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Mod




Mathematica Notation

Traditional Notation









Integer Functions > Mod[m,n] > Integration > Indefinite integration > Involving only one direct function with respect to n





http://functions.wolfram.com/04.06.21.0004.01









  


  








Input Form





Integrate[Mod[m, n], n] == (1/2) n (m + Mod[m, n])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]], RowBox[List["\[DifferentialD]", "n"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", "n", " ", RowBox[List["(", RowBox[List["m", "+", RowBox[List["Mod", "[", RowBox[List["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> <mrow> <mo> &#8747; </mo> <mrow> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> n </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> + </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mi> n </mi> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> n </ci> </bvar> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <ci> n </ci> <apply> <plus /> <ci> m </ci> <apply> <rem /> <ci> $CellContext`m </ci> <ci> $CellContext`n </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["Mod", "[", RowBox[List["m_", ",", "n_"]], "]"]], RowBox[List["\[DifferentialD]", "n_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "n", " ", RowBox[List["(", RowBox[List["m", "+", RowBox[List["Mod", "[", RowBox[List["m", ",", "n"]], "]"]]]], ")"]]]]]]]]


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





2001-10-29