WeierstrassInvariants[{Subscript[\[Omega], 1] + n Subscript[\[Omega], 3], Subscript[\[Omega], 3]}] == WeierstrassInvariants[ {Subscript[\[Omega], 1], Subscript[\[Omega], 3]}] /; Element[n, Integers]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["\[Omega]", "1"], "+", RowBox[List["n", " ", SubscriptBox["\[Omega]", "3"]]]]], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]], "\[Equal]", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]", "1"], ",", SubscriptBox["\[Omega]", "3"]]], "}"]], "]"]]]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]

<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> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> + </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> , </mo> <mrow> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mo> ( </mo> <mrow> <msub> <mi> &#969; </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> &#969; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#969; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </list> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["\[Omega]_", "1"], "+", RowBox[List["n_", " ", SubscriptBox["\[Omega]_", "3"]]]]], ",", SubscriptBox["\[Omega]_", "3"]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["WeierstrassInvariants", "[", RowBox[List["{", RowBox[List[SubscriptBox["\[Omega]\[Omega]", "1"], ",", SubscriptBox["\[Omega]\[Omega]", "3"]]], "}"]], "]"]], "/;", RowBox[List["n", "\[Element]", "Integers"]]]]]]]]

2007-05-02