x == 4^(1/3) WeierstrassP[2^(1/3) z, {4^(1/3) (a^2/3 - b), (a b)/3 - (2 a^3)/27}] - a/3 /; {x, y} == EllipticExp[z, {a, b}]

Cell[BoxData[RowBox[List[RowBox[List["x", "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["4", RowBox[List["1", "/", "3"]]], " ", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", "z"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox["4", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["a", "2"], "3"], "-", "b"]], ")"]]]], ",", RowBox[List[FractionBox[RowBox[List["a", " ", "b"]], "3"], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["a", "3"]]], "27"]]]]], "}"]]]], "]"]]]], "-", FractionBox["a", "3"]]]]], "/;", RowBox[List[RowBox[List["{", RowBox[List["x", ",", "y"]], "}"]], "\[Equal]", RowBox[List["EllipticExp", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> x </mi> <mo> &#10869; </mo> <mrow> <mrow> <mroot> <mn> 4 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mroot> <mn> 2 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ; </mo> <mrow> <mroot> <mn> 4 </mn> <mn> 3 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> , </mo> <mrow> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mn> 3 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mn> 27 </mn> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mi> a </mi> <mn> 3 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> x </mi> <mo> , </mo> <mi> y </mi> </mrow> <mo> } </mo> </mrow> <mo> &#10869; </mo> <mrow> <mi> eexp </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <mi> a </mi> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <ci> x </ci> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <ci> WeierstrassP </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <ci> z </ci> </apply> <list> <apply> <times /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> b </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 27 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </list> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <list> <ci> x </ci> <ci> y </ci> </list> <apply> <ci> eexp </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <ci> a </ci> </apply> <ci> b </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "x_", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["4", RowBox[List["1", "/", "3"]]], " ", RowBox[List["WeierstrassP", "[", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["1", "/", "3"]]], " ", "z"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SuperscriptBox["4", RowBox[List["1", "/", "3"]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["a", "2"], "3"], "-", "b"]], ")"]]]], ",", RowBox[List[FractionBox[RowBox[List["a", " ", "b"]], "3"], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["a", "3"]]], "27"]]]]], "}"]]]], "]"]]]], "-", FractionBox["a", "3"]]], "/;", RowBox[List[RowBox[List["{", RowBox[List["x", ",", "y"]], "}"]], "\[Equal]", RowBox[List["EllipticExp", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List["a", ",", "b"]], "}"]]]], "]"]]]]]]]]]]

2001-10-29