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WeierstrassP




Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Representations through equivalent functions > With inverse function





http://functions.wolfram.com/09.13.27.0002.01









  


  








Input Form





WeierstrassP[InverseWeierstrassP[{Subscript[z, 1], Subscript[z, 2]}, {Subscript[g, 2], Subscript[g, 3]}], {Subscript[g, 2], Subscript[g, 3]}] == Subscript[z, 1] /; Subscript[z, 2] == Sqrt[4 Subscript[z, 1]^3 - Subscript[g, 2] Subscript[z, 1] - Subscript[g, 3]]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], "\[Equal]", SubscriptBox["z", "1"]]], "/;", RowBox[List[SubscriptBox["z", "2"], "\[Equal]", SqrtBox[RowBox[List[RowBox[List["4", " ", SubsuperscriptBox["z", "1", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", SubscriptBox["z", "1"]]], "-", SubscriptBox["g", "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> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <msup> <mi> &#8472; </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mrow> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mrow> <msub> <mi> z </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> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> /; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mn> 3 </mn> </msubsup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassP </ci> <apply> <ci> InverseWeierstrassP </ci> <list> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </list> <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> <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> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <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> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SubscriptBox["zz", "1"], "/;", RowBox[List[SubscriptBox["z", "2"], "\[Equal]", SqrtBox[RowBox[List[RowBox[List["4", " ", SubsuperscriptBox["zz", "1", "3"]]], "-", RowBox[List[SubscriptBox["g", "2"], " ", SubscriptBox["zz", "1"]]], "-", SubscriptBox["g", "3"]]]]]]]]]]]]


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





2001-10-29