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http://functions.wolfram.com/13.08.03.0005.01
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JacobiSymbol[n, p] == (-1)^Sum[Mod[2 n j, p], {j, 1, Floor[p/2]}] /;
Element[p, Primes] && p > 2
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiSymbol", "[", RowBox[List["n", ",", "p"]], "]"]], "\[Equal]", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["Floor", "[", FractionBox["p", "2"], "]"]]], RowBox[List["Mod", "[", RowBox[List[RowBox[List["2", " ", "n", " ", "j"]], ",", "p"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["p", "\[Element]", "Primes"]], "\[And]", RowBox[List["p", ">", "2"]]]]]]]]
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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> <semantics> <mrow> <mo> ( </mo> <mfrac> <mi> n </mi> <mi> p </mi> </mfrac> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List["(", FractionBox["n", "p"], ")"]], JacobiSymbol, Rule[Editable, False]] </annotation> </semantics> <mo> ⩵ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <munderover> <mo> ∑ </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <mo> ⌊ </mo> <mfrac> <mi> p </mi> <mn> 2 </mn> </mfrac> <mo> ⌋ </mo> </mrow> </munderover> <semantics> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> n </mi> <mo> ⁢ </mo> <mi> j </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> mod </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> FE`Conversion`Private`n </ci> <ci> FE`Conversion`Private`j </ci> </apply> <ci> FE`Conversion`Private`p </ci> </apply> </annotation-xml> </semantics> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> p </mi> <mo> ∈ </mo> <semantics> <mi> ℙ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalP]", Function[Primes]] </annotation> </semantics> </mrow> <mo> ∧ </mo> <mrow> <mi> p </mi> <mo> > </mo> <mn> 2 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> JacobiSymbol </ci> <ci> n </ci> <ci> p </ci> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <sum /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <ci> p </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <rem /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> FE`Conversion`Private`n </ci> <ci> FE`Conversion`Private`j </ci> </apply> <ci> FE`Conversion`Private`p </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> p </ci> <primes /> </apply> <apply> <gt /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiSymbol", "[", RowBox[List["n_", ",", "p_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], RowBox[List["Floor", "[", FractionBox["p", "2"], "]"]]], RowBox[List["Mod", "[", RowBox[List[RowBox[List["2", " ", "n", " ", "j"]], ",", "p"]], "]"]]]]], "/;", RowBox[List[RowBox[List["p", "\[Element]", "Primes"]], "&&", RowBox[List["p", ">", "2"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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