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Mod




Mathematica Notation

Traditional Notation









Integer Functions > Mod[m,n] > Transformations > Transformations and argument simplifications > Argument involving related functions





http://functions.wolfram.com/04.06.16.0020.01









  


  








Input Form





Mod[Ceiling[m], n] == Ceiling[m] - n Floor[Ceiling[m]/n]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Mod", "[", RowBox[List[RowBox[List["Ceiling", "[", "m", "]"]], ",", "n"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Ceiling", "[", "m", "]"]], "-", RowBox[List["n", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Ceiling", "[", "m", "]"]], "n"], "]"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <mrow> <mo> &#8968; </mo> <mi> m </mi> <mo> &#8969; </mo> </mrow> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <apply> <ceiling /> <ci> FE`Conversion`Private`m </ci> </apply> <ci> FE`Conversion`Private`n </ci> </apply> </annotation-xml> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> &#8968; </mo> <mi> m </mi> <mo> &#8969; </mo> </mrow> <mo> - </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mo> &#8968; </mo> <mi> m </mi> <mo> &#8969; </mo> </mrow> <mi> n </mi> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <rem /> <apply> <ceiling /> <ci> FE`Conversion`Private`m </ci> </apply> <ci> FE`Conversion`Private`n </ci> </apply> <apply> <plus /> <apply> <ceiling /> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> n </ci> <apply> <floor /> <apply> <times /> <apply> <ceiling /> <ci> m </ci> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Mod", "[", RowBox[List[RowBox[List["Ceiling", "[", "m_", "]"]], ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Ceiling", "[", "m", "]"]], "-", RowBox[List["n", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Ceiling", "[", "m", "]"]], "n"], "]"]]]]]]]]]]


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





2007-05-02