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

Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["z", ",", SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]], ",", " ", RowBox[List["WeierstrassZeta", "[", RowBox[List["z", ",", RowBox[List["{", RowBox[List[SubscriptBox["g", "2"], ",", SubscriptBox["g", "3"]]], "}"]]]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List["Complexes", ",", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]

<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> <mi> z </mi> <mo> * </mo> <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> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <semantics> <mrow> <mi> &#950; </mi> <mo> &#8289; </mo> <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> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[Zeta]&quot;, &quot;(&quot;, RowBox[List[RowBox[List[TagBox[&quot;z&quot;, Rule[Editable, True]], &quot;;&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;2&quot;], Rule[Editable, True]]]], &quot;,&quot;, TagBox[SubscriptBox[&quot;g&quot;, &quot;3&quot;], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[WeierstrassZeta[Slot[1], List[Slot[2], Slot[3]]]]]] </annotation> </semantics> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mrow> <mo> { </mo> <mrow> <mi> &#8450; </mi> <mo> &#8855; </mo> <mi> &#8450; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mi> &#8450; </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <times /> <ci> z </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> </apply> <apply> <ci> WeierstrassZeta </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> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <ci> &#8450; </ci> <list> <apply> <ci> CircleTimes </ci> <ci> &#8450; </ci> <ci> &#8450; </ci> </apply> </list> </apply> <ci> &#8450; </ci> </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["z_", ",", SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]], ",", RowBox[List["WeierstrassZeta", "[", RowBox[List["z_", ",", RowBox[List["{", RowBox[List[SubscriptBox["g_", "2"], ",", SubscriptBox["g_", "3"]]], "}"]]]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["PowerProduct", "[", RowBox[List["Complexes", ",", RowBox[List["ProductSet", "[", RowBox[List["Complexes", ",", "Complexes"]], "]"]]]], "]"]], "\[LongRightArrow]", "Complexes"]]]]]]

2001-10-29