </ci> <ci> &#963; </ci> <ci> k </ci> </apply> <apply> <ci> CompoundExpression </ci> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <ci> z </ci> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <in /> <list> <ci> i </ci> <ci> j </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> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e_", "k"], "-", SubscriptBox["e_", "j"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["i_", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e_", "i_"], "-", SubscriptBox["e_", "k"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["j", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["e_", "j"], "-", SubscriptBox["e_", "i_"]]], ")"]], " ", SuperscriptBox[RowBox[List["WeierstrassSigma", "[", RowBox[List["k", ",", "z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List["i", ",", "j"]], "}"]], "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]], "&&", RowBox[List["i", "\[NotEqual]", "j"]]]]]]]]]]

2001-10-29