DomainAndRange[Function[{Subscript[g, 2], Subscript[g, 3]}, WeierstrassHalfPeriods[{Subscript[g, 2], Subscript[g, 3]}]]] == ProductSet[Complexes, Complexes] \[LongRightArrow] ProductSet[Complexes, Complexes]

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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> <mo> { </mo> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> &#8902; </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> } </mo> </mrow> <mo> &#10230; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mstyle scriptlevel='0'> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> <mstyle scriptlevel='0'> <mo> , </mo> </mstyle> <mrow> <mstyle scriptlevel='0'> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mstyle> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> </mstyle> <mstyle scriptlevel='0'> <mo> ) </mo> </mstyle> </mrow> </mrow> <mstyle scriptlevel='0'> <mo> } </mo> </mstyle> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> <mo> &#10230; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <list> <apply> <ci> Star </ci> <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> </apply> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <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> </apply> <apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> <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> </apply> </list> </apply> <apply> <ci> LongRightArrow </ci> <list> <apply> <ci> CircleTimes </ci> <ci> &#8450; </ci> <ci> &#8450; </ci> </apply> </list> <list> <apply> <ci> CircleTimes </ci> <ci> &#8450; </ci> <ci> &#8450; </ci> </apply> </list> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], ",", RowBox[List["WeierstrassHalfPeriods", "[", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]], "\[LongRightArrow]", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]]]]]]

2001-10-29