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InverseEllipticNomeQ






Mathematica Notation

Traditional Notation









Elliptic Functions > InverseEllipticNomeQ[z] > Identities > Functional identities





http://functions.wolfram.com/09.52.17.0005.01









  


  










Input Form





u^8 + 28 v^6 u^6 + 70 v^4 u^4 + 28 v^2 u^2 + v^8 - 56 v^3 u^3 - 56 v^5 u^5 - 8 v^7 u^7 - 8 u v == 0 /; u == InverseEllipticNomeQ[z^7]^(1/8) && v == InverseEllipticNomeQ[z]^(1/8) && 0 <= z <= 1










Standard Form





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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> <msup> <mi> u </mi> <mn> 8 </mn> </msup> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 7 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 70 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 56 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28 </mn> <mo> &#8290; </mo> <msup> <mi> v </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> u </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> v </mi> <mo> &#8290; </mo> <mi> u </mi> </mrow> <mo> + </mo> <msup> <mi> v </mi> <mn> 8 </mn> </msup> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> u </mi> <mo> &#10869; </mo> <mroot> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> <mo> ) </mo> </mrow> <mn> 8 </mn> </mroot> </mrow> <mo> &#8743; </mo> <mrow> <mi> v </mi> <mo> &#10869; </mo> <mroot> <mrow> <msup> <semantics> <mi> q </mi> <annotation-xml encoding='MathML-Content'> <ci> EllipticNomeQ </ci> </annotation-xml> </semantics> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 8 </mn> </mroot> </mrow> <mo> &#8743; </mo> <mrow> <mn> 0 </mn> <mo> &#8804; </mo> <mi> z </mi> <mo> &#8804; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <plus /> <apply> <power /> <ci> u </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 7 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 56 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 70 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 56 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28 </cn> <apply> <power /> <ci> v </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> u </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> v </ci> <ci> u </ci> </apply> </apply> <apply> <power /> <ci> v </ci> <cn type='integer'> 8 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <ci> u </ci> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <apply> <eq /> <ci> v </ci> <apply> <power /> <apply> <ci> InverseEllipticNomeQ </ci> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <apply> <leq /> <cn type='integer'> 0 </cn> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["u_", "8"], "+", RowBox[List["28", " ", SuperscriptBox["v_", "6"], " ", SuperscriptBox["u_", "6"]]], "+", RowBox[List["70", " ", SuperscriptBox["v_", "4"], " ", SuperscriptBox["u_", "4"]]], "+", RowBox[List["28", " ", SuperscriptBox["v_", "2"], " ", SuperscriptBox["u_", "2"]]], "+", SuperscriptBox["v_", "8"], "-", RowBox[List["56", " ", SuperscriptBox["v_", "3"], " ", SuperscriptBox["u_", "3"]]], "-", RowBox[List["56", " ", SuperscriptBox["v_", "5"], " ", SuperscriptBox["u_", "5"]]], "-", RowBox[List["8", " ", SuperscriptBox["v_", "7"], " ", SuperscriptBox["u_", "7"]]], "-", RowBox[List["8", " ", "u_", " ", "v_"]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["u", "\[Equal]", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", SuperscriptBox["z", "7"], "]"]], RowBox[List["1", "/", "8"]]]]], "&&", RowBox[List["v", "\[Equal]", SuperscriptBox[RowBox[List["InverseEllipticNomeQ", "[", "z", "]"]], RowBox[List["1", "/", "8"]]]]], "&&", RowBox[List["0", "\[LessEqual]", "z", "\[LessEqual]", "1"]]]]]]]]]]










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





2001-10-29





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