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http://functions.wolfram.com/09.22.04.0013.01
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RamificationIndex[InverseWeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}],
z, Root[Function[z, 4 z^3 - Subscript[g, 2] z - Subscript[g, 3]], k]] ==
2 /; Element[k, {1, 2, 3}]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]], ",", "z", ",", 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"]]]]], "]"]], ",", "k"]], "]"]]]], "]"]], "\[Equal]", "2"]], "/;", RowBox[List["k", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "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> <msub> <mi> ℛ </mi> <mi> z </mi> </msub> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ℘ </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> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mn> 2 </mn> </mrow> <mo> /; </mo> <mrow> <mi> k </mi> <mo> ∈ </mo> <mrow> <mo> { </mo> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mn> 3 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> ℛ </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> <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> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <in /> <ci> k </ci> <list> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <cn type='integer'> 3 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["RamificationIndex", "[", RowBox[List[RowBox[List["InverseWeierstrassP", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]], ",", "z_", ",", 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"]]]]], "]"]], ",", "k"]], "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["2", "/;", RowBox[List["k", "\[Element]", RowBox[List["{", RowBox[List["1", ",", "2", ",", "3"]], "}"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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