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http://functions.wolfram.com/09.18.13.0001.01
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(Subscript[g, 2]^3 - 27 Subscript[g, 3]^2) D[Subscript[\[Omega], 1],
Subscript[g, 2]] + (1/4) Subscript[g, 2]^2 Subscript[\[Omega], 1] -
(9/2) Subscript[g, 3] WeierstrassZeta[Subscript[\[Omega], 1],
{Subscript[g, 2], Subscript[g, 3]}] == 0 /;
{Subscript[\[Omega], 1], Subscript[\[Omega], 3]} ==
WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] &&
(Subscript[g, 2]^3 - 27 Subscript[g, 3]^2) D[Subscript[\[Omega], 3],
Subscript[g, 2]] + (1/4) Subscript[g, 2]^2 Subscript[\[Omega], 3] -
(9/2) Subscript[g, 3] WeierstrassZeta[Subscript[\[Omega], 3],
{Subscript[g, 2], Subscript[g, 3]}] == 0 &&
{Subscript[\[Omega], 1], Subscript[\[Omega], 3]} ==
WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["g", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g", "3", "2"]]]]], ")"]], RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["g", "2"]], SubscriptBox["\[Omega]", "1"]]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["g", "2", "2"], " ", SubscriptBox["\[Omega]", "1"]]], "-", RowBox[List[FractionBox["9", "2"], " ", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "\[And]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["g", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g", "3", "2"]]]]], ")"]], RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["g", "2"]], SubscriptBox["\[Omega]", "3"]]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["g", "2", "2"], " ", SubscriptBox["\[Omega]", "3"]]], "-", RowBox[List[FractionBox["9", "2"], " ", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", 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> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <msubsup> <mi> g </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mfrac> <mrow> <mo> ∂ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </mrow> <mrow> <mo> ∂ </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ω </mi> <mn> 1 </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> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["\[Omega]", "1"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </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'> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </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> <mo> ∧ </mo> <mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 3 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 27 </mn> <mo> ⁢ </mo> <msubsup> <mi> g </mi> <mn> 3 </mn> <mn> 2 </mn> </msubsup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mfrac> <mrow> <mo> ∂ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mrow> <mo> ∂ </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <msubsup> <mi> g </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 9 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ⁢ </mo> <semantics> <mrow> <mi> ζ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msub> <mi> ω </mi> <mn> 3 </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> <annotation encoding='Mathematica'> TagBox[RowBox[List["\[Zeta]", "(", RowBox[List[RowBox[List[TagBox[SubscriptBox["\[Omega]", "3"], Rule[Editable, True]], ";", TagBox[SubscriptBox["g", "2"], Rule[Editable, True]]]], ",", TagBox[SubscriptBox["g", "3"], Rule[Editable, True]]]], ")"]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> </mrow> <mo> ⩵ </mo> <mn> 0 </mn> </mrow> <mo> ∧ </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> ⩵ </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <msub> <mi> ω </mi> <mn> 1 </mn> </msub> </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'> <msub> <mi> ω </mi> <mn> 3 </mn> </msub> </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> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> D </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 9 <sep /> 2 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> WeierstrassZeta </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </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> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <list> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </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> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </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> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 27 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> D </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 9 <sep /> 2 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> WeierstrassZeta </ci> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </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> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <eq /> <list> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </apply> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 1 </cn> </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> <ci> Subscript </ci> <ci> ω </ci> <cn type='integer'> 3 </cn> </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> </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[SubsuperscriptBox["g_", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g_", "3", "2"]]]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["g_", "2"]]]], SubscriptBox["\[Omega]_", "1"]]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["g_", "2", "2"], " ", SubscriptBox["\[Omega]_", "1"]]], "-", RowBox[List[FractionBox["9", "2"], " ", SubscriptBox["g_", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]_", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["g", "2", "3"], "-", RowBox[List["27", " ", SubsuperscriptBox["g", "3", "2"]]]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["g", "2"]]]], SubscriptBox["\[Omega]", "3"]]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SubsuperscriptBox["g", "2", "2"], " ", SubscriptBox["\[Omega]", "3"]]], "-", RowBox[List[FractionBox["9", "2"], " ", SubscriptBox["g", "3"], " ", RowBox[List["WeierstrassZeta", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]]]], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", 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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){kind=small}
