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Signature




Mathematica Notation

Traditional Notation









Integer Functions > Signature[{n1,n2,...,nd}] > Complex characteristics > Absolute value





http://functions.wolfram.com/04.21.19.0003.01









  


  








Input Form





Abs[Signature[{Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, d]}]] == Sqrt[Signature[{Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, d]}]^2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n", "1"], ",", SubscriptBox["n", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "d"]]], "}"]], "]"]], "]"]], "\[Equal]", SqrtBox[SuperscriptBox[RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n", "1"], ",", SubscriptBox["n", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "d"]]], "}"]], "]"]], "2"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> &#949; </mi> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mtext> </mtext> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mi> d </mi> </msub> </mrow> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <msqrt> <msup> <msub> <mi> &#949; </mi> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mtext> </mtext> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mi> d </mi> </msub> </mrow> </msub> <mn> 2 </mn> </msup> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <abs /> <apply> <ci> Signature </ci> <list> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> d </ci> </apply> </list> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Signature </ci> <list> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> d </ci> </apply> </list> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n_", "1"], ",", SubscriptBox["n_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "d_"]]], "}"]], "]"]], "]"]], "]"]], "\[RuleDelayed]", SqrtBox[SuperscriptBox[RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["nn", "1"], ",", SubscriptBox["nn", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["nn", "d"]]], "}"]], "]"]], "2"]]]]]]


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





2001-10-29