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 | | http://functions.wolfram.com/09.20.26.0001.01 | 
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 | | WeierstrassPHalfPeriodValues[{Subscript[g, 2], Subscript[g, 3]}] == 
  {WeierstrassP[Subscript[\[Omega], 1], {Subscript[g, 2], Subscript[g, 3]}], 
   WeierstrassP[Subscript[\[Omega], 2], {Subscript[g, 2], Subscript[g, 3]}], 
   WeierstrassP[Subscript[\[Omega], 3], {Subscript[g, 2], 
     Subscript[g, 3]}]} /; 
 {Subscript[\[Omega], 1], Subscript[\[Omega], 3]} == 
   WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}] && 
  Subscript[\[Omega], 2] == -Subscript[\[Omega], 1] - Subscript[\[Omega], 3] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "}"]]]], "/;", 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[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "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>  <mo> { </mo>  <mrow>  <mrow>  <mstyle scriptlevel='0'>  <msub>  <mi> e </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> e </mi>  <mn> 2 </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>  <mo> , </mo>  <mrow>  <mstyle scriptlevel='0'>  <msub>  <mi> e </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>  <mo> ⩵ </mo>  <mrow>  <mo> { </mo>  <mrow>  <mrow>  <mi> ℘ </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>  <mo> , </mo>  <mrow>  <mi> ℘ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <msub>  <mi> ω </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>  <mo> , </mo>  <mrow>  <mi> ℘ </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>  </mrow>  <mo> } </mo>  </mrow>  </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>  <mstyle scriptlevel='0'>  <mo> { </mo>  </mstyle>  <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>  <msub>  <mi> ω </mi>  <mn> 2 </mn>  </msub>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mo> - </mo>  <mstyle scriptlevel='0'>  <msub>  <mi> ω </mi>  <mn> 1 </mn>  </msub>  </mstyle>  </mrow>  <mo> - </mo>  <mstyle scriptlevel='0'>  <msub>  <mi> ω </mi>  <mn> 3 </mn>  </msub>  </mstyle>  </mrow>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <list>  <apply>  <apply>  <ci> Subscript </ci>  <ci> e </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> e </ci>  <cn type='integer'> 2 </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> e </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>  <list>  <apply>  <ci> WeierstrassP </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>  <ci> WeierstrassP </ci>  <apply>  <ci> Subscript </ci>  <ci> ω </ci>  <cn type='integer'> 2 </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>  <ci> WeierstrassP </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>  </list>  </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>  <ci> Subscript </ci>  <ci> ω </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Subscript </ci>  <ci> ω </ci>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <ci> Subscript </ci>  <ci> ω </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassPHalfPeriodValues", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "2"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]], ",", RowBox[List["WeierstrassP", "[", RowBox[List[SubscriptBox["\[Omega]", "3"], ",", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]]]], "]"]]]], "}"]], "/;", RowBox[List[RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["gg", "2"], ",", SubscriptBox["gg", "3"]]], "}"]], "]"]]]], "&&", RowBox[List[SubscriptBox["\[Omega]", "2"], "\[Equal]", RowBox[List[RowBox[List["-", SubscriptBox["\[Omega]", "1"]]], "-", SubscriptBox["\[Omega]", "3"]]]]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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