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variants of this functions
InverseWeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseWeierstrassP[z,{g2,g3}] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/09.22.04.0012.01









  


  










Input Form





BranchPoints[InverseWeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}], z] == {Root[Function[z, 4 z^3 - Subscript[g, 2] z - Subscript[g, 3]], 1], Root[Function[z, 4 z^3 - Subscript[g, 2] z - Subscript[g, 3]], 2], Root[Function[z, 4 z^3 - Subscript[g, 2] z - Subscript[g, 3]], 3], ComplexInfinity}










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", "z"]], "-", SubscriptBox["g", "3"]]]]], "]"]], ",", "1"]], "]"]], ",", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", "z"]], "-", SubscriptBox["g", "3"]]]]], "]"]], ",", "2"]], "]"]], ",", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", "z"]], "-", SubscriptBox["g", "3"]]]]], "]"]], ",", "3"]], "]"]], ",", " ", "ComplexInfinity"]], "}"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> &#8492;&#119979; </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <msup> <mi> &#8472; </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <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> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 1 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> , </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> , </mo> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119979; </ci> <ci> z </ci> </apply> <apply> <ci> InverseWeierstrassP </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> <list> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ci> OverTilde </ci> <infinity /> </apply> </list> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["{", RowBox[List[RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["gg", "2"], " ", "z"]], "-", SubscriptBox["gg", "3"]]]]], "]"]], ",", "1"]], "]"]], ",", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["gg", "2"], " ", "z"]], "-", SubscriptBox["gg", "3"]]]]], "]"]], ",", "2"]], "]"]], ",", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[RowBox[List["4", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List[SubscriptBox["gg", "2"], " ", "z"]], "-", SubscriptBox["gg", "3"]]]]], "]"]], ",", "3"]], "]"]], ",", "ComplexInfinity"]], "}"]]]]]]










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





2001-10-29