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Cyclotomic




Mathematica Notation

Traditional Notation









Polynomials > Cyclotomic[n,z] > Transformations > Multiple arguments





http://functions.wolfram.com/05.11.16.0003.01









  


  








Input Form





Cyclotomic[n p, z^p^(k - 1)] == Cyclotomic[n p^k, z] /; Element[n, Integers] && n >= 0 && Element[p, Integers] && p >= 0 && Element[k, Integers] && k > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List[RowBox[List["n", " ", "p"]], ",", SuperscriptBox["z", SuperscriptBox["p", RowBox[List["k", "-", "1"]]]]]], "]"]], "\[Equal]", RowBox[List["Cyclotomic", "[", RowBox[List[RowBox[List["n", " ", SuperscriptBox["p", "k"]]], ",", "z"]], "]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["p", "\[Element]", "Integers"]], "\[And]", RowBox[List["p", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]]]]]]]]








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> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> </msub> <mo> ( </mo> <msup> <mi> z </mi> <msup> <mi> p </mi> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> </msup> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msub> <semantics> <mi> C </mi> <annotation encoding='Mathematica'> TagBox[&quot;C&quot;, Cyclotomic] </annotation> </semantics> <mrow> <mi> n </mi> <mo> &#8290; </mo> <msup> <mi> p </mi> <mi> k </mi> </msup> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> p </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Cyclotomic </ci> <apply> <times /> <ci> n </ci> <ci> p </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <power /> <ci> p </ci> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Cyclotomic </ci> <apply> <times /> <ci> n </ci> <apply> <power /> <ci> p </ci> <ci> k </ci> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> <apply> <in /> <ci> p </ci> <ci> &#8469; </ci> </apply> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Cyclotomic", "[", RowBox[List[RowBox[List["n_", " ", "p_"]], ",", SuperscriptBox["z_", SuperscriptBox["p_", RowBox[List["k_", "-", "1"]]]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Cyclotomic", "[", RowBox[List[RowBox[List["n", " ", SuperscriptBox["p", "k"]]], ",", "z"]], "]"]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["p", "\[Element]", "Integers"]], "&&", RowBox[List["p", "\[GreaterEqual]", "0"]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]]]]]]]]]]


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





2001-10-29