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Cyclotomic




Mathematica Notation

Traditional Notation









Polynomials > Cyclotomic[n,z] > Specific values > Specialized values > For fixed z





http://functions.wolfram.com/05.11.03.0001.01









  


  








Input Form





Cyclotomic[p, z] == Sum[z^k, {k, 0, p - 1}] /; Element[p, Primes]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List["p", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], SuperscriptBox["z", "k"]]]]], "/;", " ", RowBox[List["p", "\[Element]", "Primes"]]]]]]








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> <msub> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, Cyclotomic] </annotation> </semantics> <mi> p </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mi> p </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </munderover> <msup> <mi> z </mi> <mi> k </mi> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <semantics> <mi> &#8473; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalP]&quot;, Function[Primes]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Cyclotomic </ci> <ci> p </ci> <ci> z </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> p </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <power /> <ci> z </ci> <ci> k </ci> </apply> </apply> </apply> <apply> <in /> <ci> p </ci> <primes /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cyclotomic", "[", RowBox[List["p_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["p", "-", "1"]]], SuperscriptBox["z", "k"]]], "/;", RowBox[List["p", "\[Element]", "Primes"]]]]]]]]


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





2001-10-29