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WeierstrassInvariants






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassInvariants[{w1,w3}] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.19.13.0001.01









  


  










Input Form





Subscript[\[Omega], 1] D[{Subscript[g, 2], Subscript[g, 3]}, Subscript[\[Omega], 1]] + Subscript[\[Omega], 3] D[{Subscript[g, 2], Subscript[g, 3]}, Subscript[\[Omega], 3]] + {4, 6} {Subscript[g, 2], Subscript[g, 3]} == 0 /; {Subscript[g, 2], Subscript[g, 3]} == WeierstrassInvariants[ {Subscript[\[Omega], 1], Subscript[\[Omega], 3]}]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[Omega]", "1"], " ", RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["\[Omega]", "1"]], RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]]]], "+", RowBox[List[SubscriptBox["\[Omega]", "3"], " ", RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["\[Omega]", "3"]], RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]]]], "+", RowBox[List[RowBox[List["{", RowBox[List["4", ",", "6"]], "}"]], RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]]]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mn> 4 </mn> <mo> , </mo> <mn> 6 </mn> </mrow> <mo> } </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> D </ci> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> D </ci> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <list> <cn type='integer'> 4 </cn> <cn type='integer'> 6 </cn> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SubscriptBox["\[Omega]_", "1"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["\[Omega]_", "1"]]]], RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]]]], "+", RowBox[List[SubscriptBox["\[Omega]_", "3"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["\[Omega]_", "3"]]]], RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]]]], "+", RowBox[List[RowBox[List["{", RowBox[List["4", ",", "6"]], "}"]], " ", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], "\[Equal]", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29