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JacobiSymbol




Mathematica Notation

Traditional Notation









Number Theory Functions > JacobiSymbol[n,m] > General characteristics > Domain and analyticity





http://functions.wolfram.com/13.08.04.0001.01









  


  








Input Form





DomainAndRange[Function[{n, m}, JacobiSymbol[n, m]]] == ProductSet[Integers, Integers] \[LongRightArrow] {-1, 0, 1}








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n", ",", "m"]], "}"]], ",", " ", RowBox[List["JacobiSymbol", "[", RowBox[List["n", ",", "m"]], "]"]]]], "]"]], "]"]], " ", "\[Equal]", "\[IndentingNewLine]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Integers"]], "]"]], "\[LongRightArrow]", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0", ",", "1"]], "}"]]]]]]]]








MathML Form







<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> n </mi> <mo> &#8902; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <mo> ( </mo> <mfrac> <mi> n </mi> <mi> m </mi> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> &#8759; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> <mo> &#8855; </mo> <mi> &#8484; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#10230; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> } </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportion </ci> <apply> <ci> LongRightArrow </ci> <apply> <ci> Star </ci> <ci> n </ci> <ci> m </ci> </apply> <apply> <times /> <ci> n </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> LongRightArrow </ci> <apply> <ci> CircleTimes </ci> <integers /> <ci> &#8484; </ci> </apply> <list> <cn type='integer'> -1 </cn> <cn type='integer'> 0 </cn> <cn type='integer'> 1 </cn> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["DomainAndRange", "[", RowBox[List["Function", "[", RowBox[List[RowBox[List["{", RowBox[List["n_", ",", "m_"]], "}"]], ",", RowBox[List["JacobiSymbol", "[", RowBox[List["n_", ",", "m_"]], "]"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["ProductSet", "[", RowBox[List["Integers", ",", "Integers"]], "]"]], "\[LongRightArrow]", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0", ",", "1"]], "}"]]]]]]]]


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





2001-10-29